Predictor-feedback stabilization of two-input nonlinear systems with distinct and state-dependent input delays

Abstract

This paper deals with the predictor-feedback stabilization problem of two-input nonlinear systems with distinct and state-dependent input delays. Since each individual channel may induce a different delay, a sequential approach is employed for the construction of two predictors such that the corresponding input delays can be compensated. Concretely, the predictor over the prediction horizon which corresponds to the smaller input delay is first constructed, and the predictor over the remaining time horizon that corresponds to the larger input delay is in turn constructed, by utilizing the first predictor signal as a basis. The feedback controllers are given based on the predictors. Due to the inherent constraint on the rates of the state-dependent input delays, regional stability results are achieved. Specifically, if the system is forward-complete, for the closed-loop nonlinear system, an estimation of the region of attraction is provided, and for the linear system, the exponential stability is guaranteed. The methodology is applied to the bilateral boundary control problem of hyperbolic partial differential equations (PDEs) with a moving boundary, for illustration of the effectiveness of the methodology.