Synthesis of Non Linear Controllers

Abstract

A family of nonlinear multivariable controllers is developed for multivariable linear systems by modifications of a class of optimal linear controllers. These underlying linear problems minimize only quadratic control costs, but respond to state deviations through constraints that x(t) should approach zero at a virtual horizon time. The nonlinear controllers are developed by making the effective horizon a function of the current state. These nonlinear controllers retain the computational simplicity of the linear horizon constraint designs, while adding the advantage of bigger effective gains for large state deviations. While the nonlinear controllers obtained in this way do not explicitly minimize any performance indices, it is possible to find conditions which assure that the resulting closed loops systems will be asymptotically stable. Moreover, numerical examples are presented to demonstrate the feasibility of on-line implementation of the corresponding algorithms.