Integral manifold and H-infinity control in weak nonlinear systems

For a weak nonlinear system the authors obtained sufficient conditions for locking the solution of a differential equation system of the weak nonlinea r type within a stable integral manifold, while satisfying the saddle point conditions of the optimal control evaluation function. The resulting solut ion can be used as a state feedback solution for the problem of H-infinity regulator in weak nonlinear systems. By using the P solution of a Riccati m atrix, sufficient conditions for obtaining the state feedback rule were der ived 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 feedb ack rule. (C) 2000 Scripta Technica.