Related papers: Optimal control of variable-exponent subdiffusion

We consider the bilinear optimal control of an advection-reaction-diffusion system, where the control arises as the velocity field in the advection term. Such a problem is generally challenging from both theoretical analysis and algorithmic…

Diffusion-based planning, learning, and control methods present a promising branch of powerful and expressive decision-making solutions. Given the growing interest, such methods have undergone numerous refinements over the past years.…

This paper is concerned with data-driven optimal control of nonlinear systems. We present a convex formulation to the optimal control problem (OCP) with a discounted cost function. We consider OCP with both positive and negative discount…

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets.…

Stochastic maximum principle of nonlinear controlled forward-backward systems, where the set of strict (classical) controls need not be convex and the diffusion coefficient depends explicitly on the variable control, is an open problem…

Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challenge. As a consequence, we present a rigorous framework of…

We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the $p$-Laplacian operator. We establish existence and…

We consider the linear quadratic regulator (LQR) for one-dimensional linear evolution partial differential equations (PDEs) on a finite interval in space. The control is applied as an additive forcing term to PDEs. Existing methods for…

This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…

In this paper, we consider the optimal control problem for a class of evolution inclusions with Volterra type operators, which can be history-dependent. We establish the existence of a solution to the stated optimal control problem under…

We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…

Controllable diffusion generation often relies on various heuristics that are seemingly disconnected without a unified understanding. We bridge this gap with Diffusion Controller (DiffCon), a unified control-theoretic view that casts…

Spin squeezing serves as both a fundamental witness of quantum entanglement and a critical resource for quantum-enhanced metrology. While generating substantial spin squeezing in finite-range interacting systems remains challenging, such…

We prove convergence of the proximal policy gradient method for a class of constrained stochastic control problems with control in both the drift and diffusion of the state process. The problem requires either the running or terminal cost…

This paper deals with a stochastic recursive optimal control problem, where the diffusion coefficient depends on the control variable and the control domain is not necessarily convex. We focus on the connection between the general maximum…

We propose a two-scale neural network method for optimal control problems governed by convection-dominated convection-diffusion-reaction equations. Building on two-scale architectures developed for singularly perturbed forward problems, we…

Existing approaches to diffusion-based inverse problem solvers frame the signal recovery task as a probabilistic sampling episode, where the solution is drawn from the desired posterior distribution. This framework suffers from several…

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The…

Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms, a case that cannot easily be accommodated using…

In this paper, we study an optimal control problem for a coupled non-linear system of reaction-diffusion equations with degenerate diffusion, consisting of two partial differential equations representing the density of cells and the…