Related papers: Operator learning for prescribed-time stabilizatio…
We study a class of regularized proximal operators in Wasserstein-2 space. We derive their solutions by kernel integration formulas. We obtain the Wasserstein proximal operator using a pair of forward-backward partial differential equations…
We develop a non-collocated, observer-based output-feedback law for a class of continua of linear hyperbolic PDE systems, which are viewed as the continuum version of $n+m$, general heterodirectional hyperbolic systems as $n\to\infty$. The…
We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be…
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…
Achieving rapid and time-deterministic stabilization for complex systems characterized by strong nonlinearities and parametric uncertainties presents a significant challenge. Traditional model-based control relies on precise system models,…
Identifying differential operators from data is essential for the mathematical modeling of complex physical and biological systems where massive datasets are available. These operators must be stable for accurate predictions for dynamics…
Accurate modeling of personalized cardiovascular dynamics is crucial for non-invasive monitoring and therapy planning. State-of-the-art physics-informed neural network (PINN) approaches employ deep, multi-branch architectures with…
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…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
We develop reinforcement learning (RL) boundary controllers to mitigate stop-and-go traffic congestion on a freeway segment. The traffic dynamics of the freeway segment are governed by a macroscopic Aw-Rascle-Zhang (ARZ) model, consisting…
This paper deals with the development and analysis of novel time-optimal point-to-point model predictive control concepts for nonlinear systems. Recent approaches in the literature apply a time transformation, however, which do not maintain…
The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…
Neural PDE solvers are often described as learning solution operators that map problem data to PDE solutions. In this work, we argue that this interpretation is generally incorrect when boundary conditions vary. We show that standard neural…
Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…
Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…
Time distributed optimization is an implementation strategy that can significantly reduce the computational burden of model predictive control by exploiting its robustness to incomplete optimization. When using this strategy, optimization…
This paper presents a control-oriented delay-based modeling approach for the exponential stabilization of a scalar neutral functional differential equation, which is then applied to the local exponential stabilization of a one-layer neural…
When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…