scholarly journals Necessary Conditions for Optimal Control of Forward-Backward Stochastic Systems with Random Jumps

2012 ◽  
Vol 2012 ◽  
pp. 1-50 ◽  
Author(s):  
Jingtao Shi
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Systems ◽  
Necessary Conditions ◽  
Control Variable ◽  
Optimal Controls ◽  
Linear Quadratic ◽  
Forward Equation ◽  
Random Jumps

This paper deals with the general optimal control problem for fully coupled forward-backward stochastic differential equations with random jumps (FBSDEJs). The control domain is not assumed to be convex, and the control variable appears in both diffusion and jump coefficients of the forward equation. Necessary conditions of Pontraygin's type for the optimal controls are derived by means of spike variation technique and Ekeland variational principle. A linear quadratic stochastic optimal control problem is discussed as an illustrating example.

scholarly journals Maximum Principle for Stochastic Recursive Optimal Control Problems Involving Impulse Controls

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhen Wu ◽  
Feng Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimality Conditions ◽  
Control Variable ◽  
Necessary Optimality Conditions ◽  
Sufficient Optimality Conditions ◽  
Linear Quadratic ◽  
Regular Control

We consider a stochastic recursive optimal control problem in which the control variable has two components: the regular control and the impulse control. The control variable does not enter the diffusion coefficient, and the domain of the regular controls is not necessarily convex. We establish necessary optimality conditions, of the Pontryagin maximum principle type, for this stochastic optimal control problem. Sufficient optimality conditions are also given. The optimal control is obtained for an example of linear quadratic optimization problem to illustrate the applications of the theoretical results.

scholarly journals On linear-quadratic optimal control of implicit difference equations

2018 ◽  
Vol 36 (3) ◽  
pp. 779-833
Author(s):  
Daniel Bankmann ◽  
Matthias Voigt
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Difference Equations ◽  
Matrix Pencil ◽  
Spectral Structure ◽  
Optimal Controls ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Quadratic Optimal Control

Abstract In this work we investigate explicit and implicit difference equations and the corresponding infinite time horizon linear-quadratic optimal control problem. We derive conditions for feasibility of the optimal control problem as well as existence and uniqueness of optimal controls under certain weaker assumptions compared to the standard approaches in the literature which are using algebraic Riccati equations. To this end, we introduce and analyse a discrete-time Lur’e equation and a corresponding Kalman–Yakubovich–Popov (KYP) inequality. We show that solvability of the KYP inequality can be characterized via the spectral structure of a certain palindromic matrix pencil. The deflating subspaces of this pencil are finally used to construct solutions of the Lur’e equation. The results of this work are transferred from the continuous-time case. However, many additional technical difficulties arise in this context.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (2) ◽  
pp. 302-309 ◽  
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

Optimal feedback control of stochastic McShane differential systems

1974 ◽  
Vol 11 (02) ◽  
pp. 302-309
Author(s):  
N. U. Ahmed ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Parabolic Type ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Necessary Conditions For Optimality ◽  
Reduced Problem

In this paper, the optimal control problem of system described by stochastic McShane differential equations is considered. It is shown that this problem can be reduced to an equivalent optimal control problem of distributed parameter systems of parabolic type with controls appearing in the coefficients of the differential operator. Further, to this reduced problem, necessary conditions for optimality and an existence theorem for optimal controls are given.

scholarly journals The Optimal Control Problem with State Constraints for Fully Coupled Forward-Backward Stochastic Systems with Jumps

2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
Qingmeng Wei
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Systems ◽  
Stochastic Maximum Principle ◽  
Quadratic Model ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
Fully Coupled

We focus on the fully coupled forward-backward stochastic differential equations with jumps and investigate the associated stochastic optimal control problem (with the nonconvex control and the convex state constraint) along with stochastic maximum principle. To derive the necessary condition (i.e., stochastic maximum principle) for the optimal control, first we transform the fully coupled forward-backward stochastic control system into a fully coupled backward one; then, by using the terminal perturbation method, we obtain the stochastic maximum principle. Finally, we study a linear quadratic model.

scholarly journals The Delayed Doubly Stochastic Linear Quadratic Optimal Control Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yan Chen ◽  
Jie Xu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Riccati Equation ◽  
Control Variable ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Doubly Stochastic ◽  
Quadratic Optimal Control

In this paper, the delayed doubly stochastic linear quadratic optimal control problem is discussed. It deduces the expression of the optimal control for the general delayed doubly stochastic control system which contained time delay both in the state variable and in the control variable at the same time and proves its uniqueness by using the classical parallelogram rule. The paper is concerned with the generalized matrix value Riccati equation for a special delayed doubly stochastic linear quadratic control system and aims to give the expression of optimal control and value function by the solution of the Riccati equation.

scholarly journals Necessary conditions of optimal impulse controls for distributed parameter systems

1992 ◽  
Vol 45 (2) ◽  
pp. 305-326 ◽  
Author(s):  
Jiongmin Yong ◽  
Pingjian Zhang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Necessary Conditions ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Optimal Controls ◽  
Optimal Impulse ◽  
Impulse Controls

Optimal control problem of semilinear evolutionary distributed parameter systems with impulse controls is considered. Necessary conditions of optimal controls are derived. The result generalises the usual Pontryagin's maximum principle.

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