Dynamic output feedback model predictive control for asynchronous Markovian jump systems under try‐once‐discard protocol

Abstract

AbstractThis paper is concerned with the dynamic output feedback robust model predictive control (RMPC) problem for a class of discrete‐time asynchronous Markovian jump systems (MJSs) subject to polytopic parameter uncertainties and hard constraints on states and inputs. A hidden Markov model is employed to describe the asynchronous phenomenon between the detected modes and the system modes. For the purpose of improving the network utilization as well as reducing the transmission burden and avoiding data collisions, the try‐once‐discard (TOD) protocol is deployed in the shared communication network between sensor nodes and the controller node. Considering the difficulty of obtaining the system state in the practice, the dynamic output‐feedback control in the framework of RMPC is adopted, and the worst‐case optimization problem over the infinite moving horizon is formulated for the performance analysis and control synthesis. By means of the Lyapunov‐like function approach, free weighting matrices and inequality techniques such as the ‐procedure are introduced to deal with the non‐convexity caused by couplings between decisive variables and the negative influence resulting from the data orchestration is mitigated. Based on the delicate establishments, a certain upper bound of the objective function is employed to construct an auxiliary optimization problem with solvability to find the desired controllers, and sufficient conditions are obtained to guarantee that the MJSs under the proposed RMPC‐based controllers are mean‐square stable. Finally, an illustrative example is used to demonstrate the validity of the proposed methods.