The capabilities and art of state-dependent Riccati equation-based design

Abstract

State-dependent Riccati equation (SDRE) techniques are general design methods which provide a systematic and effective means of designing nonlinear controllers, observers, and filters. The paper provides an overview of the capabilities of SDRE control and goes into detail concerning the art of carrying out effective SDRE designs for both systems that conform and do not conform to the basic structure and conditions required by the method. The paper is centered around the SDRE nonlinear regulator. The following situations which prevent a straightforward application of the SDRE method to the control problem at hand are addressed: the existence of state-independent terms, the existence of state-dependent terms which do not go to zero as the state vector goes to zero, the existence of nonlinearity in the controls, and the existence of uncontrollable and unstable but bounded state dynamics.