Asynchronous Quantized Control of Piecewise-Affine Systems

This technical note proposes a novel asynchronous control approach for discrete-time piecewise-affine (PWA) systems with logarithmic quantization of both multiple inputs and multiple state measurements. Since the actual system state and the quantized state may not always be in the same operating region due to quantization-induced uncertainties, the operating modes of the PWA system and the controller that depends on the quantized states may be asynchronous. Aiming at reducing the computational cost and the conservatism of the results, a mapping region-based algorithm is first proposed to determine the reachable dwelling regions for the quantized state. By using a convex combination model to approximate the quantization-induced uncertainties, a novel piecewise Lyapunov function taking into consideration the uncertainties is then proposed. It is shown that with the newly proposed Lyapunov function, the desired asynchronous controller can be obtained and the resulting closed-loop system is asymptotically stable. A simulated chemical reactor example is presented to illustrate the effectiveness and the superiority of the proposed asynchronous control approach.