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27
Adaptive dynamic programming for finitehorizon optimal control of discretetime nonlinear systems with error bound
 IEEE Trans. Neural Netw
, 2011
"... Abstract — In this paper, we study the finitehorizon optimal control problem for discretetime nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to ..."
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Cited by 15 (4 self)
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Abstract — In this paper, we study the finitehorizon optimal control problem for discretetime nonlinear systems using the adaptive dynamic programming (ADP) approach. The idea is to use an iterative ADP algorithm to obtain the optimal control law which makes the performance index function close to the greatest lower bound of all performance indices within an εerror bound. The optimal number of control steps can also be obtained by the proposed ADP algorithms. A convergence analysis of the proposed ADP algorithms in terms of performance index function and control policy is made. In order to facilitate the implementation of the iterative ADP algorithms, neural networks are used for approximating the performance index function, computing the optimal control policy, and modeling the nonlinear system. Finally, two simulation examples are employed to illustrate the applicability of the proposed method. Index Terms — Adaptive critic designs, adaptive dynamic programming, approximate dynamic programming, learning control, neural control, neural dynamic programming, optimal control, reinforcement learning. I.
Stabilization of switched systems via optimal control
 In Proc. 16th IFAC World Congress
, 2005
"... We consider switched systems composed of linear time invariant unstable dynamics and we deal with the problem of computing an appropriate switching law such that the controlled system is globally asymptotically stable. On the basis of our previous results in this framework, we first present a metho ..."
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Cited by 9 (4 self)
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We consider switched systems composed of linear time invariant unstable dynamics and we deal with the problem of computing an appropriate switching law such that the controlled system is globally asymptotically stable. On the basis of our previous results in this framework, we first present a method to design a feedback control law that minimizes a linear quadratic (LQ) performance index when an infinite number of switches is allowed and at least one dynamics is stable. Then, we show how this approach can be useful when dealing with the stabilization problem of switched systems characterized by unstable dynamics, by applying the proposed procedure to a “dummy ” system, augmented with a stable dynamics. If the system with unstable dynamics is globally exponentially stabilizable, then our method provides the feedback control law that minimizes the chosen quadratic performance index, and that guarantees the closed loop system to be globally asymptotically stable. Published as:
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 switching control design for polynomial systems: an LMI approach
, 2013
"... We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear programming (LP) problem in the space of occupation measures. ..."
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Cited by 5 (2 self)
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We propose a new LMI approach to the design of optimal switching sequences for polynomial dynamical systems with state constraints. We formulate the switching design problem as an optimal control problem which is then relaxed to a linear programming (LP) problem in the space of occupation measures. This infinitedimensional LP can be solved numerically and approximately with a hierarchy of convex finitedimensional LMIs. In contrast with most of the existing work on LMI methods, we have a guarantee of global optimality, in the sense that we obtain an asympotically converging (i.e. with vanishing conservatism) hierarchy of lower bounds on the achievable performance. We also explain how to construct an almost optimal switching sequence. 1
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.
Robust output stabilization: improving performance via supervisory control
, 906
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Optimal control of switched homogeneous systems
 In Proceedings of the American Control Conference
, 2007
"... Abstract—In this paper, we present a method for designing discretetime statefeedback controllers for a class of continuoustime switched homogeneous systems which includes switched linear systems as a special case. A discretetime approximate value iteration over a quantization of the unit sphere ..."
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Cited by 2 (0 self)
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Abstract—In this paper, we present a method for designing discretetime statefeedback controllers for a class of continuoustime switched homogeneous systems which includes switched linear systems as a special case. A discretetime approximate value iteration over a quantization of the unit sphere is used to compute an approximation of the continuoustime value function over the entire unbounded state space. Properties of the value function and its approximations are elicited and used to provide conditions under which statefeedback controllers with provable guarantees in stability and performance can be constructed. To illustrate the results, the methodology is applied to an example switched system possessing two unstable modes, one of which is nonlinear. I.