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Inverse optimal control and construction of control Lyapunov functions

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Abstract

In this paper, the construction of CLFs for nonlinear systems and a new inverse optimal control law are presented. The construction of a CLF for an affine nonlinear system is reduced to the construction of a CLF for a simpler system, and a new L g V type control law with respect to a CLF is provided. This control law is a generalization of Sontag’s formula and contains a design parameter. Tuning this parameter gives many suboptimal solutions for the optimization problem. Also, the gain margin and sector margin of the control law are calculated. Examples are provided to illustrate the main theoretical results of the paper.

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Authors and Affiliations

  1. Shahrood University of Technology, Faculty of Electrical and Robotic Engineering, Shahrood, Iran

    A. Shahmansoorian

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  1. A. Shahmansoorian
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Correspondence to A. Shahmansoorian.

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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal Control, 2008.

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Shahmansoorian, A. Inverse optimal control and construction of control Lyapunov functions. J Math Sci 161, 297–307 (2009). https://doi.org/10.1007/s10958-009-9553-5

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  • DOI: https://doi.org/10.1007/s10958-009-9553-5

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