47 Most Cited papers in control

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What is Control? here is a nice definition according to Wikipedia:

Control engineering or control systems engineering is an engineering discipline that deals with control systems, applying control theory to design equipment and systems with desired behaviors in control environments. The discipline of controls overlaps and is usually taught along with electrical engineering and mechanical engineering at many institutions around the world.

The practice uses sensors and detectors to measure the output performance of the process being controlled; these measurements are used to provide corrective feedback helping to achieve the desired performance. Systems designed to perform without requiring human input are called automatic control systems (such as cruise control for regulating the speed of a car). Multi-disciplinary in nature, control systems engineering activities focus on implementation of control systems mainly derived by mathematical modeling of a diverse range of systems.

To come up with this list, we have used Google Scholar. In there we have done some extensive search and found 47 most cited papers in control. Usually the more a paper is cited the more impact and importance it has. For each paper, we include its authors, number of citations, publication year and the jornal or conference that the paper was published in, as well as a summary.

1. Linear matrix inequalities in system and control theory

Authors: S Boyd, L El Ghaoui, E Feron, V Balakrishnan
Published in: Philadelphia, USA: SIAM, 1994
Number of citations: 26,647
Summary: The basic topic of this book is solving problems from system and control theory using convex optimization. We show that a wide variety of problems arising in system and control theory can be reduced to a handful of standard convex and quasiconvex optimization problems that involve matrix inequalities. For a few special cases there are “analytic solutions” to these problems, but our main point is that they can be solved numerically in all cases. These standard problems can be solved in polynomial-time (by, eg, the ellipsoid algorithm of Shor, Nemirovskii, and Yudin), and so are tractable, at least in a theoretical sense. Recently developed interior-point methods for these standard problems have been found to be extremely efficient in practice. Therefore, we consider the original problems from system and control theory as solved. This book is primarily intended for the researcher in system and control theory, but can …

Linear matrix inequalities in system and control theory
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2. YALMIP: A toolbox for modeling and optimization in MATLAB

Authors: Johan Löfberg
Published in: IEEE International Symposium on Computer Aided Control Systems Design, 2004
Number of citations: 9,694
Summary: The MATLAB toolbox YALMIP is introduced. It is described how YALMIP can be used to model and solve optimization problems typically occurring in systems and control theory. In this paper, free MATLAB toolbox YALMIP, developed initially to model SDPs and solve these by interfacing eternal solvers. The toolbox makes development of optimization problems in general, and control oriented SDP problems in particular, extremely simple. In fact, learning 3 YALMIP commands is enough for most users to model and solve the optimization problems.

YALMIP: A toolbox for modeling and optimization in MATLAB
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3. State-space solutions to standard H

Authors: John Doyle, Keith Glover, Pramod Khargonekar, Bruce Francis
Published in: 1988 American Control Conference, 1988
Number of citations: 8,548
Summary: Simple state-space formulas are presented for a controller solving a standard H∞ -problem. The controller has the same state-dimension as the plant, its computation involves only two Riccati equations, and it has a separation structure reminiscent of classical LQG (i.e., H 2 ) theory. This paper is also intended to be of tutorial value, so a standard H 2 -solution is developed in parallel.

State-space solutions to standard H
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4. State-space solutions to standard H2 and H-infinity control problems

Authors: John C Doyle, Keith Glover, Pramod P Khargonekar, Bruce A Francis
Published in: IEEE Transactions on Automatic Control, 1989
Number of citations: 8,546
Summary: Simple state-space formulas are derived for all controllers solving the following standard H∞ problem: For a given number gamma >0, find all controllers such that the H∞ / norm of the closed-loop transfer function is (strictly) less than gamma . It is known that a controller exists if and only if the unique stabilizing solutions to two algebraic Riccati equations are positive definite and the spectral radius of their product is less than gamma-2. Under these conditions, a parameterization of all controllers solving the problem is given as a linear fractional transformation (LFT) on a contractive, stable, free parameter. The state dimension of the coefficient matrix for the LFT, constructed using the two Riccati solutions, equals that of the plant and has a separation structure reminiscent of classical LQG (i.e. H-2) theory. This paper is intended to be of tutorial value, so a standard H-2 solution is developed in parallel.

State-space solutions to standard H2 and H-infinity control problems
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5. Variable structure systems with sliding modes

Authors: Vadim Utkin
Published in: IEEE Transactions on Automatic control, 1977
Number of citations: 6,650
Summary: Variable structure systems consist of a set of continuous subsystems together with suitable switching logic. Advantageous properties result from changing structures according to this switching logic. Design and analysis for this class of systems are surveyed in this paper.

