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In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are…
We address optimal control problems on the space of measures for an objective containing a smooth functional and an optimal transport regularization. That is, the quadratic Monge-Kantorovich distance between a given prior measure and the…
We consider nonsmooth optimal control problems subject to a linear elliptic partial differential equation with homogeneous Dirichlet boundary conditions. It is well-known that local solutions satisfy the celebrated Pontryagin maximum…
Model predictive control offers a powerful framework for managing constrained systems, but its repeated online optimization can become computationally prohibitive. Multiparametric programming addresses this challenge by precomputing optimal…
An optimal guidance law for impact time control with field-of-view constraint is presented. The guidance law is derived by first converting the inequality-constrained nonlinear optimal control problem into an equality-constrained one…
This paper is a survey on some recent aspects and developments in stochastic control. We discuss the two main historical approaches, Bellman's optimality principle and Pontryagin's maximum principle, and their modern exposition with…
We consider an optimal control problem subject to the thin-film equation which is deduced from the Navier--Stokes equation. The PDE constraint lacks well-posedness for general right-hand sides due to possible degeneracies; state constraints…
We derive the explicit solution of the problem of time-optimal control by a common magnetic fields for two independent spin-$\frac{1}{2}$ particles. Our approach is based on the Pontryagin Maximum Principle and a novel symmetry reduction…
We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of…
We discuss a mathematical framework for analysis of optimal control problems on infinite-dimensional manifolds. Such problems arise in study of optimization for partial differential equations with some symmetry. It is shown that some…
In this article we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss-Newton method…
Motivated by the control of invasive biological populations, we consider a class of optimization problems for moving sets $t\mapsto \Omega(t)\subset\mathbb{R}^2$. Given an initial set $\Omega_0$, the goal is to minimize the area of the…
In this paper, we study a class of fractional optimal control problems. A necessary condition for the existence of an optimal control is provided in the literature. It is commonly given as the existence of a solution of a fractional…
In this paper we give a new approach to introduce switching strategies in a special class of optimal multiprocesses. Defined as the set of partitions of the time interval, switching strategies become the character of a classical control.…
This paper aims to address the nonlinear optimal guidance problem with impact-time and impact-angle constraints, which is fundamentally important for multiple pursuers to collaboratively achieve a target. Addressing such a guidance problem…
The paper addresses an optimal ensemble control problem for nonlocal continuity equations on the space of probability measures. We admit the general nonlinear cost functional, and an option to directly control the nonlocal terms of the…
Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal…
Fractional optimal control problems via a wide class of fractional operators with a general analytic kernel are introduced. Necessary optimality conditions of Pontryagin type for the considered problem are obtained after proving a Gronwall…
We study an explicit mirror-descent method for finite-horizon deterministic optimal control problems. The method is motivated by Pontryagin's maximum principle: at each iteration, one solves the state and adjoint equations and updates the…
This paper concerns some time optimal control problems of three different ordinary differential equations in $\mathbb{R}^2$. Corresponding to certain initial data and controls, the solutions of the systems quench at finite time. The goal to…