Dual-mode Predictive Control of Constrained Nonlinear Sytems via Linear Differential Inclusion

Presented in the paper is a nonlinear predictive control method. It is known that some nonlinear plants can be transferred into linear time-varying systems after being globally linearized. So it is feasible to solve some certain problems of nonlinear systems via dealing with the corresponding linear uncertainty systems. Based on this idea, a dual-mode predictive control method for a class of constrained nonlinear systems whose trajectories can be embedded within polytopic linear differential inclusions is proposed. After being linearized through the tailor series, the initial nonlinear systems can be embedded into the polytopic description systems by using the maximum and minimum of each partial derivative over a bounded region of the state space. Then polytopic invariance is constructed on the polytopic description system to propose a predictive control algorithm, which is unlike earlier nonlinear predictive control methods that have to tackle online a complex nonlinear non-convex optimization problem, requires the solution of a semi-definite programming with linear matrix inequalities. And this can satisfy the demand of online optimization. Meanwhile, the stability of initial nonlinear system is based on the polytopic description system.