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.

This paper investigates the parameter-dependent open-loop model predictivecontrol (PDOLMPC) scheme for systems with a polytopic uncertaintydescription. PDOLMPC parameterizes the infinite horizon control moves intoa number of free control moves followed by a single state feedback law.The free control moves (excluding the first one) are parameter dependentand constructed upon all of the extreme realizations of the uncertainty beforethe switching horizon N. Our primary contribution is to point out that thisPDOLMPC is a relaxed version of the feedback MPC. Thus, some propertiesof nominal MPC, such as enhancement of optimality and enlargement ofregion of attraction by increasing the switching horizon, can be inherited inPDOLMPC. These properties are theoretically important for robust MPC anda simulation example is given for demonstration.

This paper studies poly-quadratic stability of nonlinear systems representedby a Takagi-Sugeno (T-S) discrete fuzzy model. A system is polyquadraticallystable when its stability can be verified by a parameter dependentLyapunov function. There are already some results in this area. This paper,however, presents less conservative results by adopting more slack-matrixvariablesin the linear matrix inequalities (LMIs). The parallel distributedcompensation (PDC) law is utilized in both the analysis and the synthesisproblems. The effectiveness of the new results in this paper is validated by asimulation example.

This paper gives two alternative off-line synthesis approaches to robust model predictive control (RMPC) for systems with polytopic description. In each approach, a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off-line. In order to accommodate a wider class of systems, nominal performance cost is chosen to substitute the "worst-case" one in an existing technique. In the design of control law for a larger ellipsoid, the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids, so as to further improve feasibility and optimality. The effectiveness of the alternative approaches is illustrated by a simulation example.