Variable structure systems with sliding modes
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6. Generalized predictive control—Part I. The basic algorithm

Authors: David W Clarke, Coorous Mohtadi, PS Tuffs
Published in: Automatica, 1987
Number of citations: 5,907
Summary: Current self-tuning algorithms lack robustness to prior choices of either dead-time or model order. A novel method—generalized predictive control or GPC—is developed which is shown by simulation studies to be superior to accepted techniques such as generalized minimum-variance and pole-placement. This receding-horizon method depends on predicting the plant's output over several steps based on assumptions about future control actions. One assumption—that there is a “control horizon” beyond which all control increments become zero—is shown to be beneficial both in terms of robustness and for providing simplified calculations. Choosing particular values of the output and control horizons produces as subsets of the method various useful algorithms such as GMV, EPSAC, Peterka's predictive controller (1984, Automatica, 20, 39–50) and Ydstie's extended-horizon design (1984, IFAC 9th World Congress …

Generalized predictive control—Part I. The basic algorithm
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7. Sliding mode control on electro-mechanical systems

Authors: Vadim I Utkin, Hao-Chi Chang
Published in: Mathematical problems in Engineering, 2002
Number of citations: 5,706
Summary: The first sliding mode control application may be found in the papers back in the 1930s in Russia. With its versatile yet simple design procedure the methodology is proven to be one of the most powerful solutions for many practical control designs. For the sake of demonstration this paper is oriented towards application aspects of sliding mode control methodology. First the design approach based on the regularization is generalized for mechanical systems. It is shown that stability of zero dynamics should be taken into account when the regular form consists of blocks of second-order equations. Majority of applications in the paper are related to control and estimation methods of automotive industry. New theoretical methods are developed in the context of these studies: sliding made nonlinear observers, observers with binary measurements, parameter estimation in systems with sliding mode control.

Sliding mode control on electro-mechanical systems
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8. A survey of recent results in networked control systems

Authors: Joo P Hespanha, Payam Naghshtabrizi, Yonggang Xu
Published in: Proceedings of the IEEE, 2007
Number of citations: 4,163
Summary: Networked control systems (NCSs) are spatially distributed systems for which the communication between sensors, actuators, and controllers is supported by a shared communication network. We review several recent results on estimation, analysis, and controller synthesis for NCSs. The results surveyed address channel limitations in terms of packet-rates, sampling, network delay, and packet dropouts. The results are presented in a tutorial fashion, comparing alternative methodologies.

A survey of recent results in networked control systems
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9. Flatness and defect of non-linear systems: introductory theory and examples

Authors: Michel Fliess, Jean Lévine, Philippe Martin, Pierre Rouchon
Published in: International Journal of Control, 1995
Number of citations: 3,654
Summary: We introduce flat systems, which are equivalent to linear ones via a special type of feedback called endogenous. Their physical properties are subsumed by a linearizing output and they might be regarded as providing another nonlinear extension of Kalman's controllability. The distance to flatness is measured by a non-negative integer, the defect. We utilize differential algebra where flatness- and defect are best defined without distinguishing between input, state, output and other variables. Many realistic classes of examples are flat. We treat two popular ones: the crane and the car with n trailers, the motion planning of which is obtained via elementary properties of plane curves. The three non-flat examples, the simple, double and variable length pendulums, are borrowed from non-linear physics. A high frequency control strategy is proposed such that the averaged systems become flat.

Flatness and defect of non-linear systems: introductory theory and examples
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10. Multivariable feedback design: Concepts for a classical/modern synthesis

Authors: John Doyle, Gunter Stein
Published in: IEEE transactions on Automatic Control, 1981
Number of citations: 3,142
Summary: This paper presents a practical design perspective on multivariable feedback control problems. It reviews the basic issue-feedback design in the face of uncertainties-and generalizes known single-input, single-output (SISO) statements and constraints of the design problem to multiinput, multioutput (MIMO) cases. Two major MIMO design approaches are then evaluated in the context of these results.

