A Method for Construction of Suboptimal Nonlinear Regulators

Abstract

A method is proposed for an approximate construction of the optimal state regulator for an autonomous nonlinear system with quadratic performance index. This method is based upon the instantaneous linearization technique developed by Pearson. The nonlinear system is approximated by a state-dependent linear system. First, a theorem is established to give a necessary condition for Pearson's control law to be optimal. 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 over all state variables considered. The validity of the present method is shown by examining typical examples.