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Optimal control of continuoustime switched affine systems
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2006
"... This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the s ..."
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Cited by 26 (5 self)
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This paper deals with optimal control of switched piecewise affine autonomous systems, where the objective is to minimize a performance index over an infinite time horizon. We assume that the switching sequence has a finite length, and that the decision variables are the switching instants and the sequence of operating modes. We present two different approaches for solving such an optimal control problem. The first approach iterates between a procedure that finds an optimal switching sequence of modes, and a procedure that finds the optimal switching instants. The second approach is inspired by dynamic programming and identifies the regions of the state space where an optimal mode switch should occur, therefore providing a state feedback control law.
A masterslave algorithm for the optimal control of continuoustime switched affine systems
 In Proc. 41th IEEE Conf. on Decision and Control, Las Vegas
, 2002
"... For continuoustime switched affine systems, this paper proposes an approach for solving infinitehorizon optimal control problems where the decision variables are the switching instants and the sequence of operating modes. The procedure iterates between a "master " procedure that finds a ..."
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Cited by 13 (3 self)
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For continuoustime switched affine systems, this paper proposes an approach for solving infinitehorizon optimal control problems where the decision variables are the switching instants and the sequence of operating modes. The procedure iterates between a "master " procedure that finds an optimal switching sequence of modes, and a "slave" procedure that finds the optimal switching instants. 1
Efficient suboptimal solutions of switched LQR problems
 IN PROCEEDINGS OF THE AMERICAN CONTROL CONFERENCE, ST
, 2009
"... This paper studies the discretetime switched LQR (DSLQR) problem using a dynamic programming approach. Based on some nice properties of the value functions, efficient algorithms are proposed to solve the finitehorizon and infinitehorizon suboptimal DSLQR problems. More importantly, we establish ..."
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Cited by 8 (5 self)
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This paper studies the discretetime switched LQR (DSLQR) problem using a dynamic programming approach. Based on some nice properties of the value functions, efficient algorithms are proposed to solve the finitehorizon and infinitehorizon suboptimal DSLQR problems. More importantly, we establish analytical conditions under which the strategies generated by the algorithms are stabilizing and suboptimal. These conditions are derived explicitly in terms of subsystem matrices and are thus very easy to verify. The proposed algorithms and the analysis provide a systematical way of solving the DSLQR problem with guaranteed closeloop stability and suboptimal performance. Simulation results indicate that the proposed algorithms can efficiently solve not only specific but also randomly generated DSLQR problems, making NPhard problems numerically tractable.
On optimal quadratic regulation for discretetime switched linear systems
 IN HYBRID SYSTEMS: COMPUTATION AND CONTROL, SER. LECTURE NOTES IN COMPUTER SCIENCE, M. EGERSTEDT AND
"... This paper studies the discretetime linear quadratic regulation problem for switched linear systems (DLQRS) based on dynamic programming approach. The unique contribution of this paper is the analytical characterizations of both the value function and the optimal control strategies for the DLQRS p ..."
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Cited by 6 (5 self)
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This paper studies the discretetime linear quadratic regulation problem for switched linear systems (DLQRS) based on dynamic programming approach. The unique contribution of this paper is the analytical characterizations of both the value function and the optimal control strategies for the DLQRS problem. Based on the particular structures of these analytical expressions, an efficient algorithm suitable for solving an arbitrary DLQRS problem is proposed. Simulation results indicate that the proposed algorithm can solve randomly generated DLQRS problems with very low computational complexity. The theoretical analysis in this paper can significantly simplify the computation of the optimal strategy, making an NP hard problem numerically tractable.
Optimal feedback switching laws for autonomous hybrid automata
 In Proceedings IEEE International Symposium on Intelligent Control
, 2004
"... We define a new class of hybrid systems called Autonomous Hybrid Automata that can be seen as a generalization of the class of switched systems we have considered in previous works. In this new model there are two types of edges: a controllable edge represents a mode switch that can be triggered by ..."
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Cited by 5 (3 self)
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We define a new class of hybrid systems called Autonomous Hybrid Automata that can be seen as a generalization of the class of switched systems we have considered in previous works. In this new model there are two types of edges: a controllable edge represents a mode switch that can be triggered by the controller; an autonomous edge represents a mode switch that is triggered by the continuous state of the system as it reaches a given threshold. We show how to solve an infinite time horizon quadratic optimization problem with a numerically viable procedure for such a class of Hybrid Automata; the optimal control law is a statefeedback.
