Nonlinear Predictor Feedback for Input-Affine Systems with Distributed Input Delays
This work provides a theoretical framework for stabilizing a class of nonlinear systems with distributed delays, which is a known bottleneck in control theory.
The paper extends predictor feedback to control-affine systems with distributed input delays, proving exponential stability under global assumptions. The approach uses a prediction-based transformation and Lyapunov-Krasovskii theory to achieve stabilization.
Prediction-based transformation is applied to control-affine systems with distributed input delays. Transformed system state is calculated as a prediction of the system's future response to the past input with future input set to zero. Stabilization of the new system leads to Lyapunov-Krasovskii proven stabilization of the original one. Conditions on the original system are: smooth linearly bounded open-loop vector field and smooth uniformly bounded input vectors. About the transformed system which turns out to be affine in the undelayed input but with input vectors dependent on the input history and system state, we assume existence of a linearly bounded stabilizing feedback and quadratically bounded control-Lyapunov function. If all assumptions hold globally, then achieved exponential stability is global, otherwise local. Analytical and numerical control design examples are provided.