Constructive model predictive control for constrained nonlinear systems

Abstract

This paper develops a new model predictive control (MPC) design for stabilization of continuous-time nonlinear systems subject to state and input constraints. The key idea is to construct an analytic form of the controller with some undetermined parameters and to calculate the parameters by minimizing online a performance index. By using the method of control Lyapunov functions (CLFs), we construct an appropriate variation on Sontag's formula, with one degree of freedom reflecting 'decay rate' of CLFs. Moreover, the constructed univariate control law is used to characterize the terminal region that guarantees the feasibility of the optimal control problem. Provided that the initial feasibility of the optimization problem is satisfied, the stability of the control scheme can be guaranteed. An example is given to illustrate the application of the constructive MPC design. Copyright © 2008 John Wiley & Sons, Ltd.