Related papers: Adaptive Neural-Operator Backstepping Control of a…
We develop a novel multi-layer predictor-feedback to achieve exact compensation of state-dependent input delay of general nonlinear integro-differential equations. The system of interest is an unconventional mixed Partial Differential…
Recent research shows that supervised learning can be an effective tool for designing near-optimal feedback controllers for high-dimensional nonlinear dynamic systems. But the behavior of neural network controllers is still not well…
Impulse-to-peak response (I2P) analysis for state-space ordinary differential equation (ODE) systems is a well-studied classical problem. However, the techniques employed for I2P optimal control of ODEs have not been extended to partial…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
Modelling complex multiphysics systems governed by nonlinear and strongly coupled partial differential equations (PDEs) is a cornerstone in computational science and engineering. However, it remains a formidable challenge for traditional…
It is nontrivial to achieve global zero-error regulation for uncertain nonlinear systems. The underlying problem becomes even more challenging if mismatched uncertainties and unknown time-varying control gain are involved, yet certain…
Classical discrete-time adaptive controllers provide asymptotic stabilization. While the original adaptive controllers did not handle noise or unmodelled dynamics well, redesigned versions were proven to have some tolerance; however,…
Neural operators have emerged as a promising paradigm for learning solution operators of partial differential equa- tions (PDEs) directly from data. Existing methods, such as those based on Fourier or graph techniques, make strong as-…
This work establishes the first rigorous stability guarantees for approximate predictors in delay-adaptive control of nonlinear systems, addressing a key challenge in practical implementations where exact predictors are unavailable. We…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a…
Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…
This work introduces a paradigm for constructing parametric neural operators that are derived from finite-dimensional representations of Green's operators for linear partial differential equations (PDEs). We refer to such neural operators…
Neural networks with a large number of parameters admit a mean-field description, which has recently served as a theoretical explanation for the favorable training properties of "overparameterized" models. In this regime, gradient descent…
The inherent approximation ability of neural networks plays an essential role in adaptive neural control, where the prerequisite for existence of the compact set is crucial in the control designs. Instead of using practical system state, in…
This article proposes a data-driven PID controller design based on the principle of adaptive gain optimization, leveraging Physics-Informed Neural Networks (PINNs) generated for predictive modeling purposes. The proposed control design…
This paper presents a safe delay-adaptive control for a strict-feedback nonlinear ODE with a delayed actuator, whose dynamic is also a strict-feedback nonlinear ODE and the delay length is unknown. By formulating the delay as a transport…
We consider the use of Gaussian Processes (GPs) or Neural Networks (NNs) to numerically approximate the solutions to nonlinear partial differential equations (PDEs) with rough forcing or source terms, which commonly arise as pathwise…
This paper addresses the problem of optimal robust stabilization of a discrete-time minimum-phase plant in the framework of robust control theory in the $\ell_1$ setup and under poor a priori information. Coefficients of the transfer…
In this paper, a backstepping control of the one-phase Stefan Problem, which is a 1-D diffusion Partial Differential Equation (PDE) defined on a time varying spatial domain described by an ordinary differential equation (ODE), is studied. A…