Robust/Optimal Control of Minimum-Phase Nonlinear Systems

Abstract

This thesis proposes a framework that provides suboptimal control laws for a class of minimum-phase nonlinear systems. This class includes systems whose state dynamics are an algebraic sum of their linear and nonlinear sub-dynamics. We propose a systematic method of designing a robust and optimal control law which essentially consists of two components - a linear and a nonlinear. It is shown that the proposed control scheme achieves stabilization while providing suboptimality for the class of systems under consideration. Furthermore, the framework provides for a mechanism which is suitable for handling tracking and regulation problems for the class of minimum-phase nonlinear systems by using the Internal Model Principle. A striking feature of the proposed framework is the flexibility of starting with synthesizing a Linear-Quadratic-Regulator for linear sub-dynamics of the system and then including a nonlinear control component that stabilizes the nonlinear sub-dynamics of the system. The flexibility offered by the proposed framework is applied firstly to a general class of linear parameter-varying and linear time-varying systems. We extend the flexibility obtained for these two systems to the class of minimum-phase nonlinear systems which are decomposable through existence of an appropriate transformation into their linear and nonlinear subdynamics. Moreover, we also propose a simplified approach to obtain an approximate yet practical solution to the nonlinear optimal control problem by replacing the requirement of solving Hamilton-Jacobi-Bellman equations with that of the Riccati partial differential equations, and then synthesizing the nonlinear component of the control law to achieve robust and suboptimal stabilization.