Related papers: Singular Perturbation of Zero-Sum Linear-Quadratic…
We propose a simple and original approach for solving linear-quadratic mean-field stochastic control problems. We study both finite-horizon and infinite-horizon problems, and allow notably some coefficients to be stochastic. Our method is…
We consider a zero-sum stochastic game for continuous-time Markov chain with countable state space and unbounded transition and pay-off rates. The additional feature of the game is that the controllers together with taking actions are also…
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…
We study an iteration approach to solve the coupled algebraic Riccati equations when they appear in general two player closed-loop type Nash differential games over an infinite time horizon. Also, we propose an effective algorithm for…
This paper is concerned with a linear-quadratic non-zero sum differential game with asymmetric delayed information. To be specific, two players exist time delays simultaneously which are different, leading the dynamical system being an…
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…
This paper focuses on a kind of linear quadratic non-zero sum differential game driven by backward stochastic differential equation with asymmetric information, which is a natural continuation of Wang and Yu [IEEE TAC (2010) 55: 1742-1747,…
The solvability of equilibrium Riccati equations (EREs) plays a central role in the study of time-inconsistent stochastic linear-quadratic optimal control problems, because it paves the way to constructing a closed-loop equilibrium…
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 propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…
In this paper, the open-loop, closed-loop, and weak closed-loop solvability for discrete-time linear-quadratic (LQ) control problem is considered due to the fact that it is always open-loop optimal solvable if the LQ control problem is…
In this paper, we study a class of zero-sum two-player stochastic differential games with the controlled stochastic differential equations and the payoff/cost functionals of recursive type. As opposed to the pioneering work by Fleming and…
The paper is concerned with a zero-sum continuous-time stochastic differential game with a dynamics controlled by a Markov process and a terminal payoff. The value function of the original game is estimated using the value function of a…
We present a continuous-time equivalent to the well-known iterative linear-quadratic algorithm including an implementation of a backtracking line-search policy and a novel regularization approach based on the necessary conditions in the…
We study zero-sum stochastic differential games with player dynamics governed by a nondegenerate controlled diffusion process. Under the assumption of uniform stability, we establish the existence of a solution to the Isaac's equation for…
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…
Many problems in robotics involve multiple decision making agents. To operate efficiently in such settings, a robot must reason about the impact of its decisions on the behavior of other agents. Differential games offer an expressive…
This paper is concerned with a non-zero sum differential game problem of an anticipated forward-backward stochastic differential delayed equation under partial information. We establish a necessary maximum principle and sufficient…
Zero-sum stochastic games generalize the notion of Markov Decision Processes (i.e. controlled Markov chains, or stochastic dynamic programming) to the 2-player competitive case : two players jointly control the evolution of a state…
We prove that for a class of zero-sum differential games with incomplete information on both sides, the value admits a probabilistic representation as the value of a zero-sum stochastic differential game with complete information, where…