Suboptimal Design of a Nonlinear Feedback System

Abstract

A method is developed for the approximate design of an optimal state regulator for a nonlinear system with quadratic performance index. The nonlinearity is taken to be a perturbation to the system. By making use of a power-series expansion in a small parameter, matrix equations are derived for the stepwise determination of a suboptimal feedback law. Given a polynomial nonlinearity of an arbitrary form, explicit solutions have been obtained for those matrix equations. A necessary and sufficient condition for the existence and uniqueness of the solution is also shown. Further, the performance analysis reveals the fact that the l-th order approximation in the feedback law results in the (2l+1)th order approximation to the optimal performance index. The method may effectively be used in a computer programmed computation.