Approximation of general nonlinear control systems with linear time varying systems

Abstract

Since control of general nonlinear control systems is very difficult and there isn't any analytic solution for these systems specially for non affine nonlinear control systems, in this paper we propose a novel method for finding a Linear Time Varying (LTV) equivalent system for these systems based on solving a sequence of Linear Programming Problems (LPP) corresponding to our original problem. First, we transfer the original problem to a new problem in the form of calculus of variations. Then we discretize the new problem and try to solve it approximately by using Nonlinear Programming (NLP) methods. For this, the solution of our NLP problem is transferred to solution a sequence of LPP, such that empowering us to use powerful linear problem soft wares. Finally, efficiency of our method is confirmed by solving some nonlinear control problems.