Control Of Stochastic Differential Equations Research Articles

Optimal control of stochastic differential equations with dynamical boundary conditions

In this paper we investigate the optimal control problem for a class of stochastic Cauchy evolution problems with nonstandard boundary dynamic and control. The model is composed by an infinite dimensional dynamical system coupled with a finite dimensional dynamics, which describes the boundary conditions of the internal system. In other terms, we are concerned with nonstandard boundary conditions, as the value at the boundary is governed by a different stochastic differential equation.

Controlled stochastic differential equations under Poisson uncertainty and with unbounded utility

The present paper is concerned with the optimal control of stochastic differential equations, where uncertainty stems from Poisson processes. Optimal behavior (e.g., optimal consumption) is usually determined by employing the Hamilton–Jacobi–Bellman equation. This requires strong assumptions on the model, such as a bounded utility function and bounded coefficients in the controlled differential equation. The present paper relaxes these assumptions. We show that one can still use the Hamilton–Jacobi–Bellman equation as a necessary criterion for optimality if the utility function and the coefficients are linearly bounded. We also derive sufficiency in a verification theorem without imposing any boundedness condition at all. It is finally shown that, under very mild assumptions, an optimal Markov control is optimal even within the class of general controls.

On a universal formula for the stabilization of control stochastic nonlinear systems

This paper presents an explicit formula for a stabilizing feedback law for control stochastic differential equations. This result extends Artstein's theorem to nonlinear control systems corrupted by noise

The Maximum Principle for Partially Observed Optimal Control of Stochastic Differential Equations

This paper concerns partially observed optimal control of possibly degenerate stochastic differential equations, with correlated noises between the system and the observation. The control is allowed to enter into all the coefficients. A general maximum principle is proved for the partially observed optimal control, and the relations among the adjoint processes are established. Adjoint vector fields, which are adapted to the past and present observations, are introduced as the solutions to some backward stochastic partial differential equations (BSPDEs), and their relations are established. Under suitable conditions, the adjoint processes are characterized in terms of the adjoint vector fields, their differentials and Hessians, along the optimal state process. Some other formulations of the partially observed stochastic maximum principle are then derived.

A Jurdjevic-Quinn Theorem for Stochastic Nonlinear Systems

In this paper, we provide a formula for a stabilizing feedback law for control stochastic differential equations. This result extends Jurdjevic-Quinn's theorem to nonlinear control systems corrupted by noise

Optimal control of semilinear stochastic evolution equations

THE AIM of this paper is to initiate a semigroup theory-based approach to characterization of optimal Markov controls for controlled semilinear stochastic evolution equations. (It may be recalled that Markov controls are those that depend only on the current state at each time.) For finite dimensional controlled stochastic differential equations with a nondegenerate diffusion matrix, this task is traditionally achieved through the Hamilton-Jacobi-Bellman equation of dynamic programming associated with the problem and an accompanying verification theorem. The latter states that an optimal Markov control can be explicitly obtained by the pointwise minimization of a Hamiltonian derivable from the solution of the HJB equation. Moreover, any optimal Markov control is obtainable in this manner.

A stochastic version of Jurdjevic–Quinn theorem

The purpose of this paper is to extend the result proved by Jurdjevic and Quinn [6] on the stabilizability of deterministic control systems to the feedback stabilization of control stochastic differential equations

A universal formula for the stabilization of control stochastic differential equations

In this paper, we provide a formula for a stabilizing feedback law for control stochastic differential equations. This result extends Artstein's theorem to nonlinear control systems corrupted by noise.

Optimal control of certain hyperbolic and integral stochastic equations

Using Gateaux differentiation of the quality functional we obtain necessary conditions for optimality of a control for stochastic differential equations of hyperbolic type containing two-parameter white noise and for stochastic integral equations.

Gradient method for computing optimal controls for stochastic differential equations

Three techniques are described for solving completely observable stochastic control problems. Known optimality conditions are used to develop gradient–type algorithms. Numerical results are presented for illustration and comparison purposes

Control of systems with jump Markov disturbances

Abstract-Control of stochastic differential equations of the form dot{x}=f^{r(t)}(t,x,u) in which r(t) is a fiie-state Markov p n m s is discussed Dynamic programming optimalityconditions are shown to be necessary and sufficient for oplimality. A stochastic minimom principle whose adjoints satisfy deterministic integral equations is defiied and shorn to be necessary and snffiaent for optimality.

On Volterra’s Population Equation

On Volterra’s Population Equation