Related papers: Indefinite Linear Quadratic Mean Field Social Cont…
The optimal stochastic control problem with a quadratic cost functional for linear partial differential equations (PDEs) driven by a state-and control-dependent white noise is formulated and studied. Both finite-and infinite-time horizons…
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…
This paper investigates a conditional mean-field type linear quadratic (LQ) optimal control problem with partial observation and regime switching, where the conditional expectations of the state and control given the history of Markov chain…
The standard linear quadratic Gaussian (LQG) framework assumes a Brownian noise process and relies on classical stochastic calculus tools, such as those based on It\^o calculus. In this paper, we solve a generalized linear quadratic optimal…
In this paper, we study a class of linear-quadratic (LQ) mean-field games in which the individual control process is constrained in a closed convex subset $\Gamma$ of full space $\mathbb{R}^m$. The decentralized strategies and consistency…
This paper focuses on linear-quadratic (LQ for short) mean-field games described by forward-backward stochastic differential equations (FBSDEs for short), in which the individual control region is postulated to be convex. The decentralized…
This paper develops a quantitative framework for analyzing the mean-square exponential stabilization of stochastic linear systems with multiplicative noise, focusing specifically on the optimal stabilizing rate, which characterizes the…
In this paper, we formulate a general time-inconsistent stochastic linear--quadratic (LQ) control problem. The time-inconsistency arises from the presence of a quadratic term of the expected state as well as a state-dependent term in the…
The optimal control problem for discrete-time systems with colored multiplicative noise is discussed in this paper. The problem will be more difficult to deal with than the case of white noise due to the correlation of the adjoining state.…
This paper studies several problems related to quadratic matrix inequalities (QMI's), i.e., inequalities in the Loewner order involving quadratic functions of matrix variables. In particular, we provide conditions under which the solution…
This paper investigates an infinite horizon discounted linear-quadratic (LQ) optimal control problem for stochastic differential equations (SDEs) incorporating regime switching and mean-field interactions. The regime switching is modeled by…
We present a data-driven method for solving the linear quadratic regulator problem for systems with multiplicative disturbances, the distribution of which is only known through sample estimates. We adopt a distributionally robust approach…
In this paper, we study the social optimality for mean field linear quadratic control systems following the direct approach, where subsystems are coupled via individual dynamics and costs according to a network topology. A graph is…
We propose controller synthesis for state regulation problems in which a human operator shares control with an autonomy system, running in parallel. The autonomy system continuously improves over human action, with minimal intervention, and…
A detailed study of the mean-field solution of Langevin equations with multiplicative noise is presented. Three different regimes depending on noise-intensity (weak, intermediate, and strong-noise) are identified by performing a…
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.…
This article is concerned with an optimal control problem derived by mean-field forward-backward stochastic differential equation with noisy observation, where the drift coefficients of the state equation and the observation equation are…
We provide a thorough study of a general class of linear-quadratic extended mean field games and control problems in any dimensions where the mean field terms are allowed to be unbounded and there are also presence of cross terms in the…
An optimal control problem is considered for linear stochastic differential equations with quadratic cost functional. The coefficients of the state equation and the weights in the cost functional are bounded operators on the spaces of…
We propose and analyze a framework for discrete-time robust mean-field control problems under common noise uncertainty. In this framework, the mean-field interaction describes the collective behavior of infinitely many cooperative agents'…