Related papers: Discrete Time Mean-Field Stochastic Linear-Quadrat…
The distributed optimal synchronization problem with linear quadratic cost is solved in this paper for multi-agent systems with an undirected communication topology. For the first time, the optimal synchronization problem is formulated as a…
We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…
This paper mainly investigates the optimal control and stabilization problems for linear discrete-time Markov jump systems. The general case for the finite-horizon optimal controller is considered, where the input weighting matrix in the…
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…
This paper investigates the stochastic linear-quadratic control problems with affine constraints, in which both equality and inequality constraints are involved. With the help of the Pontryagin maximum principle and Lagrangian duality…
We study the linear-quadratic control problem for a class of non-exchangeable mean-field systems, which model large populations of heterogeneous interacting agents. We explicitly characterize the optimal control in terms of a new…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…
In this paper, we propose a unified stochastic optimal control framework that integrates time-optimal control problems with classical stochastic optimal control formulations. Unlike conventional deterministic time-optimal control models,…
The minimum-time control problem consists in finding a control policy that will drive a given dynamic system from a given initial state to a given target state (or a set of states) as quickly as possible. This is a well-known challenging…
This paper applies a reinforcement learning (RL) method to solve infinite horizon continuous-time stochastic linear quadratic problems, where drift and diffusion terms in the dynamics may depend on both the state and control. Based on…
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…
This paper investigates the stochastic linear quadratic (LQ, for short) optimal control problem of Markov regime switching system. The representation of the cost functional for the stochastic LQ optimal control problem of Markov regime…
Decentralized stochastic control (DSC) considers the optimal control problem of a multi-agent system. However, DSC cannot be solved except in the special cases because the estimation among the agents is generally intractable. In this work,…
This paper studies the stochastic optimal control problem for systems with unknown dynamics. First, an open-loop deterministic trajectory optimization problem is solved without knowing the explicit form of the dynamical system. Next, a…
Conditions are established under which the optimal control of processes having both absolutely continuous and singular (with respect to time) controls are equivalent to linear programs over a space of measures on the state and control…
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations…
In this paper, our goal is to study fundamental foundations of linear quadratic Gaussian (LQG) control problems for stochastic linear time-invariant systems via Lagrangian duality of semidefinite programming (SDP) problems. In particular,…
This paper is concerned with linear quadratic graphon field social control problem where the noises of individual agents are correlated. Compared with the well-studied mean field system, the graphon field system consists of a large number…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…