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Optimal Control of Switching Surfaces in Hybrid Dynamical Systems

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Abstract

This paper concerns an optimal control problem defined on a class of switched-mode hybrid dynamical systems. The system's mode is changed (switched) whenever the state variable crosses a certain surface in the state space, henceforth called a switching surface. These switching surfaces are parameterized by finite-dimensional vectors called the switching parameters. The optimal control problem is to minimize a cost functional, defined on the state trajectory, as a function of the switching parameters. The paper derives the gradient of the cost functional in a costate-based formula that reflects the special structure of hybrid systems. It then uses the formula in a gradient-descent algorithm for solving an obstacle-avoidance problem in robotics.

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Authors and Affiliations

  1. Dipartimento di Ingegneria Elettronica e dell'Informazione, Università di Perugia, 06125, Perugia, Italy

    M. Boccadoro

  2. School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Y. Wardi, M. Egerstedt & E. Verriest

Authors
  1. M. Boccadoro
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  2. Y. Wardi
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  3. M. Egerstedt
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  4. E. Verriest
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Corresponding author

Correspondence to Y. Wardi.

Additional information

The work of Boccadoro has been partially supported by MIUR under Grant PRIN 2003090090.

The work of Wardi has been partly supported by a grant from the Georgia Tech Manufacturing Research Center.

The work of Egerstedt has been partly supported by the National Science Foundation under Grant \# 0237971 ECS NSF-CAREER, and by a grant from the Georgia Tech Manufacturing Research Center.

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Boccadoro, M., Wardi, Y., Egerstedt, M. et al. Optimal Control of Switching Surfaces in Hybrid Dynamical Systems. Discrete Event Dyn Syst 15, 433–448 (2005). https://doi.org/10.1007/s10626-005-4060-4

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  • DOI: https://doi.org/10.1007/s10626-005-4060-4

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