Observer-Based ${\mathscr {H}}_{\infty }$ Control of Time-Varying Systems with Random Access Protocol

Abstract

This chapter is concerned with the finite-horizon ${\mathscr {H}}_{\infty }$ control problem for linear time-varying systems under the scheduling of Random Access Protocol. Two communication networks (i.e. the sensor-to-controller network and the controller-to-actuator network) are employed to realize the signal transmissions between the linear time-varying systems and the controller. Two Random Access Protocols are utilized to determine which sensor and actuator obtains the access to the communication networks. The mapping technique is utilized to model the transmission behavior under the joint scheduling effects of the two Random Access Protocols. The aim of the problem addressed is to develop an observer-based controller such that the required ${\mathscr {H}}_{\infty }$ performance of the closed-loop system is ensured over a given finite horizon. The desired controller parameters are calculated through the solution of two coupled backward recursive difference equations. Finally, the impact of the protocol scheduling on the characteristic of the controller parameters is analyzed.