On the value functions of the discretetime switched lqr problem,”
 IEEE Trans. Autom. Control,
, 2009
"... AbstractIn this paper, we derive some important properties for the finitehorizon and the infinitehorizon value functions associated with the discretetime switched LQR (DSLQR) problem. It is proved that any finitehorizon value function of the DSLQR problem is the pointwise minimum of a finite n ..."
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Cited by 5 (2 self)
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AbstractIn this paper, we derive some important properties for the finitehorizon and the infinitehorizon value functions associated with the discretetime switched LQR (DSLQR) problem. It is proved that any finitehorizon value function of the DSLQR problem is the pointwise minimum of a finite number of quadratic functions that can be obtained recursively using the socalled switched Riccati mapping. It is also shown that under some mild conditions, the family of the finitehorizon value functions is homogeneous (of degree 2), is uniformly bounded over the unit ball, and converges exponentially fast to the infinitehorizon value function. The exponential convergence rate of the value iterations is characterized analytically in terms of the subsystem matrices.
Optimal Control of Switched Hybrid Systems: A Brief Survey
 INTERDISCIPLINARY STUDIES IN INTELLIGENT SYSTEMS
, 2011
"... Switched systems are a particular class of hybrid systems consisting of several subsystems and a switching law specifying the active subsystems at each time instant. Examples of switched systems can be found in chemical engineering, automotive systems, and electrical circuit systems, to name a few. ..."
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Cited by 2 (1 self)
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Switched systems are a particular class of hybrid systems consisting of several subsystems and a switching law specifying the active subsystems at each time instant. Examples of switched systems can be found in chemical engineering, automotive systems, and electrical circuit systems, to name a few. The problem of determining optimal control laws for hybrid systems and in particular for switched systems,
Electrical and Computer Engineering ECE Technical Reports Purdue Libraries Year
"... Abstract This paper studies the discretetime switched LQR (DSLQR) problem based on a dynamic programming approach. One contribution of this paper is the analytical characterization of both the value function and the optimal hybridcontrol strategy of the DSLQR problem. Their connections to the Ricc ..."
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Abstract This paper studies the discretetime switched LQR (DSLQR) problem based on a dynamic programming approach. One contribution of this paper is the analytical characterization of both the value function and the optimal hybridcontrol strategy of the DSLQR problem. Their connections to the Riccati equation and the Kalman gain of the classical LQR problem are also discussed. Several interesting properties of the value functions are derived. In particular, we show that under some mild conditions, the family of finitehorizon value functions of the DSLQR problem is homogeneous (of degree 2), uniformly bounded over the unit ball, and converges exponentially fast to the infinitehorizon value function. Based on these properties, efficient algorithms are proposed to solve the finitehorizon and infinitehorizon DSLQR problems. More importantly, we establish conditions under which the strategies generated by the algorithms are stabilizing and suboptimal. These conditions are derived explicitly in terms of subsystem matrices and are thus very easy to verify. The proposed algorithms and the analysis provide a systematic way of solving the DSLQR problem with guaranteed closedloop stability and suboptimal performance. Simulation results indicate that the proposed algorithms can efficiently solve not only specific but also randomly generated DSLQR problems, making the NPhard problems numerically tractable.
Statistical Learning for Optimal Control of Hybrid Systems
"... Abstract — In this paper we explore a randomized alternative for the optimization of hybrid systems ’ performance. The basic approach is to generate samples from the family of possible solutions, and to test them on the plant’s model to evaluate their performance. This result is obtained by first pr ..."
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Abstract — In this paper we explore a randomized alternative for the optimization of hybrid systems ’ performance. The basic approach is to generate samples from the family of possible solutions, and to test them on the plant’s model to evaluate their performance. This result is obtained by first presenting the general hybrid optimal control problem, and then converting it into an optimization problem within a statistical learning framework. The results are applied to examples already existing in the literature, in order to highlight certain operational aspects of the proposed methods. I.
unknown title
, 2004
"... Optimal control of hybrid automata: an application to the design of a semiactive suspension∗ ..."
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Optimal control of hybrid automata: an application to the design of a semiactive suspension∗