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Optimal Control

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Hybrid Dynamical Systems

Part of the book series: Advanced Textbooks in Control and Signal Processing ((C&SP))

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Abstract

In the optimal control of hybrid systems, a stabilizing control law is designed to optimize, i.e., minimize or maximize, an appropriate performance criterion. Optimal control has been an active research area in Systems and Control, at least, since the 1950s, when seminal contributions such as Pontryagin’s minimum principle and Bellman’s dynamic programming were introduced. Optimal control problems for hybrid systems have attracted considerable attention since the mid 1990s, and extensive studies have been reported in the literature. Early studies may be found in the control systems literature involving relays or dynamical systems with hysteresis [1]. Significant efforts have been devoted to the extensions of dynamic programming and Pontryagin’s minimum principle to hybrid systems using different formalisms, see e.g., [2,3,4,5,6,7] and the references therein.

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Notes

  1. 1.

    Here, \(f\in \mathcal {C}^{h}\) means that the function f is a h-times continuously differentiable function with \(h\ge 0\) being an integer, for \(h=0\) f is just continuous, and \(\mathcal {C}^{\infty }\) means the function f is smooth, or infinitely many times differentiable.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Notre Dame, Notre Dame, IN, USA

    Hai Lin & Panos J. Antsaklis

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  1. Hai Lin
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  2. Panos J. Antsaklis
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Correspondence to Hai Lin .

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Lin, H., Antsaklis, P.J. (2022). Optimal Control. In: Hybrid Dynamical Systems. Advanced Textbooks in Control and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-030-78731-8_5

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