Switched predictor feedbacks for reaction–diffusion PDEs and globally Lipschitz non-linear ODE systems subject to almost state and input quantization

We develop switched predictor-feedback control laws to achieve global asymptotic stabilization for both finite-dimensional non-linear systems and infinite-dimensional reaction–diffusion partial differential equations (PDEs) subject to input delay and almost state quantization. The proposed approach generalizes the predictor-feedback framework, for non-linear systems and reaction diffusion PDEs, introduced by Krstic in the seminal papers Krstic (2009a, Systems Control Lett., 58, 773–82) and Krstic (2009b, IEEE Trans. Autom. Control, 55, 287–303), by incorporating quantized measurements of the plant and actuator states into the predictor state formulation. To address constraints imposed by quantization, we introduce a dynamic switching strategy that adjusts the quantizer’s range in a piecewise constant manner—initially capturing large states and subsequently refining precision to reduce quantization error. Stability of the closed-loop systems is established using backstepping transformations combined with small-gain and input-to-state stability arguments. The developed results are further extended to account for almost input quantization, for both non-linear ordinary differential equation and reaction–diffusion PDE systems with input delay.