This article addresses robust model predictive control (MPC) for systems with polytopicdescription. An existing off-line robust MPC enables the on-line computation as simple assearching a state feedback gain among the look-up table. We consider enlarging the region ofattraction of the off-line MPC by incorporating free perturbation items. First, a largerellipsoidal region of attraction is off-line constructed, in which a simple optimization problemis solved on-line. Then, outside of this larger ellipsoid, a standard robust MPC is solved onlinesuch that the overall region of attraction can be rendered as a much larger nonellipsoidalone. The proposed approach possesses all the merits of the off-line MPC and greatly enlargesthe region of attraction. A simulation example is given to demonstrate the effectiveness.

This paper considers an infinite-horizon min–max model predictive control (MPC) problemfor time-delay discrete systems with a polytopic uncertainty description, which has rarely beenaddressed in the literature. Several new solutions to this problem are proposed which are intercomplementary.If there is an input delay, then the single state feedback solution requires allthe system matrices to be stable. This deficiency can be removed by adding free control movesbefore a modified state feedback law. If there is no input delay, then a computationallyefficient off-line state feedback solution can be applied. In order to obtain desirable region ofattraction while at the same time preserve reasonably low on-line computational effort, onecan choose the standard solution. Simulation results are given to illustrate these new solutions.

A suboptimal solution to constrained linear time varying quadratic regulation (CLTVQR)is proposed. In a neighborhood of the origin, the problem is formulated as a min-max LQRbased on polytopic inclusion of the dynamics in this neighborhood. Outside thisneighborhood, the control moves are obtained by solving a constrained finite horizonoptimization problem. The main contribution is to obtain a cost value arbitrarily close (butnot equal) to that of the optimal CLTVQR. The suboptimal CLTVQR preserves the feasibihtyof the optimal CLTVQR if and only if the min-max LQR exists feasible solution. By mildmodification, this suboptimal method can be applied to nonlinear systems.

The two-step model predictive control is designed for input saturated Hammerstein systems. It first applies the unconstrained linear dynamic subsystem to get the desired intermediate variable, and then obtains the actual control action by solving nonlinear algebraic equation group and desaturation. The stability of the closed-loop system is analysed and its domain of attraction is designed applying semi-global stabilization techniques. The stability conclusions are illustrated with an example. Copyright # 2006 John Wiley & Sons, Ltd.