Nonlinear observer-based optimal control using the state-dependent Riccati equation for a class of non-affine control systems

Abstract

The present study uses a combination of a state-dependent Riccati equation (SDRE) controller and SDRE observer to control a class of nonlinear non-affine control systems. This type of nonlinear system features control nonlinearities that change the formulation of the SDRE and its solution techniques. Control law is obtained using the exact solution method for low-order and uncomplicated systems; numerical approaches are available for complex and high order systems. Both solution methods must use integral control formulation or solve the system equation using control law simultaneously to treat control nonlinearities. The closed loop feedback of the system is partially available, providing an observer for estimation of full-state feedback. The efficacy, advantages and compatibility of the controller with the observer guides the choices to the SDRE observer. The stability proof of the SDRE controller in the non-affine structure is presented and four case studies are simulated and discussed. Two were selected from previous studies to verify the proposed algorithm. The third, more complicated model, shows the ability of the controller to solve complex and high order systems. A brief discussion of the suboptimal cheap control problem and an example are also presented.