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Extended Casimir Approach to Controlled Hamiltonian Systems

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Abstract

In this paper, we first propose an extended Casimir method for energy-shaping. Then it is used to solve some control problems of Hamiltonian systems. To solve the H ∞ control problem, the energy function of a Hamiltonian system is shaped to such a form that could be a candidate solution of HJI inequality. Next, the energy function is shaped as a candidate of control ISS-Lyapunov function, and then the input-to-state stabilization of port-controlled Hamiltonian systems is achieved. Some easily verifiable sufficient conditions are presented.

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Authors and Affiliations

  1. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China

    Yuqian Guo & Daizhan Cheng

Authors
  1. Yuqian Guo
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  2. Daizhan Cheng
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Correspondence to Yuqian Guo.

Additional information

Supported by the National Natural Science Foundation of China under Grants 60221301 and 60334040.

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Guo, Y., Cheng, D. Extended Casimir Approach to Controlled Hamiltonian Systems. Jrl Syst Sci & Complex 19, 211–218 (2006). https://doi.org/10.1007/s11424-006-0211-4

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  • DOI: https://doi.org/10.1007/s11424-006-0211-4

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