Optimal control of switching systems
Optimal control of switching systems
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DOI：
10.1016/j.automatica.2004.08.003
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
S. Bengea;R. Decarlo
中科院分区：
文献类型：
--
作者：
S. Bengea;R. Decarlo
This paper considers an optimal control problem for a switching system. For solving this problem we do not make any assumptions about the number of switches nor about the mode sequence, they are determined by the solution of the problem. The switching system is embedded into a larger family of systems and the optimization problem is formulated for the latter. It is shown that the set of trajectories of the switching system is dense in the set of trajectories of the embedded system. The relationship between the two sets of trajectories (1) motivates the shift of focus from the original problem to the more general one and (2) underlies the engineering relevance of the study of the second problem. Sufficient and necessary conditions for optimality are formulated for the second optimization problem. If they exist, bang–bang-type solutions of the embedded optimal control problem are solutions of the original problem. Otherwise, suboptimal solutions are obtained via the Chattering Lemma.
