Adaptive quantized control for linear uncertain discrete-time systems

A direct adaptive control framework for linear uncertain systems for using communication channels is developed. Specifically, the control signals are to be quantized and sent over a communication channel to the actuator. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability, that is, Lyapunov stability of the closed-loop system states and attraction with respect to the plant states. The quantizers are logarithmic and characterized by sector-bound conditions, with the conic sectors adjusted at each time instant by the adaptive controller, in conjunction with the system response. Furthermore, we extend the scheme to the case where the logarithmic quantizer has a deadzone around the origin so that only a finite number of quantization levels is required to achieve practical stability. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.