Multivariable feedback design: Concepts for a classical/modern synthesis
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11. Optimal feedback control as a theory of motor coordination

Authors: Emanuel Todorov, Michael I Jordan
Published in: Nature neuroscience, 2002
Number of citations: 3,009
Summary: A central problem in motor control is understanding how the many biomechanical degrees of freedom are coordinated to achieve a common goal. An especially puzzling aspect of coordination is that behavioral goals are achieved reliably and repeatedly with movements rarely reproducible in their detail. Existing theoretical frameworks emphasize either goal achievement or the richness of motor variability, but fail to reconcile the two. Here we propose an alternative theory based on stochastic optimal feedback control. We show that the optimal strategy in the face of uncertainty is to allow variability in redundant (task-irrelevant) dimensions. This strategy does not enforce a desired trajectory, but uses feedback more intelligently, correcting only those deviations that interfere with task goals. From this framework, task-constrained variability, goal-directed corrections, motor synergies, controlled parameters, simplifying …

Optimal feedback control as a theory of motor coordination
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12. The internal model principle of control theory

Authors: Bruce A Francis, Walter Murray Wonham
Published in: Automatica, 1976/
Number of citations: 2,851
Summary: The classical regulator problem is posed in the context of linear, time-invariant, finite-dimensional systems with deterministic disturbance and reference signals. Control action is generated by a compensator which is required to provide closed loop stability and output regulation in the face of small variations in certain system parameters. It is shown, using the geometric approach, that such a structurally stable synthesis must utilize feedback of the regulated variable, and incorporate in the feedback path a suitably reduplicated model of the dynamic structure of the disturbance and reference signals. The necessity of this control structure constitutes the Internal Model Principle. It is shown that, in the frequency domain, the purpose of the internal model is to supply closed loop transmission zeros which cancel the unstable poles of the disturbance and reference signals. Finally, the Internal Model Principle is extended to …

The internal model principle of control theory
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13. Analysis of feedback systems with structured uncertainties

Authors: John Doyle
Published in: IEE Proceedings of Control Theory and Applications, 1982
Number of citations: 2,836
Summary: The paper introduces a general approach for analysing linear systems with structured uncertainty based on a new generalised spectral theory for matrices. The results of the paper naturally extend techniques based on singular values and eliminate their most serious difficulties.

Analysis of feedback systems with structured uncertainties
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14. Bilateral control of teleoperators with time delay

Authors: Robert J Anderson, Mark W Spong
Published in: Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics, 1988
Number of citations: 2,775
Summary: When a robot is operated remotely by use of a teleoperator, it is desirable to communicate contact force information from the slave to the master, in order to kinesthetically couple the operator to the environment and increase the sense of telepresence. One problem, however, recognized as early as 1965, has remained unsolved until now: How to maintain stability in a force-reflecting bilateral teleoperator in the presence of substantial time delay? In this paper, we present a solution to this problem.

Bilateral control of teleoperators with time delay
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15. Hybrid dynamical systems

Authors: Rafal Goebel, Ricardo G Sanfelice, Andrew R Teel
Published in: IEEE Control Systems Magazine, 2009
Number of citations: 2,768
Summary: A dynamical system is usually classified as either a continuous-time dynamical system or a discrete-time dynamical system. For example, classical mechanical systems and analog electronic circuits evolving in time according to principles of physics, such as Newton’s and Kirchoff’s laws, can be viewed naturally as continuous-time dynamical systems. Financial accounts, optimization algorithms, and digital systems can be viewed naturally as discrete-time dynamical systems.

Hybrid dynamical systems
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16. Mujoco: A physics engine for model-based control

Authors: Emanuel Todorov, Tom Erez, Yuval Tassa
Published in: IEEE/RSJ International Conference on Intelligent Robots and Systems, 2012
Number of citations: 2,739
Summary: We describe a new physics engine tailored to model-based control. Multi-joint dynamics are represented in generalized coordinates and computed via recursive algorithms. Contact responses are computed via efficient new algorithms we have developed, based on the modern velocity-stepping approach which avoids the difficulties with spring-dampers. Models are specified using either a high-level C++ API or an intuitive XML file format. A built-in compiler transforms the user model into an optimized data structure used for runtime computation. The engine can compute both forward and inverse dynamics. The latter are well-defined even in the presence of contacts and equality constraints. The model can include tendon wrapping as well as actuator activation states (e.g. pneumatic cylinders or muscles). To facilitate optimal control applications and in particular sampling and finite differencing, the dynamics can be …

Mujoco: A physics engine for model-based control
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17. Kalman filtering with intermittent observations

Authors: Bruno Sinopoli, Luca Schenato, Massimo Franceschetti, Kameshwar Poolla, Michael I Jordan, Shankar S Sastry
Published in: IEEE transactions on Automatic Control, 2004
Number of citations: 2,645
Summary: Motivated by navigation and tracking applications within sensor networks, we consider the problem of performing Kalman filtering with intermittent observations. When data travel along unreliable communication channels in a large, wireless, multihop sensor network, the effect of communication delays and loss of information in the control loop cannot be neglected. We address this problem starting from the discrete Kalman filtering formulation, and modeling the arrival of the observation as a random process. We study the statistical convergence properties of the estimation error covariance, showing the existence of a critical value for the arrival rate of the observations, beyond which a transition to an unbounded state error covariance occurs. We also give upper and lower bounds on this expected state error covariance.

