Coding–Decoding-Based Sliding Mode Control for Markovian Jump Systems Under Constrained Bit Rate: An Adaptive Quantizer Approach

This article investigates the asynchronous sliding mode control (SMC) issue for uncertain hidden Markovian jump systems under a constrained bit rate. An improved coding–decoding procedure with state-dependent adaptive quantization parameters is established to enable the controller to decode state and mode information from the system and the detector, respectively. Based on this procedure, a decoded-data-based asynchronous SMC strategy is provided, and sufficient conditions are developed to ensure that the closed-loop dynamics are exponentially ultimately bounded and the system state is driven onto a sliding region simultaneously in the sense of mean square. The desired parameters of the quantizer and controller are obtained by solving an optimization problem, in which the objective function is constructed by using the tradeoff between the ultimate state bound and the decay rate. Moreover, the integrative design of the bit rate allocation protocol and quantizer as well as control parameters are converted into a nonlinear programming problem with integer constraint, which is solved by means of an improved sparrow search algorithm. Finally, a direct current motor system is employed to illustrate the effectiveness of the present approach under three different cases.