Optimal Control Of Stochastic Systems Research Articles

A System of Nonlinear Partial Differential Equations Arising in the Optimal Control of Stochastic Systems with Switching Costs

The problem of optimal switching control of a diffusion process with costly switchings leads to a system of fully nonlinear elliptic partial differential equations with implicit obstacles. We obtain results on the existence, uniqueness and regularity of the solution of this system.

On the optimal control of stochastic systems with an exponential-of-integral performance index

In this paper a theory of optimal control is developed for stochastic systems whose performance is measured by the exponential of an integral form. Such a formulation of the cost function is shown to be not only general and useful but also analytically tractable. Starting with very general classes of stochastic systems, optimality conditions are obtained which exploit the multiplicative decomposability of the exponential-of-integral form. Specializing to partially observed systems of stochastic differential equations with Brownian Motion disturbances, optimality conditions are obtained which parallel those for systems with integral costs. Also treated are the special cases of linear systems with exponential of quadratic costs for which explicit optimal controls are obtainable. In addition, several general results of independent interest are obtained, which concern optimality of stochastic systems.

Optimal control of stochastic systems with interrupted observations

An optimal control problem is considered for a nonlinear stochastic system with an interrupted observation mechanism that is characterized in terms of a jump Markov process taking on the values 0 or 1. The state of the system is described by a diffusion process, but the observation has components modulated by the jump process. The admissible control laws are smooth functions of the observation. Using the calculus of variations, necessary conditions on optimal controls are derived. These conditions amount to solving a set of four coupled nonlinear partial differential equations. A numerical procedure for solving these equations is suggested and an example dealt with numerically.

Optimum control of stochastic differential equation systems

This paper is an exposition of the basic technique of optimal control for stochastic systems in continuous time and of several important economic applications. Sections 2 through 5 and 10 develop the technique in an elementary fashion. The remaining sections cover applications to consumption and portfolio selection over time, the theory of mutual funds and capital asset pricing, the pricing of stock options, and the optimum consumption and exploration of a limited natural resource.

Existence of an optimal control for stochastic systems governed by ito equations

We give existence theorems for stochastic control problems with a lower semicontinuous cost functional and governed by Ito equations. We prove that two formulations of the fundamental problem are equivalent, one involving nonanticipative controls and the other involving (measurable) feedback controls. We then use the concept ofconvergence in distribution to prove existence for the first problem, and hence for the second as well. While our work has certain similarities with a paper of Kushner, our techniques are different and lead to more general results.

Some Types of Optimal Control of Stochastic Systems

Abstract : The optimal control of stochastic systems is considered. Under various assumptions concerning the information available to the controller, different optimal control rules result. For certain specific problems, the different control schemes are analyzed and compared, and the vast superiority of feedback over open-loop control is demonstrated.