Feedback Stabilization of Nonlinear Systems with Model Predictive Control

Professor James B. Rawlings, Department of Chemical Engineering, University of Texas at Austin

This seminar provides an overview of model predictive control, also known as receding horizon of moving horizon control. The two primary problems of interest are feedback control of linear plants subject to input and state inequality constraints, and feedback control of nonlinear plants. The talk begins with an overview of a typical industrial model predictive control algorithm, QDMC, that became popular in the chemical process industries in the early 1980s. QDMC was designed to handle linear plants subject to saturation type input constraints. The stability properties of the linear quadratic regulator on which QDMC is based are critiqued. From this analysis a modified linear quadratic regulator is proposed that improves the nominal stability properties of this kind of controller. Lyapunov function arguments are presented to show the stability of this approach even for the case of input and state inequality constraints. The case of incomplete state measurement can be handled with the usual linear state estimator. The stability of the interconnected state estimator and constrained regulator is disucssed. Finally, the extensions to handle disturbance models, reference tracking and non-square systems are presented. The theory for stabilization of nonlinear plants of the from x_k+1 = f(k_k, u_k) with model predictive control is presented. The nonlinear receding horizon controller is shown via an extended Lyapunov function argument to be asymptotically stabilizing for a large class of nonlinear systems. In particular, all nonlinear systems that can be globally feedback linearized can be globally stabilized with nonlinear model predictive control. An example of a conrollable plant that cannot be even locally asymptotically stabilized with continuous feedback, u(x), will be presented. Receding horizong control will be shown to be stabilizing for this example. The discontinuous u(x) generated by receding horizon control will be examined and numerical simulations will be presented.