Related papers: Weakly chained matrices, policy iteration, and imp…
We study a class of mean-field control problems under partial observation. The controlled dynamics are of McKean-Vlasov type and are subject to regime switching driven by a hidden Markov chain. The observation process depends on the control…
We consider the problem of optimally controlling stochastic, Markovian systems subject to joint chance constraints over a finite-time horizon. For such problems, standard Dynamic Programming is inapplicable due to the time correlation of…
This paper considers consumption and portfolio optimization problems with recursive preferences in both infinite and finite time regions. Specially, the financial market consists of a risk-free asset and a risky asset that follows a general…
We introduce some approximation schemes for linear and fully non-linear diffusion equations of Bellman-Isaacs type. Although they are not monotone one can prove their convergence to the viscosity solution of the problem. Effective…
The article poses a general model for optimal control subject to information constraints, motivated in part by recent work of Sims and others on information-constrained decision-making by economic agents. In the average-cost optimal control…
We study optimal stochastic control problems of general coupled systems of forward-backward stochastic differential equations with jumps. By means of the It\^o-Ventzell formula the system is transformed to a controlled backward stochastic…
Systems of Hamilton-Jacobi equations arise naturally when we study the optimal control problems with pathwise deterministic trajectories with random switching. In this work, we are interested in the large time behavior of weakly coupled…
In this article we study a finite horizon optimal control problem with monotone controls. We consider the associated Hamilton-Jacobi-Bellman (HJB) equation which characterizes the value function. We consider the totally discretized problem…
This work proposes a novel numerical scheme for solving the high-dimensional Hamilton-Jacobi-Bellman equation with a functional hierarchical tensor ansatz. We consider the setting of stochastic control, whereby one applies control to a…
In this work, we propose a class of numerical schemes for solving semilinear Hamilton-Jacobi-Bellman-Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We…
In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…
We consider piecewise-deterministic optimal control problems in which the environment randomly switches among several deterministic modes, and the goal is to optimize the expected cost up to the termination while taking the likelihood of…
We consider fully nonlinear Hamilton-Jacobi-Bellman equations associated to diffusion control problems involving a finite set-valued (or switching) control and possibly a continuum-valued control. We construct a lower complexity…
We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
We study a class of structured optimal control problems in which the main diagonal of the dynamic matrix is a linear function of the design variable. While such problems are in general challenging and nonconvex, for positive systems we…
In this paper we investigate a kind of optimal control problem of coupled forward-backward stochastic system with jumps whose cost functional is defined through a coupled forward-backward stochastic differential equation with Brownian…
We consider impulse control problems in finite horizon for diffusions with decision lag and execution delay. The new feature is that our general framework deals with the important case when several consecutive orders may be decided before…
In this work, we present a second-order numerical scheme to address the solution of optimal control problems constrained by the evolution of nonlinear Fokker-Planck equations arising from socio-economic dynamics. In order to design an…
Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…