Integral manifold andH? control in weak nonlinear systems

Abstract

For a weak nonlinear system the authors obtained sufficient conditions for locking the solution of a differential equation system of the weak nonlinear type within a stable integral manifold, while satisfying the saddle point conditions of the optimal control evaluation function. The resulting solution can be used as a state feedback solution for the problem of H∞ regulator in weak nonlinear systems. By using the P solution of a Riccati matrix, sufficient conditions for obtaining the state feedback rule were derived from the results of discussion relating to the integral manifold. Then, the effectiveness of feedback of the weak nonlinear type was confirmed by simulation in a simple system. In addition, the Lyapunov function was used to evaluate stability of a closed-loop system obtained based on this feedback rule. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(1): 43–56, 2001