Robust Nonlinear Control Design via Stable Manifold Method

Yoshiki Abe, Gou Nishida, Noboru Sakamoto and Yutaka Yamamoto

Mathematical Problems in Engineering, 2015, vol. 2015, 1-8

Abstract:

This paper proposes a systematic numerical method for designing robust nonlinear controllers without a priori lower-dimensional approximation with respect to solutions of the Hamilton-Jacobi equations. The method ensures the solutions are globally calculated with arbitrary accuracy in terms of the stable manifold method that is a solver of Hamilton-Jacobi equations in nonlinear optimal control problems. In this realization, the existence of stabilizing solutions of the Hamilton-Jacobi equations can be derived from some properties of the linearized system and the equivalent Hamiltonian system that is obtained from a transformation of the Hamilton-Jacobi equation. A numerical example is shown to validate the design method.

Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:198380

DOI: 10.1155/2015/198380

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