Related papers: Linear-quadratic optimal control for abstract diff…
It has been recently established that a deterministic infinite horizon discounted optimal control problem in discrete time is closely related to a certain infinite dimensional linear programming problem and its dual. In the present paper,…
In this paper, we study the irregular output feedback linear quadratic (LQ) control problem, which is a continuous work of previous works for irregular LQ control [33] where the state is assumed to be exactly known priori. Different from…
We consider a class of $\ell_0$-regularized linear-quadratic (LQ) optimal control problems. This class of problems is obtained by augmenting a penalizing sparsity measure to the cost objective of the standard linear-quadratic regulator…
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…
This paper investigates an infinite-horizon linear quadratic stochastic (LQS) optimal control problem for a class of continuous-time stochastic systems. By employing the technique of adaptive dynamic programming (ADP), we propose a novel…
In this paper, we consider the problem of distributed optimal control of linear dynamical systems with a quadratic cost criterion. We study the case of output feedback control for two interconnected dynamical systems, and show that the…
We study the exploration-exploitation dilemma in the linear quadratic regulator (LQR) setting. Inspired by the extended value iteration algorithm used in optimistic algorithms for finite MDPs, we propose to relax the optimistic optimization…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…
We analyze strict dissipativity of generalized linear quadratic optimal control problems on Hilbert spaces. Here, the term ``generalized'' refers to cost functions containing both quadratic and linear terms. We characterize strict…
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 extend the family of problems that may be implemented on an adiabatic quantum optimizer (AQO). When a quadratic optimization problem has at least one set of discrete controls and the constraints are linear, we call this a quadratic…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Current research suggests the use of a liner quadratic performance index for optimal control of regulators in various applications. Some examples include correcting the trajectory of rocket and air vehicles, vibration suppression 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…
This paper is concerned with a stochastic linear-quadratic (LQ) optimal control problem on infinite time horizon, with regime switching, random coefficients, and cone control constraint. To tackle the problem, two new extended stochastic…
In this paper, we present solvable, convex formulations of $H_2$-optimal state estimation and state-feedback control problems for a general class of linear Partial Differential Equations (PDEs) with one spatial dimension. These convex…
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…
In this article we study the optimal control problem with quadratic functionals for a linear Volterra integro-differential equation in Hilbert spaces. With the finite history seen as an (additional) initial datum for the evolution,…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…