Kalman filtering with intermittent observations
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18. A control engineer's guide to sliding mode control

Authors: K David Young, Vadim I Utkin, Umit Ozguner
Published in: IEEE transactions on control systems technology, 1999
Number of citations: 2,633
Summary: Presents a guide to sliding mode control for practicing control engineers. It offers an accurate assessment of the so-called chattering phenomenon, catalogs implementable sliding mode control design solutions, and provides a frame of reference for future sliding mode control research.

A control engineer’s guide to sliding mode control
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19. Stability of switched systems with average dwell-time

Authors: Joao P Hespanha, A Stephen Morse
Published in: Proceedings of the 38th IEEE conference on decision and control, 1999
Number of citations: 2,580
Summary: It is shown that switching among stable linear systems results in a stable system provided that switching is "slow-on-the-average". In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several input-to-state induced norms are bounded uniformly over all slow-on-the-average switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scale-independent hysteresis can produce switching that is slow-on-the-average and therefore the results mentioned above can be used to study the stability of hysteresis-based …

Stability of switched systems with average dwell-time
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20. A survey of iterative learning control

Authors: Douglas A Bristow, Marina Tharayil, Andrew G Alleyne
Published in: IEEE control systems magazine, 2006
Number of citations: 2,573
Summary: This article surveyed the major results in iterative learning control (ILC) analysis and design over the past two decades. Problems in stability, performance, learning transient behavior, and robustness were discussed along with four design techniques that have emerged as among the most popular. The content of this survey was selected to provide the reader with a broad perspective of the important ideas, potential, and limitations of ILC. Indeed, the maturing field of ILC includes many results and learning algorithms beyond the scope of this survey. Though beginning its third decade of active research, the field of ILC shows no sign of slowing down.

A survey of iterative learning control
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21. Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators

Authors: Jean-Jacques Slotine, S Shankar Sastry
Published in: International journal of control, 1983
Number of citations: 2,483
Summary: A methodology of feedback control is developed to achieve accurate tracking in a. class of non-linear, time-varying systems in the presence of disturbances and para meter variations. The methodology uses in its idealized form piecewise continuous feedback control, resulting in the state trajectory sliding along a time-varying sliding surface in the state space. This idealized control law achieves perfect tracking; however, non-idealities in its implementation result in the generation of an undesirable high-frequency component in the state trajectory. To rectify this, it is shown how continuous control laws may be used to approximate the discontinuous control law to obtain robust tracking to within a prescribed accuracy without generating undesirable high-frequency signal. The method is applied to the control of a two-link manipulator handling variable loads in a flexible manufacturing system environment.

Tracking control of non-linear systems using sliding surfaces, with application to robot manipulators
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22. Nonholonomic motion planning: Steering using sinusoids

Authors: Richard M Murray, Sosale Shankara Sastry
Published in: IEEE transactions on Automatic Control, 1993
Number of citations: 2,221
Summary: Methods for steering systems with nonholonomic c.onstraints between arbitrary configurations are investigated. Suboptimal trajectories are derived for systems that are not in canonical form. Systems in which it takes more than one level of bracketing to achieve controllability are considered. The trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. A class of systems that can be steered using sinusoids (claimed systems) is defined. Conditions under which a class of two-input systems can be converted into this form are given.

Nonholonomic motion planning: Steering using sinusoids
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23. Simple analytic rules for model reduction and PID controller tuning

Authors: Sigurd Skogestad
Published in: Journal of process control, 2003
Number of citations: 2,088
Summary: The aim of this paper is to present analytic rules for PID controller tuning that are simple and still result in good closed-loop behavior. The starting point has been the IMC-PID tuning rules that have achieved widespread industrial acceptance. The rule for the integral term has been modified to improve disturbance rejection for integrating processes. Furthermore, rather than deriving separate rules for each transfer function model, there is a just a single tuning rule for a first-order or second-order time delay model. Simple analytic rules for model reduction are presented to obtain a model in this form, including the “half rule” for obtaining the effective time delay.

