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94
Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization
, 2000
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Stability and Stabilizability of Switched Linear Systems: A Short Survey of Recent Results
, 2005
"... During the last decade, there has been increasing interest in the stability analysis and switching control design for switched linear systems. This paper aims to briefly survey recent results in this field, focusing on stability analysis and switching stabilization problems. First, the stability an ..."
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Cited by 126 (10 self)
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During the last decade, there has been increasing interest in the stability analysis and switching control design for switched linear systems. This paper aims to briefly survey recent results in this field, focusing on stability analysis and switching stabilization problems. First, the stability analysis problem for switched linear systems is reviewed. We focus on the asymptotic stability analysis for switched linear systems under arbitrary switching, and highlight necessary and sufficient conditions for this problem. Secondly, the switching stabilization problem is studied, and a variety of switching stabilization methods found in the literature are outlined. One of the most elusive problems in the switched systems literature has been the switching stabilizability problem, that is under what condition it is possible to stabilize a switched system by properly designing switching control laws. Necessary and sufficient conditions for asymptotic stabilizability of switched linear systems are described.
Piecewise linear quadratic optimal control
 in Proc. American Control Conf
, 1997
"... Abstract—The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an ..."
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Cited by 98 (7 self)
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Abstract—The use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control. Lower bounds on the optimal control cost are obtained by semidefinite programming based on the Bellman inequality. This also gives an approximation to the optimal control law. An upper bound to the optimal cost is obtained by another convex optimization problem using the given control law. A compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy. Index Terms—Nonlinear systems, optimal control, semidefinite programming. I.
Optimal Control of Hybrid Systems
 IN PROCEEDINGS OF THE 38TH IEEE CONFERENCE ON DECISION AND CONTROL
, 1999
"... This paper presents a method for optimal control of hybrid systems. An inequality of Bellman type is considered and every solution to this inequality gives a lower bound on the optimal value function. A discretization of this "hybrid Bellman inequality" leads to a convex optimization probl ..."
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Cited by 94 (3 self)
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This paper presents a method for optimal control of hybrid systems. An inequality of Bellman type is considered and every solution to this inequality gives a lower bound on the optimal value function. A discretization of this "hybrid Bellman inequality" leads to a convex optimization problem in terms of finitedimensional linear programming. From the solution of the discretized problem, a value function that preserves the lower bound property can be constructed. An approximation of the optimal feedback control law is given and tried on some examples.
Optimal Control of Switched Systems Based on Parameterization of the Switching Instants
, 2001
"... This paper presents an approach for solving optimal control problems for switched systems ..."
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Cited by 54 (4 self)
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This paper presents an approach for solving optimal control problems for switched systems
Controlling mechanical systems with backlash—A survey
 Automatica
, 2002
"... Backlash is one of the most important nonlinearities that limit the performance of speed and position control in industrial, robotics, automotive, automation and other applications. The control of systems with backlash has been the subject of study since the 1940's. This survey reveals that s ..."
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Cited by 32 (1 self)
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Backlash is one of the most important nonlinearities that limit the performance of speed and position control in industrial, robotics, automotive, automation and other applications. The control of systems with backlash has been the subject of study since the 1940's. This survey reveals that surprisingly few control innovations have been presented since the early path breaking papers that introduced the describing function analysis of systems with backlash  indeed, some recent papers rediscover early results without quoting them! Promising developments are however taking place using adaptive and nonlinear control strategies. 1
Optimal Control of Switched Systems via Nonlinear Optimization Based on Direct Differentiations of Value Functions
, 2001
"... This paper presents an approach for solving optimal control problems of switched systems. In general, in ..."
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Cited by 26 (2 self)
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This paper presents an approach for solving optimal control problems of switched systems. In general, in
Lecture notes on hybrid systems
, 2004
"... The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be hi ..."
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Cited by 21 (0 self)
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The aim of this course is to introduce some fundamental concepts from the area of hybrid systems, that is dynamical systems that involve the interaction of continuous (real valued) states and discrete (finite valued) states. Applications where these types of dynamics play a prominent role will be highlighted. We will introduce general methods for investigating properties such as existence of solutions, reachability and decidability of hybrid systems. The methods will be demonstrated on the motivating applications. Students who successfully complete the course should be able to appreciate the diversity of phenomena that arise in hybrid systems and how discrete “discrete ” entities and concepts such as automata, decidability and bisimulation can coexist with continuous entities and
MPC for continuous piecewiseaffine systems — Addendum
, 2003
"... MPC for continuous piecewiseaffine systems ∗ B. De Schutter and T.J.J. van den Boom If you want to cite this report, please use the following reference instead: ..."
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Cited by 20 (6 self)
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MPC for continuous piecewiseaffine systems ∗ B. De Schutter and T.J.J. van den Boom If you want to cite this report, please use the following reference instead:
Explicit Suboptimal Linear Quadratic Regulation with State and Input Constraints
, 2000
"... Optimal feedback solutions to the infinite horizon LQR problem with state and input constraints based on receding horizon realtime quadratic programming are well known. In this paper we develop an explicit solution to the same problem, eliminating the need for realtime optimization. A suboptimal st ..."
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Cited by 18 (11 self)
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Optimal feedback solutions to the infinite horizon LQR problem with state and input constraints based on receding horizon realtime quadratic programming are well known. In this paper we develop an explicit solution to the same problem, eliminating the need for realtime optimization. A suboptimal strategy, based on a suboptimal choice of a finite horizon and imposing additional limitations on the allowed switching between active constraint sets on the horizon, is suggested in order to address the computer memory and processing capacity requirements of the explicit solution. It is shown that the resulting feedback controller is piecewise linear, and the piecewise linear structure is explored and exploited for computational analysis of stability and performance of the suboptimal constrained LQR. The piecewise linear structure can also be exploited for efficient realtime implementation of the controller.