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This article provides a brief review of recent developments on two nonlocal operators: fractional Laplacian and fractional time derivative. We start by accounting for several applications of these operators in imaging science, geophysics,…
In this paper, we first prove that the mean-field stochastic linear quadratic (MFSLQ for short) control problem with random coefficients has a unique optimal control and derive a preliminary stochastic maximum principle to characterize this…
Efficient trajectory generation is crucial for autonomous systems; however, current numerical methods often struggle to handle periodic behaviors effectively, particularly when the onboard sensors require equidistant temporal sampling. This…
We address the solution of the distributed control problem for the steady, incompressible Navier--Stokes equations. We propose an inexact Newton linearization of the optimality conditions. Upon discretization by a finite element scheme, we…
We present an approach for solving optimal Dirichlet boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solution to the nonlinear wave model, we propose higher order…
In ergodic singular stochastic control problems, a decision-maker can instantaneously adjust the evolution of a state variable using a control of bounded variation, with the goal of minimizing a long-term average cost functional. The cost…
In this paper, we describe a constrained Lagrangian and Hamiltonian formalism for the optimal control of nonholonomic mechanical systems. In particular, we aim to minimize a cost functional, given initial and final conditions where the…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
We consider the Lagrange problem of optimal control with unrestricted controls and address the question: under what conditions we can assure optimal controls are bounded? This question is related to the one of Lipschitzian regularity of…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
Understanding the optimization landscape of linear quadratic regulation (LQR) problems is fundamental to the design of efficient reinforcement learning solutions. Recent work has made significant progress in characterizing the landscape of…
Motion planning for manipulators under task space constraints is difficult as it constrains the joint configurations to always lie on an implicitly defined manifold. It is possible to view task constrained motion planning as an optimization…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
This paper studies a class of continuous-time scalar-state stochastic Linear-Quadratic (LQ) optimal control problem with the linear control constraints. Applying the state separation theorem induced from its special structure, we develop…
In this paper we consider an optimal control problem in large time horizon and solve it numerically. More precisely, we are interested in an aerial vehicle guidance problem: launched from a ground platform, the vehicle aims at reaching a…
Optimal control is ubiquitous in many fields of engineering. A common technique to find candidate solutions is via Pontryagin's maximum principle. An unfortunate aspect of this method is that the dimension of system doubles. When the system…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an…
This article addresses the problem of data-driven numerical optimal control for unknown nonlinear systems. In our scenario, we suppose to have the possibility of performing multiple experiments (or simulations) on the system. Experiments…