Simple analytic rules for model reduction and PID controller tuning
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24. Internal model control: PID controller design

Authors: Daniel E Rivera, Manfred Morari, Sigurd Skogestad
Published in: Industrial & engineering chemistry process design and development, 1986
Number of citations: 1,973
Summary:
For a large number of single input-single output (SISO) models typically used In the process industries, the Internal Model Control (IMC) design procedure Is shown to lead to PID controllers, occasionally augmented with a first-order lag. These PID controllers have as their only tuning parameter the closed-loop time constant or, equivalently, the closed-loop bandwidth. On-line adjustments are therefore much simpler than for general PID controllers. As a special case, PI-and PID-tuning rules for systems modeled by a first-order lag with dead time are derived analytically. The superiority of these rules In terms of both closed-loop performance and robustness is demonstrated.


Internal model control: PID controller design
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25. State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to relations to risk sensitivity

Authors: Keith Glover, John C Doyle
Published in: Systems & control letters, 1988
Number of citations: 1,915
Summary: Given a linear system, all stabilizing controllers such that a specified closed-loop transfer function has H norm less than a given scalar, are parametrized. This characterization involves the solution to two algebraic Riccati equations, each with the same order as the system, and further gives gives feasible controllers also with this order. The relationship to the risk-sensitive LQG stochastic control problem is established, giving an equivalence between robust and stochastic control.

State-space formulae for all stabilizing controllers that satisfy an H∞-norm bound and relations to relations to risk sensitivity
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26. Optimality principles in sensorimotor control

Authors: Emanuel Todorov
Published in: Nature neuroscience, 2004
Number of citations: 1,871
Summary: The sensorimotor system is a product of evolution, development, learning and adaptation—which work on different time scales to improve behavioral performance. Consequently, many theories of motor function are based on'optimal performance': they quantify task goals as cost functions, and apply the sophisticated tools of optimal control theory to obtain detailed behavioral predictions. The resulting models, although not without limitations, have explained more empirical phenomena than any other class. Traditional emphasis has been on optimizing desired movement trajectories while ignoring sensory feedback. Recent work has redefined optimality in terms of feedback control laws, and focused on the mechanisms that generate behavior online. This approach has allowed researchers to fit previously unrelated concepts and observations into what may become a unified theoretical framework for interpreting motor …

Optimality principles in sensorimotor control
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27. Distributed event-triggered control for multi-agent systems

Authors: Dimos V Dimarogonas, Emilio Frazzoli, Karl H Johansson
Published in: IEEE Transactions on Automatic Control, 2012
Number of citations: 1,851
Summary: Event-driven strategies for multi-agent systems are motivated by the future use of embedded microprocessors with limited resources that will gather information and actuate the individual agent controller updates. The controller updates considered here are event-driven, depending on the ratio of a certain measurement error with respect to the norm of a function of the state, and are applied to a first order agreement problem. A centralized formulation is considered first and then its distributed counterpart, in which agents require knowledge only of their neighbors' states for the controller implementation. The results are then extended to a self-triggered setup, where each agent computes its next update time at the previous one, without having to keep track of the state error that triggers the actuation between two consecutive update instants. The results are illustrated through simulation examples.

Distributed event-triggered control for multi-agent systems
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28. A survey on analysis and design of model-based fuzzy control systems

Authors: Gang Feng
Published in: IEEE Transactions on Fuzzy systems, 2006
Number of citations: 1,782
Summary: Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed

A survey on analysis and design of model-based fuzzy control systems
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29. Delay-dependent robust stabilization of uncertain state-delayed systems

Authors: Young Soo Moon, Poogyeon Park, Wook Hyun Kwon, Young Sam Lee
Published in: International Journal of control, 2001
Number of citations: 1,780
Summary: This paper concerns a problem of robust stabilization of uncertain state-delayed systems. A new delay-dependent stabilization condition using a memoryless controller is formulated in terms of matrix inequalities. An algorithm involving convex optimization is proposed to design a controller guaranteeing a suboptimal maximal delay such that the system can be stabilized for all admissible uncertainties.

