Related papers: Dynamic programming for discrete-time finite horiz…
This work addresses a switching control problem under which the cost associated with the changes of regimes is allowed to have discontinuities in time. Our main contribution is to show several characterizations of the optimal cost function…
We study risk-sensitive control of continuous time Markov chains taking values in discrete state space. We study both finite and infinite horizon problems. In the finite horizon problem we characterise the value function via HJB equation…
We present a dynamic programming-based solution to a stochastic optimal control problem up to a hitting time for a discrete-time Markov control process. Firstly, we determine an optimal control policy to steer the process toward a compact…
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…
The paper deals with an optimal control problem in a dynamical system described by a linear differential equation with the Caputo fractional derivative. The goal of control is to minimize a Bolza-type cost functional, which consists of two…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. We establish that these problems are related to certain infinite-dimensional linear…
We consider a discounted infinite horizon optimal stopping problem. If the underlying distribution is known a priori, the solution of this problem is obtained via dynamic programming (DP) and is given by a well known threshold rule. When…
This paper proposes a novel method for designing finite-horizon discrete-valued switching signals in linear switched systems based on discreteness-promoting regularization. The inherent combinatorial optimization problem is reformulated as…
Existing results on finite-time model predictive control (MPC) often rely on terminal equality constraint, switching inside one-step region, or terminal cost with short control horizon, leading to limited initial feasibility. This paper…
We present a novel penalty approach for a class of quasi-variational inequalities (QVIs) involving monotone systems and interconnected obstacles. We show that for any given positive switching cost, the solutions of the penalized equations…
We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…
We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…
We present stability conditions for deterministic time-varying nonlinear discrete-time systems whose inputs aim to minimize an infinite-horizon time-dependent cost. Global asymptotic and exponential stability properties for general…
In this paper, we study the finite-horizon problem of an economic agent's optimal consumption, investment, and job-switching decisions. The key new feature of our model is that the job-switching cost is time-varying. This extension leads to…
Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…
Optimization algorithms have a rich and fundamental relationship with ordinary differential equations given by its continuous-time limit. When the cost function varies with time -- typically in response to a dynamically changing environment…
We study a continuous time contracting model in which a principal hires a risk averse agent to manage a project over a finite horizon and provides sequential payments whose timing is endogenously determined. The resulting nonzero-sum…
In this paper, we study a stochastic recursive optimal control problem in which the cost functional is described by the solution of a backward stochastic differential equation driven by G-Brownian motion. Under standard assumptions, we…
In this study, we consider the infinite-horizon, discounted cost, optimal control of stochastic nonlinear systems with separable cost and constraints in the state and input variables. Using the linear-time Legendre transform, we propose a…
This paper concerns the numerical solution of the finite-horizon Optimal Investment problem with transaction costs under Potential Utility. The problem is initially posed in terms of an evolutive HJB equation with gradient constraints. In…