Related papers: Adaptive control of reaction-diffusion PDEs via ne…

Deep Neural Networks (DNNs) are increasingly used in control applications due to their powerful function approximation capabilities. However, many existing formulations focus primarily on tracking error convergence, often neglecting the…

Diffusion models have recently shown promise in offline RL. However, these methods often suffer from high training costs and slow convergence, particularly when using transformer-based denoising backbones. While several optimization…

Physics-informed neural networks (PINNs) have recently become a popular method for solving forward and inverse problems governed by partial differential equations (PDEs). By incorporating the residual of the PDE into the loss function of a…

Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with…

This paper deals with the tracking control problem for a class of unknown pure feedback system with pure state constraints on the state variables and unknown time-varying bounded disturbances. An adaptive controller is presented for such…

Quantum state engineering is a central task in Lyapunov-based quantum control. Given different initial states, better performance may be achieved if the control parameters, such as the Lyapunov function, are individually optimized for each…

Physical laws, such as the conversation of mass and momentum, are fundamental principles in many physical systems. Neural operators have achieved promising performance in learning the solutions to those systems, but often fail to ensure…

In the development of model predictive controllers for PDE-constrained problems, the use of reduced order models is essential to enable real-time applicability. Besides local linearization approaches, Proper Orthogonal Decomposition (POD)…

Recently, the problem of boundary stabilization and estimation for unstable linear constant-coefficient reaction-diffusion equation on n-balls (in particular, disks and spheres) has been solved by means of the backstepping method. However,…

For general nonlinear control systems we present a novel approach to adaptive control, which employs a certainty equivalence (indirect) control law and an identifier with event-triggered updates of the plant parameter estimates, where 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…

The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…

We propose a PDE-based accelerated gradient algorithm for optimal feedback controls of McKean-Vlasov dynamics that involve mean-field interactions both in the state and action. The method exploits a forward-backward splitting approach and…

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…

Deep learning has been proposed as an efficient alternative for the numerical approximation of PDE solutions, offering fast, iterative simulation of PDEs through the approximation of solution operators. However, deep learning solutions have…

Since the first optimality proofs for adaptive mesh refinement algorithms in the early 2000s, the theory of optimal mesh refinement for PDEs was inherently limited to stationary problems. The reason for this is that time-dependent problems…

This paper presents a PDE-based auto-aggregation model for simulating descriptive norm dynamics in autonomous multi-agent systems, capturing convergence and violation through non-local perception kernels and external potential fields.…

Convolutional neural networks (CNNs) are commonly used for image classification tasks, raising the challenge of their application on data flows. During their training, adaptation is often performed by tuning the learning rate. Usual…

This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify…

PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…