control (see [9] for a recent survey of results in this area). this a hybrid control scheme uniting bounded con-One of the key limitations imposed by constraints is that trol with model predictive control (MPC), is proposed for on the set of initial states that can be steered to the origin the stabilization of linear timeinvariant systems with in-with the available control action. An effective control polput constraints. The scheme is predicated on the idea of icy, that takes constraints into account, need provide, not switching between a ~~~~~~~~-b~~~d bounded nonlinear only the stabilizing feedback control law, but also an excontroller, for which a region of closed-loop stability un-plicit characterization of the set of initial conditions, startder constraints is explicitly characterized, and a model pre-ing from where closed-loop stability is guaranteed. The dictive controller that minimizes a quadratic performance absence of an a priori explicit characterization of this set objective subject to constraints. Switching laws, that, man-(or an appropriate estimate thereof) typically necessitates itor the evolution of the c~ose~-loop trajectory under MPC, running extensive closed-loop simulations over the whole within the stability region, and place appropriate set of possible initial conditions, to check closed-loop stations on any concomitant growth of the L~~~~~~~ function, bility, or results in limiting operation within an unnecessar-=e derived to orchestrate the transition between the two ily small (conservative) neighborhood of the nominal equicontrollers, in a way that guarantees asymptotic closed-loop librium. Motivated by these considerations, we have restability for all initial conditions within the stability region. cently developed in 141 a class of bounded robust LYaPunov-The hybrid scheme is shown to provide a computationa~~y based nonlinear controllers, inspired in part by the results efficient for the implementation of MPC by provid-on bounded control in [8], that enforce robust stability in ing, through off-line computations, a priori knowledge of the closed-loop system and provide, at the same time, an a set of initial conditions for which c~osed-loop stability is explicit characterization of the region of guaranteed closedguaranteed. The proposed approach is illustrated through loop a simulation example.Despite their well-characterized stability and constraint-K~~ words: Input constraints, ~~~~d~d ~~~~~~~~-b~~d handling properties, the above controllers are not necessarcontrol, Model predictive control, Switching laws, Stability ily optimal with respect to an arbitrary performance criregion.terion (in [4] we show that they are inverse optimal with respect to meaningful cost functionals). Currently, MPC, also known as receding horizon control, is one of the few virtually all practical control systems are subject to hard control methods for handling constraints within an optimal typically reflect natural limitations in the capacity of consolving, on-line, a finitehorizon constrained open-loop o p ...
