相关论文: Linear-Quadratic Mean Field Control with Non-Conve…
A closed quantum system is defined as completely controllable if an arbitrary unitary transformation can be executed using the available controls. In practice, control fields are a source of unavoidable noise, which has to be suppressed to…
Linear-Quadratic optimal controls are computed for a class of boundary controlled, boundary observed hyperbolic infinite-dimensional systems, which may be viewed as networks of waves. The main results of this manuscript consist in…
In this article, we provide a comprehensive study of the linear-quadratic mean field games via the adjoint equation approach; although the problem has been considered in the literature by Huang, Caines and Malhame (HCM, 2007a), their method…
In this paper, we solve the long-standing fundamental problem of irregular linear--quadratic (LQ) optimal control, which has received significant attention since the 1960s. We derive the optimal controllers via the key technique of finding…
In this paper, we address an instance of uniquely solvable mean-field game with a common noise whose corresponding counterpart without common noise has several equilibria. We study the selection problem for this mean-field game without…
The purpose of this paper is to study the mixed linear quadratic Gaussian (LQG) and $H_\infty$ optimal control problem for linear quantum stochastic systems, where the controller itself is also a quantum system, often referred to as…
We investigate time-dependent mean-field games with superquadratic Hamiltonians and a power dependence on the measure. Such problems pose substantial mathematical challenges as the key techniques used in the subquadratic case do not extend…
This paper is concerned with a discrete-time mean-field stochastic linear-quadratic optimal control problem arose from financial application. Through matrix dynamical optimization method, a group of linear feedback controls is investigated.…
This paper investigates a mean-field linear-quadratic optimal control problem where the state dynamics and cost functional incorporate both expectation and conditional expectation terms. We explicitly derive the pre-committed, na\"{\i}ve,…
In this paper, we show that the value functions of mean field control problems with common noise are the unique viscosity solutions to fully second-order Hamilton-Jacobi-Bellman equations, in a Crandall-Lions-like framework. We allow the…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…
Direct policy search has achieved great empirical success in reinforcement learning. Many recent studies have revisited its theoretical foundation for continuous control, which reveals elegant nonconvex geometry in various benchmark…
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…
The purpose of this paper is to investigate the role that the continuous-time generalised Riccati equation plays within the context of singular linear-quadratic optimal control. This equation has been defined following the analogy with the…
We consider a system of mean field games with local coupling in the deterministic limit. Under general structure conditions on the Hamiltonian and coupling, we prove existence and uniqueness of the weak solution, characterizing this…
This paper develops a unified nonconvex optimization framework for the design of group-sparse feedback controllers in infinite-horizon linear-quadratic (LQ) problems. We address two prominent extensions of the classical LQ problem: the…
We address a class of McKean-Vlasov (MKV) control problems with common noise, called polynomial conditional MKV, and extending the known class of linear quadratic stochastic MKV control problems. We show how this polynomial class can be…
Irregular linear quadratic control (LQ, was called Singular LQ) has been a long-standing problem since 1970s. This paper will show that an irregular LQ control (deterministic) is solvable (for arbitrary initial value) if and only if the LQ…
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…
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…