Robust Nonlinear H ∞ Control Design via Stable Manifold Method

Abstract EN

This paper proposes a systematic numerical method for designing robust nonlinear H ∞ 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.