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We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The…

Machine Learning · Computer Science 2019-06-21 Francis Bach

A discrete-time stochastic LQ problem with multiplicative noises and state transmission delay is studied in this paper, which does not require any definiteness constraint on the cost weighting matrices. From some abstract representations of…

Optimization and Control · Mathematics 2017-05-30 Yuan-Hua Ni , Cedric Ka-Fai Yiu , Huanshui Zhang , Ji-Feng Zhang

In this paper we consider a class of conjugate discrete-time Riccati equations, arising originally from the linear quadratic regulation problem for discrete-time antilinear systems. Under some mild assumptions and the framework of the…

Numerical Analysis · Mathematics 2022-05-31 Hung-Yuan Fan , Chun-Yueh Chiang

We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full probability. Under such a partial terminal…

Optimization and Control · Mathematics 2017-11-15 Peter Bank , Moritz Voß

A fundamental theory of deterministic linear-quadratic (LQ) control is the equivalent relationship between control problems, two-point boundary value problems and Riccati equations. In this paper, we extend the equivalence to a general…

Mathematical Finance · Quantitative Finance 2021-10-13 Hongyan Cai , Danhong Chen , Yunfei Peng , Wei Wei

We present a methodology for obtaining explicit solutions to infinite time horizon optimal stopping problems involving general, one-dimensional, It\^o diffusions, payoff functions that need not be smooth and state-dependent discounting.…

Computational Finance · Quantitative Finance 2012-10-10 Timothy C. Johnson

We study unconstrained and constrained linear quadratic problems and investigate the suboptimality of the model predictive control (MPC) method applied to such problems. Considering MPC as an approximate scheme for solving the related fixed…

Optimization and Control · Mathematics 2023-06-06 Yuchao Li , Aren Karapetyan , John Lygeros , Karl H. Johansson , Jonas Mårtensson

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…

Numerical Analysis · Mathematics 2013-11-06 Sergio Blanes

In this paper, we consider the inverse optimal control problem for the discrete-time linear quadratic regulator, over finite-time horizons. Given observations of the optimal trajectories, and optimal control inputs, to a linear…

Optimization and Control · Mathematics 2018-10-31 Han Zhang , Jack Umenberger , Xiaoming Hu

A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in…

Optimization and Control · Mathematics 2022-03-01 Jingrui Sun , Jiaqiang Wen , Jie Xiong

We propose a new algorithm for a broad class of periodic time-varying Stochastic Game-Theoretic Riccati Differential Equations arising in Zero-Sum Linear-Quadratic Stochastic Differential Games. The algorithm is constructed via dual-layer…

Numerical Analysis · Mathematics 2025-11-06 Yiyuan Wang

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost functional. The coefficients and the weighting matrices in the cost functional are all assumed to be deterministic.…

Optimization and Control · Mathematics 2016-02-26 Xun Li , Jingrui Sun , Jiongmin Yong

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…

Optimization and Control · Mathematics 2012-04-18 Ather Gattami , Omid Khorsand

This paper is concerned with a backward stochastic linear-quadratic (LQ, for short) optimal control problem with deterministic coefficients. The weighting matrices are allowed to be indefinite, and cross-product terms in the control and…

Optimization and Control · Mathematics 2021-04-13 Jingrui Sun , Zhen Wu , Jie Xiong

A new approach to solving two-point boundary value problems for a wave equation is developed. This new approach exploits the principle of stationary action to reformulate and solve such problems in the framework of optimal control. In…

Optimization and Control · Mathematics 2017-11-13 Peter M. Dower , William M. McEneaney

This paper is concerned with the linear quadratic (LQ) optimal control of continuous-time system with terminal state constraint. In particular, multiple agents exist in the system which can only access partial information of the matrix…

Optimization and Control · Mathematics 2025-10-21 Wenjing Yang , Zhaorong Zhang , Juanjuan Xu

Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati…

Numerical Analysis · Mathematics 2017-06-09 Matthew M. Lin , Chun-Yueh Chiang

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…

Systems and Control · Computer Science 2018-09-18 Forrest Laine , Claire Tomlin

This paper investigates the stochastic linear-quadratic (LQ, for short) optimal control problems with non-Markovian regime switching in a finite time horizon where the state equation is multi-dimensional. Similar to the classical stochastic…

Optimization and Control · Mathematics 2023-07-18 Yuyang Chen , Peng Luo

We introduce a new numerical method to approximate the solution of a finite horizon deterministic optimal control problem. We exploit two Hamilton-Jacobi-Bellman PDE, arising by considering the dynamics in forward and backward time. This…

Optimization and Control · Mathematics 2023-04-21 Marianne Akian , Stéphane Gaubert , Shanqing Liu