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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.
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.
OPTIMAL CONTROL FOR SWITCHED POINT DELAY SYSTEMS WITH REFRACTORY PERIOD
"... Abstract: The problem of optimal switching of a multimode time delay system is considered. The class of multimode systems consists of systems where the control variables are the switching times in a sequence of fixed vector fields. We assume that the systems considered all have a refractory period ..."
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Abstract: The problem of optimal switching of a multimode time delay system is considered. The class of multimode systems consists of systems where the control variables are the switching times in a sequence of fixed vector fields. We assume that the systems considered all have a refractory period, in the sense that once an action is taken, it takes a noninfinitesimal amount of time before a subsequent action can be taken. Necessary conditions for a stationary solution are derived for systems with a single or commensurate delays, and shown to extend those of the delay free case in (Egerstedt et al. 2003). Copyright c○2005 IFAC