Optimal Adaptive Controller Scheme for Uncertain Quantized Linear Discrete-time System

In this paper, the Bellman equation is used to solve the optimal adaptive control of quantized linear discrete-time system with unknown dynamics. To mitigate the effect of the quantization errors, the dynamics of the quantization error bound and an update law for tuning the range of the dynamic quantizer are derived. Subsequently, by using adaptive dynamic programming technique, the infinite horizon optimal regulation problem of the uncertain quantized linear discrete-time system is solved in a forward-in-time manner without using value and/or policy iterations. The asymptotic stability of the closed-loop system is verified by standard Lyapunov stability approach in the presence of state and input quantizers. The effectiveness of the proposed method is verified via simulation.