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Quadratic Optimal Control Problems for Hybrid Linear Autonomous Systems with State Jumps
 Proceedings of the American Control Conference
, 2003
"... In this paper, results for quadratic optimal control of hybrid linear autonomous systems with state jumps are reported. In particular, we focus on problems in which a prespecified sequence of active subsystems is given. In a recent paper, we have proposed an approach for optimal control problems of ..."
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In this paper, results for quadratic optimal control of hybrid linear autonomous systems with state jumps are reported. In particular, we focus on problems in which a prespecified sequence of active subsystems is given. In a recent paper, we have proposed an approach for optimal control problems of hybrid autonomous systems with state jumps. However, in applying that approach, some computational issues must be addressed for the derivation of some necessary parameters. We in this paper, by taking advantage of the special structure of linear subsystems and quadratic costs, develop a more efficient method which computes these necessary parameters and hence leads to reduced computational effort. As an application, we apply our quadratic optimal control results to address the important reachability problems. Examples illustrate the results. 1
On the Maximum Principle for Impulsive Hybrid Systems
"... Abstract. In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics wit ..."
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Abstract. In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hybrid Optimal Control Problems (IHOCPs). For these problems, we obtain a concise characterization of the Impulsive Hybrid MP (IHMP), namely, the corresponding boundaryvalue problem and some additional relations. As in the classical case, the proposed IHMP provides a basis for diverse computational algorithms for the treatment of IHOCPs. Key Words: impulsive hybrid control systems, optimal control, necessary conditions of optimality, Maximum principle.
On the LQBased Optimization Techniques for Impulsive Hybrid Control Systems
"... AbstractThis paper deals with a quadratic optimization problem for linear impulsive hybrid systems. We study a class of LQtype impulsive hybrid optimal control problems (OCPs) and consider the application of the hybrid Maximum Principle (MP). Our aim is to investigate the natural relationship bet ..."
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AbstractThis paper deals with a quadratic optimization problem for linear impulsive hybrid systems. We study a class of LQtype impulsive hybrid optimal control problems (OCPs) and consider the application of the hybrid Maximum Principle (MP). Our aim is to investigate the natural relationship between the Pontryagintype MP and the Bellman Dynamic Programming (DP) approach. As next we develop the "hybrid" Riccati formalism and discuss some related computational aspects.
Control and Cybernetics
"... Variational formalism applied to control of autonomous switching systems by ..."
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Variational formalism applied to control of autonomous switching systems by
Hybrid Function Approximation: A Variational Approach
"... Abstract — In this paper we study the problem of representing trajectories through a concatenation of trajectories obtained from solving different differential equations. These trajectories are moreover allowed to undergo discontinuous jumps in order to make the approximation better. Our solution is ..."
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Abstract — In this paper we study the problem of representing trajectories through a concatenation of trajectories obtained from solving different differential equations. These trajectories are moreover allowed to undergo discontinuous jumps in order to make the approximation better. Our solution is based on a variational approach, in which both jump heights as well as switch times are taken as optimization parameters. The main application for this method is data compression, where the original trajectory is represented through mode sequences, switch times, and jump heights. I.
Hybrid Function Approximation: A Variational Approach
"... Abstract — In this paper we study the problem of representing trajectories through a concatenation of trajectories obtained from solving different differential equations. These trajectories are moreover allowed to undergo discontinuous jumps in order to make the approximation better. Our solution is ..."
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Abstract — In this paper we study the problem of representing trajectories through a concatenation of trajectories obtained from solving different differential equations. These trajectories are moreover allowed to undergo discontinuous jumps in order to make the approximation better. Our solution is based on a variational approach, in which both jump heights as well as switch times are taken as optimization parameters. The main application for this method is data compression, where the original trajectory is represented through mode sequences, switch times, and jump heights. I.