Delay-dependent robust stabilization of uncertain state-delayed systems
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30. Adaptive motion control of rigid robots: A tutorial

Authors: Romeo Ortega, Mark W Spong
Published in: Automatica, 1989
Number of citations: 1,725
Summary: In this paper we give a tutorial account of several of the most recent adaptive control results for rigid robot manipulators. Our intent is to lend some perspective to the growing list of adaptive control results for manipulators by providing a unified framework for comparison of those adaptive control algorithms which have been shown to be globally convergent. In most cases we are able to simplify the derivations and proofs of these results as well.

Adaptive motion control of rigid robots: A tutorial
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31. Acceleration of stochastic approximation by averaging

Authors: Boris T Polyak, Anatoli B Juditsky
Published in: SIAM journal on control and optimization, 1992
Number of citations: 1,700
Summary: A new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated. Convergence with probability one is proved for a variety of classical optimization and identification problems. It is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence.

Acceleration of stochastic approximation by averaging
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32. Developments in nonholonomic control problems

Authors: Ilya Kolmanovsky, N Harris McClamroch
Published in: IEEE Control systems magazine, 1995
Number of citations: 1,665
Summary: Provides a summary of recent developments in control of nonholonomic systems. The published literature has grown enormously during the last six years, and it is now possible to give a tutorial presentation of many of these developments. The objective of this article is to provide a unified and accessible presentation, placing the various models, problem formulations, approaches, and results into a proper context. It is hoped that this overview will provide a good introduction to the subject for nonspecialists in the field, while perhaps providing specialists with a better perspective of the field as a whole. The paper is organized as follows: introduction to nonholonomic control systems and where they arise in applications, classification of models of nonholonomic control systems, control problem formulations, motion planning results, stabilization results, and current and future research topics.

Developments in nonholonomic control problems
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33. All controllers for the general H∞ control problem: LMI existence conditions and state space formulas

Authors: Tetsuya Iwasaki, Robert E Skelton
Published in: Automatica, 1994
Number of citations: 1,650
Summary: This paper presents all controllers for the general H∞ control problem (with no assumptions on the plant matrices). Necessary and sufficient conditions for the existence of an H∞ controller of any order are given in terms of three Linear Matrix Inequalities (LMIs). Our existence conditions are equivalent to Scherer's results, but with a more elementary derivation. Furthermore, we provide the set of all H∞ controllers explicitly parametrized in the state space using the positive definite solutions to the LMIs. Even under standard assumptions (full rank, etc.), our controller parametrization has an advantage over the Q-parametrization. The freedom Q (a real-rational stable transfer matrix with the H∞ norm bounded above by a specified number) is replaced by a constant matrix L of fixed dimension with a norm bound, and the solutions (X, Y) to the LMIs. The inequality formulation converts the existence conditions to a convex …

All controllers for the general H∞ control problem: LMI existence conditions and state space formulas
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34. Time-optimal control of robotic manipulators along specified paths

Authors: James E Bobrow, Steven Dubowsky, John S Gibson
Published in: The international journal of robotics research, 1985
Number of citations: 1,599
Summary: The minimum-time manipulator control problem is solved for the case when the path is specified and the actuator torque limitations are known. The optimal open-loop torques are found, and a method is given for implementing these torques with a conventional linear feedback control system. The algorithm allows bounds on the torques that may be arbitrary functions of the joint angles and angular velocities. This method is valid for any path and orientation of the end- effector that is specified. The algorithm can be used for any manipulator that has rigid links, known dynamic equations of motion, and joint angles that can be determined at a given position on the path.

Time-optimal control of robotic manipulators along specified paths
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35. Barrier Lyapunov functions for the control of output-constrained nonlinear systems

Authors: Keng Peng Tee, Shuzhi Sam Ge, Eng Hock Tay
Published in: Automatica, 2009
Number of citations: 1,572
Summary: In this paper, we present control designs for single-input single-output (SISO) nonlinear systems in strict feedback form with an output constraint. To prevent constraint violation, we employ a Barrier Lyapunov Function, which grows to infinity when its arguments approach some limits. By ensuring boundedness of the Barrier Lyapunov Function in the closed loop, we ensure that those limits are not transgressed. Besides the nominal case where full knowledge of the plant is available, we also tackle scenarios wherein parametric uncertainties are present. Asymptotic tracking is achieved without violation of the constraint, and all closed loop signals remain bounded, under a mild condition on the initial output. Furthermore, we explore the use of an Asymmetric Barrier Lyapunov Function as a generalized approach that relaxes the requirements on the initial conditions. We also compare our control with one that is based on …

Barrier Lyapunov functions for the control of output-constrained nonlinear systems
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36. Adaptive control of mechanical manipulators

Authors: John J Craig, Ping Hsu, S Shankar Sastry
Published in: The International Journal of Robotics Research, 1987
Number of citations: 1,483
Summary: When an accurate dynamic model of a mechanical manipu lator is available, it may be used in a nonlinear, model-based scheme to control the manipulator. Such a control formula tion yields a controller that suppresses disturbances and tracks desired trajectories uniformly in all configurations of the manipulator. Use of a poor dynamic model with this kind of model-based decoupling and linearizing scheme, however, may result in performance that is inferior to a much simpler, fixed-gain scheme.

