We address the distributed model predictive control (MPC) for a set of linear local systems with decoupled dynamics and acoupled global cost function. By the decomposition of the global cost function, the distributed control problem is convertedto the MPC for each local system associated with a cost involving neighboring system states and inputs. For each localcontroller, the infinite horizon control moves are parameterized as N free control moves followed by a single state feedbacklaw. An interacting compatibility condition is derived, disassembled and incorporated into the design of each local control soas to achieve the stability of the global closed-loop system. Each local system exchanges with its neighbors the current statesand the previous optimal control strategies. The global closed-loop system is shown to be exponentially stable provided thatall the local optimizers are feasible at the initial time. Copyright

This paper further studies stabilization of nonlinear systems represented by a Takagi–Sugeno (T-S) discrete fuzzy model. By extending a nonquadratic Lyapunov function and applying a nonparallel distributed compensation (non-PDC) law, a new stabilization conclusion is presented that is a generalization of some previous results in the literature. The new conclusion under a special situation is also suitable for a PDC law, which presents to be more relaxed than some existing results. An example is provided to demonstrate the effectiveness of the new conclusions.

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 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.

This paper addresses the stabilization of nonlinear systems,which is represented by a Takagi–Sugeno (T-S) model. Based on the extendednonquadratic Lyapunov function and the nonparallel distributedcompensation law, three new results are obtained by using appropriateslack matrices, collection matrices, and the higher dimensional collectionmatrix. The first two results are less conservative, and computationally lessexpensive, than some of the existing results. The third result combines theprocedures of the first two results, and is less conservative, but is computationallymore expensive than the first two results. The effectiveness of thenew results is validated by two numerical examples