Suboptimal stabilizing control for a class of nonlinear systems

Abstract

Consider a class of continuous time quadratic regulator problems involving a class of nonlinear affine dynamical systems. It is known that the optimal feedback control is directly related to the solution of the algebraic Riccati equation at every point along the state trajectory. In this paper, we propose a new practical computational method for constructing a suboptimal stabilising feedback controller. To be more specific, the state space is first partitioned into rectangular regions. The algebraic Riccati equations are then solved off-line at the geometric centre of all rectangular regions. On this basis, a suboptimal stabilizing feedback control law is constructed. A numerical example is ..