相关论文: Sparsity Preserving Optimal Control of Discretized…

In this work, we consider optimal control problems constrained by elliptic partial differential equations (PDEs) with lognormal random coefficients, which are represented by a countably infinite-dimensional random parameter with i.i.d.…

We present a method to solve fractional optimal control problems, where the dynamic depends on integer and Caputo fractional derivatives. Our approach consists to approximate the initial fractional order problem with a new one that involves…

This work introduces a new method to efficiently solve optimization problems constrained by partial differential equations (PDEs) with uncertain coefficients. The method leverages two sources of inexactness that trade accuracy for speed:…

We address the control of Partial Differential equations (PDEs) with unknown parameters. Our objective is to devise an efficient algorithm capable of both identifying and controlling the unknown system. We assume that the desired PDE is…

Reconstructing PDE solutions from sparse observations is a core challenge in scientific computing. We present FM4PDE, a flow-matching generative framework that learns the joint distribution of PDE coefficients (or initial states) and…

This work presents the solution to a class of decentralized linear quadratic state-feedback control problems, in which the plant and controller must satisfy the same combination of delay and sparsity constraints. Using a novel decomposition…

We deal with the problem of parameter estimation in stochastic differential equations (SDEs) in a partially observed framework. We aim to design a method working for both elliptic and hypoelliptic SDEs, the latters being characterized by…

Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…

We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…

This paper addresses the problem of steering the distribution of the state of a discrete-time linear system to a given target distribution while minimizing an entropy-regularized cost functional. This problem is called a maximum entropy…

We consider the task of designing sparse control laws for large-scale systems by directly minimizing an infinite horizon quadratic cost with an $\ell_1$ penalty on the feedback controller gains. Our focus is on an improved algorithm that…

In this paper, we discuss the distributed control problem governed by the following parabolic integro-differential equation (PIDE) in the abstract form \begin{eqnarray*} \frac{\partial y}{\partial t} + A y &=& \int_0^t B(t, s) y(s) ds + Gu,…

In this paper, we propose a model's sparse representation based on reduced mixed generalized multiscale finite element (GMsFE) basis methods for elliptic PDEs with random inputs. Mixed generalized multiscale finite element method (GMsFEM)…

The optimal stochastic control problem with a quadratic cost functional for linear partial differential equations (PDEs) driven by a state-and control-dependent white noise is formulated and studied. Both finite-and infinite-time horizons…

This paper considers the problem of finite dimensional output feedback H-infinity control for a class of nonlinear spatially distributed processes (SDPs) described by highly dissipative partial differential equations (PDEs), whose state is…

Propagation characteristics of a wave are defined by the dispersion relationship, from which the governing partial differential equation (PDE) can be recovered. PDEs are commonly solved numerically using the finite-difference (FD) method,…

Efficiently solving the Fokker-Planck equation (FPE) is crucial for understanding the probabilistic evolution of stochastic particles in dynamical systems, however, analytical solutions or density functions are only attainable in specific…

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

From a mathematical point of view self-organization can be described as patterns to which certain dynamical systems modeling social dynamics tend spontaneously to be attracted. In this paper we explore situations beyond self-organization,…

We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…