Event-triggered dynamic output feedback RMPC for polytopic systems with redundant channels: Input-to-state stability

Abstract

This paper is concerned with the event-triggered dynamic output feedback robust model predictive control (RMPC) problem for a class of polytopic systems subject to redundant channels and the constraints on states and inputs. The redundant channels are employed to deal with the unanticipated problems such as packet dropouts during the data transmission via network, where the investigated packet dropouts are supposed to occur in a random way modeled by a set of mutually independent Bernoulli distributed sequences. A novel event-triggered communication mechanism with the time-varying threshold is adopted when the data is transmitted from estimator side to controller side, which reduces the communication burden by canceling unnecessary data transmission and hence effectively saves energy. At each sampling instant, the optimized feedback control law is computed by minimizing the upper bound on the “worst-case” value of an event-dependent infinite horizon cost function subject to constraints on inputs and states. In virtue of the cone complementarity linearization (CCL) technique, the non-convex optimization problem is converted to a minimization problem including some linear matrix inequalities. Based on the invariant set theory, some sufficient conditions are established to guarantee the recursive feasibility and input-to-state stability (ISS) in mean square sense. An event-based dynamic output feedback RMPC algorithm is developed to implement the online computation. A numerical simulation example is given to demonstrate the validity in energy saving as well as the desirable performance insurance.