Related papers: Time-Inconsistent Singular Control Problems with a…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
In this paper, we investigate a class of time-inconsistent discrete-time stochastic linear-quadratic optimal control problems, whose time-consistent solutions consist of an open-loop equilibrium control and a linear feedback equilibrium…
An emerging and challenging area in mathematical control theory called Ensemble Control encompasses a class of problems that involves the guidance of an uncountably infinite collection of structurally identical dynamical systems, which are…
We consider the Skorokhod problem in a time-varying interval. We prove existence and uniqueness for the solution. We also express the solution in terms of an explicit formula. Moving boundaries may generate singularities when they touch. We…
We study the singularities for minimum time control-affine problems in 4D with 2D controls. After regularization, the problem boils down to the study of a bifurcation around some nilpotent equilibrium in the singular locus. We show that the…
This paper deals with a class of time inconsistent stochastic linear quadratic (SLQ) optimal control problems in Markovian framework. Three notions, i.e., closed-loop equilibrium controls/strategies, open-loop equilibrium controls and their…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
In this paper, which is a continuation of the previously published discrete time paper we develop a theory for continuous time stochastic control problems which, in various ways, are time inconsistent in the sense that they do not admit a…
This paper firstly presents the necessary and sufficient conditions for a kind of discrete-time robust stochastic optimal control problem with convex control domains. As it is an "inf sup problem", the classical variational method is…
Hybrid optimal control problems are studied for a general class of hybrid systems where autonomous and controlled state jumps are allowed at the switching instants and in addition to terminal and running costs switching between discrete…
Robust output regulation for linear time-varying systems has remained an open problem for decades. To address this, we propose the trajectory-matching system immersion framework, by reformulating the regulator equation into a more…
We consider ergodic backward stochastic differential equations in a discrete time setting, where noise is generated by a finite state Markov chain. We show existence and uniqueness of solutions, along with a comparison theorem. To obtain…
In this paper, we study an optimal stopping problem in the presence of model uncertainty and regime switching. The max-min formulation for robust control and the dynamic programming approach are adopted to establish a general theoretical…
The paper presents a novel method for designing an optimal controller for discrete-time switched linear systems. The problem is formulated as one of computing the discrete mode sequence and the continuous input sequence that jointly…
We revisit the optimal dividend problem of de Finetti by adding a variance term to the usual criterion of maximizing the expected discounted dividends paid until ruin, in a singular control framework. Investors do not like variability in…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…
We present a general theoretical framework for finding the time-optimal unitary evolution of the quantum systems when the Hamiltonian is subject to arbitrary constraints. Quantum brachistochrone (QB) is such a framework based on the…
We study a regulation problem for stochastic systems subject to both continuous fluctuations and rare but significant shocks, modeled as a jump-diffusion with uncertainty in both the drift and the jump intensity. Such settings arise in…
We study time-minimum optimal control for a class of quantum two-dimensional dissipative systems whose dynamics are governed by the Lindblad equation and where control inputs acts only in the Hamiltonian. The dynamics of the control system…
We establish a variety of results extending the well-known Pontryagin maximum principle of optimal control to discrete-time optimal control problems posed on smooth manifolds. These results are organized around a new theorem on critical and…