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Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching

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  • Hajer Bouzaouache

Abstract

This paper investigates the optimal control problem of a particular class of hybrid dynamical systems with controlled switching. Given a prespecified sequence of active subsystems, the objective is to seek both the continuous control input and the discrete switching instants that minimize a performance index over a finite time horizon. Based on the use of the calculus of variations, necessary conditions for optimality are derived. An efficient algorithm, based on nonlinear optimization techniques and numerical methods, is proposed to solve the boundary-value ordinary differential equations. In the case of linear quadratic problems, the two-point boundary-value problems can be avoided which reduces the computational effort. Illustrative examples are provided and stress the relevance of the proposed nonlinear optimization algorithm.

Suggested Citation

  • Hajer Bouzaouache, 2017. "Calculus of Variations and Nonlinear Optimization Based Algorithm for Optimal Control of Hybrid Systems with Controlled Switching," Complexity, Hindawi, vol. 2017, pages 1-11, August.
    • Handle: RePEc:hin:complx:5308013
    DOI: 10.1155/2017/5308013
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    References listed on IDEAS

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    1. Chongyang Liu & Zhaohua Gong, 2014. "Optimal Control of Switched Systems Arising in Fermentation Processes," Springer Optimization and Its Applications, Springer, edition 127, number 978-3-662-43793-3, June.
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