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This paper addresses the problem of solving a class of nonlinear optimal control problems (OCP) with infinite-dimensional linear state constraints involving Riesz-spectral operators. Each instance within this class has time/control…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
We are interested in optimally controlling a discrete time dynamical system that can be influenced by exogenous uncertainties. This is generally called a Stochas-tic Optimal Control (SOC) problem and the Dynamic Programming (DP) principle…
This article introduces a novel distributionally robust model predictive control (DRMPC) algorithm for a specific class of controlled dynamical systems where the disturbance multiplies the state and control variables. These classes of…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
Sequential-in-time methods solve a sequence of training problems to fit nonlinear parametrizations such as neural networks to approximate solution trajectories of partial differential equations over time. This work shows that…
In this paper, we design a controller for an interconnected system consisting of a linear Stochastic Differential Equation (SDE) actuated through a linear hyperbolic Partial Differential Equation (PDE). Our approach aims to minimize the…
We study an optimal control problem on infinite time horizon with semimartingale strategies, random coefficients and regime switching. The value function and the optimal strategy can be characterized in terms of three systems of backward…
Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input…
We propose two novel numerical schemes for approximate implementation of the dynamic programming~(DP) operation concerned with finite-horizon, optimal control of discrete-time systems with input-affine dynamics. The proposed algorithms…
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the sweeping type with involving variable time into optimization. We…
In this paper, near optimal tracking of a class of nonlinear systems is addressed. Adaptive (approximate) dynamic programming approach is used to calculate the optimal control in closed form. ADP (Adaptive (approximate) dynamic programming)…
We consider an optimal control problem constrained by a parabolic partial differential equation (PDE) with Robin boundary conditions. We use a well-posed space-time variational formulation in Lebesgue--Bochner spaces with minimal…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
A recent line of work in the machine learning community addresses the problem of predicting high-dimensional spatiotemporal phenomena by leveraging specific tools from the differential equations theory. Following this direction, we propose…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
There has been widespread interest in the use of grid-level storage to handle the variability from increasing penetrations of wind and solar energy. This problem setting requires optimizing energy storage and release decisions for anywhere…
Sequential Convex Programming (SCP) has recently gained significant popularity as an effective method for solving optimal control problems and has been successfully applied in several different domains. However, the theoretical analysis of…