Related papers: Numerical optimal control for delay differential e…
In this paper, we solve an open problem and obtain a general maximum principle for a stochastic optimal control problem where the control domain is an arbitrary non-empty set and all the coefficients (especially the diffusion term and the…
The control schemes of distributed energy resources (DERs) in active distribution networks (ADNs) are largely influenced by uncertainties. The uncertainties of DERs are complicated, containing spatial and temporal correlation, which makes…
This paper presents an optimal dynamic control framework for bounded Jacobian nonlinear discrete-time (DT) systems with nonlinear observations affected by both state and process noise. Rather than directly stabilizing the uncertain system,…
We consider a class of optimal control problems of stochastic delay differential equations (SDDE) that arise in connection with optimal advertising under uncertainty for the introduction of a new product to the market, generalizing…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
Ordinary Differential Equations are a simple but powerful framework for modeling complex systems. Parameter estimation from times series can be done by Nonlinear Least Squares (or other classical approaches), but this can give…
Control of the stochastic dynamics of a quantum system is indispensable in fields such as quantum information processing and metrology. However, there is no general ready-made approach to the design of efficient control strategies. Here, we…
The purpose of this work is the development of space-time discretization schemes for phase-field optimal control problems. First, a time discretization of the forward problem is derived using a discontinuous Galerkin formulation. Here, a…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
We prove a sufficient optimality condition for non-linear optimal control problems with delays in both state and control variables. Our result requires the verification of a Hamilton-Jacobi partial differential equation and is obtained…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
In this paper, we consider a discrete-time stochastic control problem with uncertain initial and target states. We first discuss the connection between optimal transport and stochastic control problems of this form. Next, we formulate a…
We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…
We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…
We propose a novel Galerkin discretization scheme for stochastic optimal control problems on an indefinite time horizon. The control problems are linear-quadratic in the controls, but possibly nonlinear in the state variables, and the…
In this paper we study the approximate controllability and existence of optimal control of impulsive fractional semilinear delay differential equations with non-local conditions. We use Sadovskii's fixed point theorem, semigroup theory of…
Neural ordinary differential equations (Neural ODEs) is a class of machine learning models that approximate the time derivative of hidden states using a neural network. They are powerful tools for modeling continuous-time dynamical systems,…
In this paper, we introduce a novel approach to solve the (mean-covariance) steering problem for a fairly general class of linear continuous-time stochastic systems subject to input delays. Specifically, we aim at steering delayed linear…
This paper develops the time-delay approach to Networked Control Systems (NCSs) in the presence of variable transmission delays, sampling intervals and communication constraints. The system sensor nodes are supposed to be distributed over a…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…