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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…
We consider the linear quadratic (LQ) optimal control problem for a class of evolution equations in infinite dimensions, in the presence of distributed and nonlocal inputs. Following the perspective taken in our previous research work on…
This article presents a method to automatically generate energy-optimal trajectories for systems with linear dynamics, linear constraints, and a quadratic cost functional (LQ systems). First, using recent advancements in optimal control, we…
We adopt the integral definition of the fractional Laplace operator and analyze an optimal control problem for a fractional semilinear elliptic partial differential equation (PDE); control constraints are also considered. We establish the…
In this paper, an extension of a linear control design for hyperbolic linear partial differential equations is presented for a first-order traffic flow model. Starting from the Lighthill-Whitham-Richards (LWR) model, variable speed limit…
We study the infinite horizon Linear-Quadratic problem and the associated algebraic Riccati equations for systems with unbounded control actions. The operator-theoretic context is motivated by composite systems of Partial Differential…
We study the Linear-Quadratic optimal control problem for a general class of infinite-dimensional passive systems, allowing for unbounded input and output operators. We show that under mild assumptions, the finite cost condition is always…
Necessary optimality conditions and numerical methods for solving an optimal control problem for a linear continuous-time dynanical system with controlled coefficients and quadratic goal functional are discussed.
An optimal control problem for semilinear parabolic partial differential equations is considered. The control variable appears in the leading term of the equation. Necessary conditions for optimal controls are established by the method of…
This paper is concerned with a linear-quadratic (LQ) leader-follower differential game with mixed deterministic and stochastic controls. In the game, the follower is a random controller which means that the follower can choose adapted…
We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness…
A linear quadratic (LQ) stochastic optimization system involving large population, which is driven by forward-backward stochastic differential equation (FBSDE), is investigated in this paper. Agents cooperate with each other to minimize the…
A solution to the suboptimal $H^\infty$-control problem is given for a class of hyperbolic partial differential equations (PDEs). The first result of this manuscript shows that the considered class of PDEs admits an equivalent…
We present an analysis and numerical study of an optimal control problem for the Landau-de Gennes (LdG) model of nematic liquid crystals (LCs), which is a crucial component in modern technology. They exhibit long range orientational order…
This paper studies uniform stabilization and social optimality for linear quadratic (LQ) mean field control problems with multiplicative noise, where agents are coupled via dynamics and individual costs. The state and control weights in…
We develop a delay-adaptive controller for a class of first-order hyperbolic partial integro-differential equations (PIDEs) with an unknown input delay. By employing a transport PDE to represent delayed actuator states, the system is…
We study linear-quadratic stochastic optimal control problems with bilinear state dependence for which the underlying stochastic differential equation (SDE) consists of slow and fast degrees of freedom. We show that, in the same way in…
We consider a linear-quadratic pde constrained optimal control problem on an evolving surface with pointwise state constraints. We reformulate the optimization problem on a fixed surface and approximate the reformulated problem by a…
This work is concerned with a class of optimal control problems governed by a partial differential equation that are motivated by an application in radiotherapy treatment planning, where the primary design objective is to minimize the…
This work studies the null controllability of a system of coupled parabolic PDEs. In particular, our work specializes to an important subclass of these control problems which are coupled by first and zero-order couplings and are,…