Related papers: Kullback-Leibler-Quadratic Optimal Control
In this paper, we study the linear quadratic (LQ) optimal control problem of linear systems with private input and measurement information. The main challenging lies in the unavailability of other regulators' historical input information.…
Motivated by continuous-time optimal inventory management, we study a class of stationary mean-field control problems with singular controls. The dynamics are modeled by a mean-reverting Ornstein-Uhlenbeck process, and the performance…
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…
In this paper, we investigate a model-free optimal control design that minimizes an infinite horizon average expected quadratic cost of states and control actions subject to a probabilistic risk or chance constraint using input-output data.…
We consider a discrete-time Linear-Quadratic-Gaussian (LQG) control problem in which Massey's directed information from the observed output of the plant to the control input is minimized while required control performance is attainable.…
This paper develops a comprehensive framework for optimal control of systems governed by fractional backward stochastic evolution equations (FBSEEs) in Hilbert spaces. We first establish a stochastic maximum principle (SMP) as a necessary…
Linear time-invariant control systems can be considered as finitely generated modules over the commutative principal ideal ring $\mathbb{R}[\frac{d}{dt}]$ of linear differential operators with respect to the time derivative. The Kalman…
This paper studies the linear quadratic regulation (LQR) problem of unknown discrete-time systems via dynamic output feedback learning control. In contrast to the state feedback, the optimality of the dynamic output feedback control for…
Linear-Quadratic (LQ) problems that arise in systems and controls include the classical optimal control problems of the Linear Quadratic Regulator (LQR) in both its deterministic and stochastic forms, as well as $H^\infty$-analysis (the…
The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…
We develop a convex analysis approach for solving LQG optimal control problems and apply it to major-minor (MM) LQG mean-field game (MFG) systems. The approach retrieves the best response strategies for the major agent and all minor agents…
We introduce a generic solver for dynamic portfolio allocation problems when the market exhibits return predictability, price impact and partial observability. We assume that the price modeling can be encoded into a linear state-space and…
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…
This paper addresses the mean-square optimal control problem for \a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have…
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…
This paper presents a mean-field control approach for Piecewise Deterministic Markov Processes (PDMPs), specifically designed for controlling a large number of agents. By modeling the interactions of a large number of agents through an…
Multi-agent reinforcement learning (MARL), despite its popularity and empirical success, suffers from the curse of dimensionality. This paper builds the mathematical framework to approximate cooperative MARL by a mean-field control (MFC)…
Sampling-based model predictive control (MPC) algorithms, such as model predictive path integral (MPPI), enable approximate, gradient-free solutions to optimal control problems by drawing samples from a proposal distribution, evaluating…
In this paper, we consider the adaptive linear quadratic Gaussian control problem, where both the linear transformation matrix of the state $A$ and the control gain matrix $B$ are unknown. The proposed adaptive optimal control only assumes…
This paper proposes a new family of lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in…