Delay-adaptive Control of Nonlinear Systems with Approximate Neural Operator Predictors
This work addresses actuator delay issues in control systems, offering a practical solution with significant performance improvements, though it builds on existing neural operator methods.
The paper tackles the problem of controlling nonlinear systems with unknown, long actuator delays by approximating the predictor with a neural operator, achieving a 15x speedup over traditional methods in a biological system.
In this work, we propose a rigorous method for implementing predictor feedback controllers in nonlinear systems with unknown and arbitrarily long actuator delays. To address the analytically intractable nature of the predictor, we approximate it using a learned neural operator mapping. This mapping is trained once, offline, and then deployed online, leveraging the fast inference capabilities of neural networks. We provide a theoretical stability analysis based on the universal approximation theorem of neural operators and the transport partial differential equation (PDE) representation of the delay. We then prove, via a Lyapunov-Krasovskii functional, semi-global practical convergence of the dynamical system dependent on the approximation error of the predictor and delay bounds. Finally, we validate our theoretical results using a biological activator/repressor system, demonstrating speedups of 15 times compared to traditional numerical methods.