Related papers: A Dynamic Programming Formulation for the Nonlinea…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
This paper studies a class of non$-$Markovian singular stochastic control problems, for which we provide a novel probabilistic representation. The solution of such control problem is proved to identify with the solution of a $Z-$constrained…
We a controlled system driven by a coupled forward-backward stochastic differential equation (FBSDE) with a non degenerate diffusion matrix. The cost functional is defined by the solution of the controlled backward stochastic differential…
This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the…
Multi stage stochastic programs arise in many applications from engineering whenever a set of inventories or stocks has to be valued. Such is the case in seasonal storage valuation of a set of cascaded reservoir chains in hydro management.…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, the…
This paper is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
We consider the approximation of some optimal control problems for the Navier-Stokes equation via a Dynamic Programming approach. These control problems arise in many industrial applications and are very challenging from the numerical point…
This paper proposes a general incremental policy iteration adaptive dynamic programming (ADP) algorithm for model-free robust optimal control of unknown nonlinear systems. The approach integrates recursive least squares estimation with…
In this paper we consider a family of optimal control problems for economic models whose state variables are driven by Delay Differential Equations (DDE's). We consider two main examples: an AK model with vintage capital and an advertising…
This work presents a convex-optimization-based framework for analysis and control of nonlinear partial differential equations. The approach uses a particular weak embedding of the nonlinear PDE, resulting in a linear equation in the space…
Dynamic programming (DP) solves a variety of structured combinatorial problems by iteratively breaking them down into smaller subproblems. In spite of their versatility, DP algorithms are usually non-differentiable, which hampers their use…
We study a control problem where the state equation is a nonlinear partial differential equation of the calculus of variation in a bounded domain, perturbed by noise. We allow the control to act on the boundary and set stochastic boundary…
Stochastic dual dynamic programming is a cutting plane type algorithm for multi-stage stochastic optimization originated about 30 years ago. In spite of its popularity in practice, there does not exist any analysis on the convergence rates…
Constrained discrete optimization problems are encountered in many areas of communication and machine learning. We consider the case where the objective function satisfies Bellman's optimality principle without the constraints on which we…
The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
This paper is concerned with the relationship between maximum principle and dynamic programming principle for risk-sensitive stochastic optimal control problems. Under the smooth assumption of the value function, relations among the adjoint…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…