Related papers: Dynamic programming principle for classical and si…

In this paper, we consider the gradual-impulse control problem of continuous-time Markov decision processes, where the system performance is measured by the expectation of the exponential utility of the total cost. We prove, under very…

We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using…

In this paper, we investigate a sequential dynamic team problem consisting of two agents with a nested information structure. We use a combination of the person-by-person and prescription approach to derive structural results for optimal…

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…

In this paper, we study one kind of stochastic recursive optimal control problem with the obstacle constraints for the cost function where the cost function is described by the solution of one reflected backward stochastic differential…

This work presents a stochastic dynamic programming (SDP) algorithm that aims at minimizing an economic criteria based on the total energy consumption of a range extender electric vehicle (REEV). This algorithm integrates information from…

We obtain the dynamic programming equations and optimality conditions akin to Pontryagin's extremum principle for certain mathematical models of hybrid control systems.

This article introduces a novel distributionally robust model predictive control (DRMPC) algorithm for a specific class of controlled dynamical systems where the disturbance multiplies the state and control variables. These classes of…

We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…

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 study deterministic nonstationary discrete-time optimal control problems in both finite and infinite horizon. With the aid of Gateaux differentials, we prove a discrete-time maximum principle in analogy with the well-known…

In this paper we define an infinite-dimensional controlled piecewise deterministic Markov process (PDMP) and we study an optimal control problem with finite time horizon and unbounded cost. This process is a coupling between a continuous…

The investigation of optimal processes has a long history in the field of thermodynamics. It is well known that finite-time processes that minimize dissipation often exhibit discontinuities. We use a combination of numerical and analytical…

Run-and-tumble particles constitute one of the simplest models of self-propelled active matter, and provide an ideal playground to the understanding of out-of-equilibrium systems. We consider an idealized setup where one such particle is…

We consider the stochastic optimal control problem for the dynamical system of the stochastic differential equation driven by a local martingale with a spatial parameter. Assuming the convexity of the control domain, we obtain the…

We study the structure of a simple dynamic optimization problem consisting of one state and one control variable, from a physicist's point of view. By using an analogy to a physical model, we study this system in the classical and quantum…

In this paper, we study the stochastic optimal control problem for control system with time-varying delay. The corresponding stochastic differential equation is a kind of stochastic differential delay equation. We prove the existence and…

This paper considers an optimal impulse control problem of dynamical systems generated by a flow. The performance criteria are total costs over the infinite time horizon. Apart from the main performance to be minimized, there are multiple…

In this paper, we study backward doubly stochastic recursive optimal control problem where the cost function is described by the solution of a backward doubly stochastic differential equation. We give the dynamical programming principle for…

We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…