A Stability Result With Application to Nonlinear Regulation1

Abstract

This work considers a class of nonlinear systems whose feedback controller is generated via the solution of a State Dependent Riccati Equation (SDRE) as proposed in Banks and Manha and Cloutier. A pseudo-linear representation of the class of nonlinear systems is described and a stability analysis is performed. This analysis leads to sufficiency conditions under which local asymptotic stability is present. These conditions allow for the computation of a Region of Attraction estimate for system stability. These results are then applied to study stability and convergence properties of closed loop systems that arise when the SDRE technique is used. Many of the benefits of Linear Quadratic (LQ) Optimal Control, such as a tradeoff between state regulation and input effort, are readily transparent in the nonlinear scheme. The tradeoff ability is the major advantage of the SDRE over several other nonlinear control schemes. The computed Region of Attraction, while sufficient, is demonstrated to also be quite conservative. An example is used to examine the SDRE approach.