Related papers: Adaptive Neural-Operator Backstepping Control of a…
Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…
Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known…
Neural operators (NOs) provide a new paradigm for efficiently solving partial differential equations (PDEs), but their training depends on costly high-fidelity data from numerical solvers, limiting applications in complex systems. We…
A novel method of exponentially stable adaptive control to compensate for matched parametric uncertainty under a mild condition of semi-persistent excitation (s-PE) of a regressor with piecewise-constant rank and nullspace is proposed. It…
In this work, we consider the adaptive nonlinear control problem for strict feedback nonlinear systems, where the functions that determine the dynamics of the system are completely unknown. We assume that certain upper bounds for the…
We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…
In this paper, we present a novel control scheme for feedback optimization. That is, we propose a discrete-time controller that can steer the steady state of a physical plant to the solution of a constrained optimization problem without…
This paper is concerned with the output feedback boundary stabilization of general 1-D reaction diffusion PDEs in the presence of an arbitrarily large input delay. We consider the cases of Dirichlet/Neumann/Robin boundary conditions for the…
We study the backstepping stabilization of higher order linear and nonlinear Schr\"odinger equations on a finite interval, where the boundary feedback acts from the left Dirichlet boundary condition. The plant is stabilized with a…
This paper deals with the trajectory tracking control problem for a class of bilinear systems with unmeasurable states and unknown parameters. Firstly, a full-information controller is suggested that guarantees global tracking under a…
Adaptive methods are popular within the control literature due to the flexibility and forgiveness they offer in the area of modelling. Neural network adaptive control is favorable specifically for the powerful nature of the machine learning…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
We present a data-driven control framework for partial differential equations (PDEs). Our approach integrates Time-Integrated Deep Operator Networks (TI-DeepONets) as differentiable PDE surrogate models within the Differentiable Predictive…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Modern automation systems rely on closed loop control, wherein a controller interacts with a controlled process, based on observations. These systems are increasingly complex, yet most controllers are linear Proportional-Integral-Derivative…
We present an adaptive event-triggered boundary control scheme for a parabolic PDE-ODE system, where the reaction coefficient of the parabolic PDE, and the system parameter of a scalar ODE, are unknown. In the proposed controller, the…
Control of distributed parameter systems affected by delays is a challenging task, particularly when the delays depend on spatial variables. The idea of integrating analytical control theory with learning-based control within a unified…
Neural operators are a popular technique in scientific machine learning to learn a mathematical model of the behavior of unknown physical systems from data. Neural operators are especially useful to learn solution operators associated with…
In this work, stabilization of an axonal growth in a neuron associated with the dynamics of tubulin concentration is proposed by designing a boundary control. The dynamics are given by a parabolic Partial Differential Equation (PDE) of the…
Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of…