Adaptive control of mechanical manipulators
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37. The swing up control problem for the acrobot

Authors: Mark W Spong
Published in: IEEE control systems magazine, 1995
Number of citations: 1,450
Summary: Underactuated mechanical systems are those possessing fewer actuators than degrees of freedom. Examples of such systems abound, including flexible joint and flexible link robots, space robots, mobile robots, and robot models that include actuator dynamics and rigid body dynamics together. Complex internal dynamics, nonholonomic behavior, and lack of feedback linearizability are often exhibited by such systems, making the class a rich one from a control standpoint. In this article the author studies a particular underactuated system known as the Acrobot: a two-degree-of-freedom planar robot with a single actuator. The author considers the so-called swing up control problem using the method of partial feedback linearization. The author gives conditions under which the response of either degree of freedom may be globally decoupled from the response of the other and linearized. This result can be used as a …

The swing up control problem for the acrobot
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38. Conflict resolution for air traffic management: A study in multiagent hybrid systems

Authors: Claire Tomlin, George J Pappas, Shankar Sastry
Published in: IEEE Transactions on automatic control, 1998
Number of citations: 1,436
Summary: Air traffic management (ATM) of the future allows for the possibility of free flight, in which aircraft choose their own optimal routes, altitudes, and velocities. The safe resolution of trajectory conflicts between aircraft is necessary to the success of such a distributed control system. In this paper, we present a method to synthesize provably safe conflict resolution manoeuvres. The method models the aircraft and the manoeuvre as a hybrid control system and calculates the maximal set of safe initial conditions for each aircraft so that separation is assured in the presence of uncertainties in the actions of the other aircraft. Examples of manoeuvres using both speed and heading changes are worked out in detail.

Conflict resolution for air traffic management: A study in multiagent hybrid systems
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39. The internal model principle for linear multivariable regulators

Authors: Bruce A Francis, William M Wonham
Published in: Applied mathematics and optimization, 1975
Number of citations: 1,434
Summary: Necessary structural criteria are obtained for linear multivariable regulators which retain loop stability and output regulation in the presence of small perturbations, of specified types, in system parameters. It is shown that structural stability thus defined requires feedback of the regulated variable, together with a suitably reduplicated model, internal to the feedback loop, of the dynamic structure of the exogenous reference and disturbance signals which the regulator is required to process. Necessity of these structural features constitutes the ‘internal model principle’.

The internal model principle for linear multivariable regulators
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40. Control methodologies in networked control systems

Authors: Yodyium Tipsuwan, Mo-Yuen Chow
Published in: Control engineering practice, 2003
Number of citations: 1,432
Summary: The use of a data network in a control loop has gained increasing attentions in recent years due to its cost effective and flexible applications. One of the major challenges in this so-called networked control system (NCS) is the network-induced delay effect in the control loop. Network delays degrade the NCS control performance and destabilize the system. A significant emphasis has been on developing control methodologies to handle the network delay effect in NCS. This survey paper presents recent NCS control methodologies. The overview on NCS structures and description of network delays including characteristics and effects are also covered.

Control methodologies in networked control systems
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41. Adaptive control of linearizable systems

Authors: Sosale Shankara Sastry, Alberto Isidori
Published in: IEEE Transactions on Automatic Control, 1989
Number of citations: 1,423
Summary: The authors give some initial results on the adaptive control of minimum-phase nonlinear systems which are exactly input-output linearizable by state feedback. Parameter adaptation is used as a technique to make robust the exact cancellation of nonlinear terms, which is called for in the linearization technique. The application of the adaptive technique to control of robot manipulators is discussed. Only the continuous-time case is considered; extensions to the discrete-time and sampled-data cases are not obvious.

