Sampling rate scheduling and optimal control co-design for networked control systems

A co-design of sampling rate scheduling and optimal control is investigated for networked control systems (NCSs) with transmission delay and packet loss. The basic purpose of proposed co-design scheme is to save substantial communication in both the sensor-to-controller channels and the controller-to-actuator channels, while guaranteeing optimal control performance of NCSs. Firstly, a switched systems model used to describe NCSs with sampling periods subject to a finite set is constructed. Secondly, guaranteed cost control is studied for NCSs in order to obtain two upper bounds of quadratic performance of systems under the two cases, (a): the worst network communication condition and the longest sampling period; (b): the best network communication condition and the shortest sampling period. After the above preparations have been done, a performance partition-based sampling rate scheduling algorithm is developed to perform co-design strategy for NCSs. Moreover, to calculate control performance in real-time approach and guarantee the asymptotically stable of systems, adaptive controllers are designed in terms of linear matrix inequality (LMI) technology. Finally, a numerical example and simulations are given to illustrate the effectiveness of the proposed method.