Related papers: On Riccati contraction in time-varying linear-quad…
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the…
This paper is devoted to analysing the explicit slow decay rate and turnpike in the infinite-horizon linear quadratic optimal control problems for hyperbolic systems. Assume that some weak observability or controllability are satisfied, by…
In this paper, we concern with the ergodic linear-quadratic closed-loop optimal control problems with random periodic coefficients. We put forward the random periodic mean-square exponentially stable condition, and prove the random…
We establish existence and uniqueness for infinite dimensional Riccati equations taking values in the Banach space L 1 ($\mu$ $\otimes$ $\mu$) for certain signed matrix measures $\mu$ which are not necessarily finite. Such equations can be…
Inspired by REINFORCE, we introduce a novel receding-horizon algorithm for the Linear Quadratic Regulator (LQR) problem with unknown dynamics. Unlike prior methods, our algorithm avoids reliance on two-point gradient estimates while…
Linear-quadratic optimal control problem for systems governed by forward-backward stochastic differential equations has been extensively studied over the past three decades. Recent research has revealed that for forward-backward control…
System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback…
We consider the Linear Quadratic Regulation for the boundary control of the one dimensional linear wave equation under both Dirichlet and Neumann activation. For each activation we present a Riccati partial differential equation that we…
This paper investigates the properties of the solutions of the generalised discrete algebraic Riccati equation arising from the solution of the classic infinite-horizon linear quadratic control problem. In particular, a geometric analysis…
We consider the application of the theory of vibrational control to H_infinity-problems. We study the possibility of introduction of high-frequency parametric vibrations in order to decrease the minimal attainable value of the…
The paper establishes the exponential turnpike property for a class of mean-field stochastic linear-quadratic (LQ) optimal control problems with periodic coefficients. It first introduces the concepts of stability, stabilizability, and…
In this paper, we construct a periodic dichotomy transformation using solutions of periodic Riccati and Lyapunov equations. As an application of this transformation, we provide an explicit representation of the optimal extremal for periodic…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
In the present note we discuss in details the Riemann problem for a one--dimensional hyperbolic conservation law subject to a point constraint. We investigate how the regularity of the constraint operator impacts the well--posedness of the…
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 optimal control problems for a linear homogeneous stochastic differential equation having regime switching with purely quadratic functional in the large time horizons. We establish the so-called turnpike…
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…
This paper considers an optimal control problem for a linear mean-field stochastic differential equation having regime switching with quadratic functional in the large time horizons. Our main contribution lies in establishing the strong…
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of…
We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new…