Abstract
A method is proposed for an approximate construction of the optimal state regulator for an autonomous nonlinear system with a quadratic performance index. The method is based upon the instantaneous linearization technique developed by Pearson. In the method of instantaneous linearization, the nonlinear system is approximated by a state-dependent linear model. The resultant problem is then solved using a technique similar to that for linear systems. However, the solution is not optimal in general because of the arbitrariness of the linearized model. The purpose of the present paper is to correct the serious shortcoming of this method.
First, an optimality condition for the control law obtained by the method of instantaneous linearization is derived. Secondly, by making use of this condition, a systematic procedure is presented to determine a suboptimal feedback control for a second-order system. A minimax algorithm is used to design the linearized model closely approximating the original system within a prescribed region in the state space. The validity of the present method is shown by examining typical examples.