Adaptive control of linearizable systems
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42. Self-tuning controller

Authors: David W Clarke, Peter J Gawthrop
Published in: Proceedings of the Institution of Electrical Engineers, 1975
Number of citations: 1,422
Summary: A strategy for the design of self-tuning controllers of systems with constant but unknown parameters is presented. A cost function which incorporates system input, output and set-point variations is selected, and a control law for a known system is derived. This control law is shown to comprise a least-squares predictor of a function related to the cost function, and the control input is chosen to make the prediction zero. The parameters of the control law for the unknown system are estimated using a recursive-least-squares algorithm, and the optimal parameters are shown to be a fixed point of the algorithm. Whilst retaining their computational simplicity, the proposed method has several advantages over self-tuning-regulator strategies which attempt to minimise the output variance alone: weighting of control is allowed for; set-point variation may be optimally followed; there is no requirement to choose a system-related …

Self-tuning controller
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43. Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor

Authors: Robert Mahony, Vijay Kumar, Peter Corke
Published in: IEEE Robotics and Automation magazine, 2012
Number of citations: 1,417
Summary: This article provides a tutorial introduction to modeling, estimation, and control for multirotor aerial vehicles that includes the common four-rotor or quadrotor case.

Multirotor aerial vehicles: Modeling, estimation, and control of quadrotor
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44. Foundations of control and estimation over lossy networks

Authors: Luca Schenato, Bruno Sinopoli, Massimo Franceschetti, Kameshwar Poolla, S Shankar Sastry
Published in: Proceedings of the IEEE, 2007
Number of citations: 1,400
Summary: This paper considers control and estimation problems where the sensor signals and the actuator signals are transmitted to various subsystems over a network. In contrast to traditional control and estimation problems, here the observation and control packets may be lost or delayed. The unreliability of the underlying communication network is modeled stochastically by assigning probabilities to the successful transmission of packets. This requires a novel theory which generalizes classical control/estimation paradigms. The paper offers the foundations of such a novel theory. The central contribution is to characterize the impact of the network reliability on the performance of the feedback loop. Specifically, it is shown that for network protocols where successful transmissions of packets is acknowledged at the receiver (e.g., TCP-like protocols), there exists a critical threshold of network reliability (i.e., critical probabilities …

Foundations of control and estimation over lossy networks
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45. Small-gain theorem for ISS systems and applications

Authors: Z-P Jiang, Andrew R Teel, Laurent Praly
Published in: Mathematics of Control, Signals and Systems, 1994
Number of citations: 1,371
Summary: We introduce a concept of input-to-output practical stability (IOpS) which is a natural generalization of input-to-state stability proposed by Sontag. It allows us to establish two important results. The first one states that the general interconnection of two IOpS systems is again an IOpS system if an appropriate composition of the gain functions is smaller than the identity function. The second one shows an example of gain function assignment by feedback. As an illustration of the interest of these results, we address the problem of global asymptotic stabilization via partial-state feedback for linear systems with nonlinear, stable dynamic perturbations and for systems which have a particular disturbed recurrent structure.

Small-gain theorem for ISS systems and applications
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46. Fast model predictive control using online optimization

Authors: Yang Wang, Stephen Boyd
Published in: IEEE Transactions on control systems technology, 2009
Number of citations: 1,314
Summary: A widely recognized shortcoming of model predictive control (MPC) is that it can usually only be used in applications with slow dynamics, where the sample time is measured in seconds or minutes. A well-known technique for implementing fast MPC is to compute the entire control law offline, in which case the online controller can be implemented as a lookup table. This method works well for systems with small state and input dimensions (say, no more than five), few constraints, and short time horizons. In this paper, we describe a collection of methods for improving the speed of MPC, using online optimization. These custom methods, which exploit the particular structure of the MPC problem, can compute the control action on the order of 100 times faster than a method that uses a generic optimizer. As an example, our method computes the control actions for a problem with 12 states, 3 controls, and horizon of 30 …

Fast model predictive control using online optimization
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47. Mittag–Leffler stability of fractional order nonlinear dynamic systems

Authors: Yan Li, YangQuan Chen, Igor Podlubny
Published in: Automatica, 2009
Number of citations: 1,303
Summary: In this paper, we propose the definition of Mittag–Leffler stability and introduce the fractional Lyapunov direct method. Fractional comparison principle is introduced and the application of Riemann–Liouville fractional order systems is extended by using Caputo fractional order systems. Two illustrative examples are provided to illustrate the proposed stability notion.

Mittag–Leffler stability of fractional order nonlinear dynamic systems
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