Delay compensation of multi-input distinct delay nonlinear systems via neural operators
This addresses stability challenges in control systems with delays, which is incremental as it extends existing predictor methods to multi-input nonlinear cases with distinct delays.
The paper tackles the problem of stabilizing multi-input nonlinear systems with distinct actuation delays by developing stability results for approximate predictors, showing that semi-global practical stability is achieved if the predictor approximation has a uniform error bound. It demonstrates this theoretically and in simulation on a mobile robot experiment using neural operators.
In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound, semi-global practical stability is correspondingly achieved. For such approximators, the required uniform error bound depends on the desired region of attraction and the number of control inputs in the system. The result is achieved through transforming the delay into a transport PDE and conducting analysis on the coupled ODE-PDE cascade. To highlight the viability of such error bounds, we demonstrate our results on a class of approximators - neural operators - showcasing sufficiency for satisfying such a universal bound both theoretically and in simulation on a mobile robot experiment.