Related papers: Time-inconsistent Linear Quadratic Optimal Control…
In this paper, we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional, with two controllers-one can choose only deterministic time functions, called the deterministic controller, while the other…
A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE) which is a matrix-valued quadratic backward…
This paper is concerned with a stochastic linear quadratic (LQ, for short) optimal control problem. The notions of open-loop and closed-loop solvabilities are introduced. A simple example shows that these two solvabilities are different.…
A general time-inconsistent optimal control problem is considered for stochastic differential equations with deterministic coefficients. Under suitable conditions, a Hamilton-Jacobi-Bellman type equation is derived for the equilibrium value…
This article explores the discrete-time stochastic optimal LQR control with delay and quadratic constraints. The inclusion of delay, compared to delay-free optimal LQR control with quadratic constraints, significantly increases the…
It is a longstanding unsolved problem to characterize the optimal feedbacks for general SLQs (i.e., stochastic linear quadratic control problems) with random coefficients in infinite dimensions; while the same problem but in finite…
In this paper, we concern with the ergodic linear-quadratic closed-loop optimal control problems, in which the state equation is the mean-field stochastic differential equation with periodic coefficients. We first study the asymptotic…
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 performance of the certainty equivalent controller on Linear Quadratic (LQ) control problems with unknown transition dynamics. We show that for both the fully and partially observed settings, the sub-optimality gap between the…
This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the…
This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing L\'evy process. We provide dynamic programming…
We present high order explicit geometric integrators to solve linear-quadratic optimal control problems and $N$-player differential games. These problems are described by a system coupled non-linear differential equations with boundary…
This paper is concerned with the linear quadratic optimal control problem for networked system simultaneously with input delay and Markovian dropout. Different from the results in the literature, we consider the hold-input strategy, which…
Optimal control deals with optimization problems in which variables steer a dynamical system, and its outcome contributes to the objective function. Two classical approaches to solving these problems are Dynamic Programming and the…
This paper studies a discrete-time stochastic control problem with linear quadratic criteria over an infinite-time horizon. We focus on a class of control systems whose system matrices are associated with random parameters involving unknown…
Linear-Quadratic (LQ) problems that arise in systems and controls include the classical optimal control problems of the Linear Quadratic Regulator (LQR) in both its deterministic and stochastic forms, as well as $H^\infty$-analysis (the…
In this paper we study the quadratic regulator problem for a process governed by a Volterra integral equation in ${\mathbb R}^n$. Our main goal is the proof that it is possible to associate a Riccati differential equation to this quadratic…
A method is presented for solving the discrete-time finite-horizon Linear Quadratic Regulator (LQR) problem subject to auxiliary linear equality constraints, such as fixed end-point constraints. The method explicitly determines an affine…
This paper addresses the challenge of time-inconsistent stochastic control within a continuous-time framework. Its primary focus lies in uncovering a probabilistic representation, specifically in the shape of a system of backward stochastic…
We consider the linear quadratic Gaussian control problem with a discounted cost functional for descriptor systems on the infinite time horizon. Based on recent results from the deterministic framework, we characterize the feasibility of…