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This paper investigates a new class of homogeneous stochastic control problems with cone control constraints, extending the classical homogeneous stochastic linear-quadratic (LQ) framework to encompass nonlinear system dynamics and…

Optimization and Control · Mathematics 2025-07-30 Ying Hu , Xiaomin Shi , Zuo Quan Xu

We consider a variant of the classical linear quadratic Gaussian regulator (LQG) in which penalties on the endpoint state are replaced by the specification of the terminal state distribution. The resulting theory considerably differs from…

Optimization and Control · Mathematics 2015-03-18 Yongxin Chen , Tryphon Georgiou , Michele Pavon

This paper is concerned with the linear quadratic optimal control of discrete-time time-varying system with terminal state constraint. The main contribution is to propose a Q-learning algorithm for the optimal controller when the…

Optimization and Control · Mathematics 2023-07-20 Juanjuan Xu , Jingmei Liu , Zhaorong Zhang , Wei Wang

We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…

Optimization and Control · Mathematics 2024-12-12 Marc Lambert , Francis Bach , Silvère Bonnabel

We consider a general linear control system and a general quadratic cost, where the state evolves continuously in time and the control is sampled, i.e., is piecewise constant over a subdivision of the time interval. This is the framework of…

Optimization and Control · Mathematics 2016-04-22 Loïc Bourdin , Emmanuel Trélat

In this work we investigate explicit and implicit difference equations and the corresponding infinite time horizon linear-quadratic optimal control problem. We derive conditions for feasibility of the optimal control problem as well as…

Optimization and Control · Mathematics 2017-10-30 Daniel Bankmann , Matthias Voigt

In standard linear quadratic (LQ) control, the first step in investigating infinite-horizon optimal control is to derive the stabilization condition with the optimal LQ controller. This paper focuses on the stabilization of an Ito…

Optimization and Control · Mathematics 2019-08-22 Hongdan Li , Qingyuan Qi , Huanshui Zhang

We consider policy gradient algorithms for the indefinite least squares stationary optimal control, e.g., linear-quadratic-regulator (LQR) with indefinite state and input penalization matrices. Such a setup has important applications in…

Optimization and Control · Mathematics 2020-02-13 Jingjing Bu , Mehran Mesbahi

In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…

Optimization and Control · Mathematics 2017-03-07 Xun Li , Yuan-Hua Ni , Ji-Feng Zhang

We here consider optimal control problems governed by nonlinear stochastic equations on a Hilbert space H with nonconvex payoff, which is rewritten as a deterministic optimal control problem governed by a Kolmogorov equation in H. We prove…

Probability · Mathematics 2019-12-16 Viorel Barbu , Michael Röckner , Deng Zhang

An optimal ergodic control problem (EC problem, for short) is investigated for a linear stochastic differential equation with quadratic cost functional. Constant nonhomogeneous terms, not all zero, appear in the state equation, which lead…

Optimization and Control · Mathematics 2020-04-24 Hongwei Mei , Qingmeng Wei , Jiongmin Yong

We consider a class of stochastic control problems with a delayed control, both in drift and diffusion, of the type dX t = $\alpha$ t--d (bdt + $\sigma$dW t). We provide a new characterization of the solution in terms of a set of Riccati…

Optimization and Control · Mathematics 2021-02-25 William Lefebvre , Enzo Miller

Stochastic algebraic Riccati equations, also known as rational algebraic Riccati equations, arising in linear-quadratic optimal control for stochastic linear time-invariant systems, were considered to be not easy to solve. The-state-of-art…

Optimization and Control · Mathematics 2024-03-06 Zhen-Chen Guo , Xin Liang

The present work addresses a finite-horizon linear-quadratic optimal control problem for uncertain systems driven by piecewise constant controls. The precise values of the system parameters are unknown, but assumed to belong to a finite set…

Systems and Control · Computer Science 2021-08-05 Félix A. Miranda , Fernando Castaños , Alexander Poznyak

We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon pro\-blems, and allow notably some coefficients to be stochastic. Extension to…

Probability · Mathematics 2018-10-26 Matteo Basei , Huyên Pham

This paper is concerned with the deterministic optimal control of Ito stochastic systems with random coefficients. The necessary and sufficient conditions for the unique solvability of the optimal control problem with random coefficients…

Optimization and Control · Mathematics 2019-03-05 Hongdan Li , Juanjuan Xu , Huanshui Zhang

We study a linear-quadratic, optimal control problem on a discrete, finite time horizon with distributional ambiguity, in which the cost is assessed via Conditional Value-at-Risk (CVaR). We take steps toward deriving a scalable dynamic…

Systems and Control · Electrical Eng. & Systems 2022-06-28 Margaret P. Chapman , Laurent Lessard

This paper deals with the long time behavior of the optimal solution of stochastic backward linear-quadratic optimal control problem over the finite time horizon. Both weak and strong turnpike properties are established under appropriate…

Optimization and Control · Mathematics 2023-09-08 Yuyang Chen , Peng Luo

A promising method for constructing a data-driven output-feedback control law involves the construction of a model-free observer. The Linear Quadratic Regulator (LQR) optimal control policy can then be obtained by both policy-iteration (PI)…

Optimization and Control · Mathematics 2025-09-24 Liquan Lin , Haoyan Lin , Jie Huang

This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…

Optimization and Control · Mathematics 2017-11-01 Shaolin Ji , Xiaole Xue