scholarly journals Stochastic Maximum Principle of Near-Optimal Control of Fully Coupled Forward-Backward Stochastic Differential Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Maoning Tang
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Backward Stochastic Differential Equation ◽  
Hamiltonian Function ◽  
Integral Form ◽  
Local Form ◽  
Fully Coupled ◽  
Convex Control ◽  
Error Order ◽  
Near Optimality

This paper first makes an attempt to investigate the near-optimal control of systems governed by fully nonlinear coupled forward-backward stochastic differential equations (FBSDEs) under the assumption of a convex control domain. By Ekeland’s variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for anyε-near optimal control in a local form with an error order of exactε1/2. Moreover, under additional convexity conditions on Hamiltonian function, we prove that anε-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality of orderε1/2.

scholarly journals Near Optimality of Linear Delayed Doubly Stochastic Control Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Jie Xu ◽  
Ruiqiang Lin
Keyword(s):  
Optimal Control ◽  
Time Delay ◽  
Control Problem ◽  
Delay System ◽  
Necessary Condition ◽  
Linear Quadratic ◽  
The Maximum Principle ◽  
Doubly Stochastic ◽  
Convex Control ◽  
Near Optimality

In this paper, we study a kind of near optimal control problem which is described by linear quadratic doubly stochastic differential equations with time delay. We consider the near optimality for the linear delayed doubly stochastic system with convex control domain. We discuss the case that all the time delay variables are different. We give the maximum principle of near optimal control for this kind of time delay system. The necessary condition for the control to be near optimal control is deduced by Ekeland’s variational principle and some estimates on the state and the adjoint processes corresponding to the system.

Near-optimal control problems for forward-backward regime-switching systems

2020 ◽  
Vol 26 ◽  
pp. 94
Author(s):  
Min Li ◽  
Zhen Wu
Keyword(s):  
Optimal Control ◽  
Regime Switching ◽  
Hamiltonian Function ◽  
Minimum Condition ◽  
Optimal Controls ◽  
Diffusion Term ◽  
Finite State ◽  
Forward Diffusion ◽  
Theoretical Results ◽  
Near Optimality

This paper investigates the near-optimality for a class of forward-backward stochastic differential equations (FBSDEs) with continuous-time finite state Markov chains. The control domains are not necessarily convex and the control variables do not enter forward diffusion term. Some new estimates for state and adjoint processes arise naturally when we consider the near-optimal control problem in the framework of regime-switching. Inspired by Ekeland’s variational principle and a spike variational technique, the necessary conditions are derived, which imply the near-minimum condition of the Hamiltonian function in an integral sense. Meanwhile, some certain convexity conditions and the near-minimum condition are sufficient for the near-optimal controls with order ε1/2. A recursive utility investment consumption problem is discussed to illustrate the effectiveness of our theoretical results.

Near-Optimality in Stochastic Control of Predator-Pray System with Markov Switching

2013 ◽  
Vol 694-697 ◽  
pp. 2153-2156
Author(s):  
Xi Ning Li ◽  
Dong Mei Wei
Keyword(s):  
Optimal Control ◽  
Variational Principle ◽  
Stochastic Control ◽  
Necessary Conditions ◽  
Markov Switching ◽  
Control Variable ◽  
Ekeland’S Variational Principle ◽  
The State ◽  
Ekeland's Variational Principle ◽  
Near Optimality

In this paper, we introduce a stochastic predator-pray system with Markov switching. We establish the necessary conditions of near-optimal control for this system. The proof of the main results are based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.

Near-Optimality in Stochastic Control of Predator-Pray System with Markov Switching

2013 ◽  
Vol 319 ◽  
pp. 558-561
Author(s):  
Xi Ning Li ◽  
Dong Mei Wei
Keyword(s):  
Optimal Control ◽  
Variational Principle ◽  
Stochastic Control ◽  
Necessary Conditions ◽  
Markov Switching ◽  
Control Variable ◽  
Ekeland’S Variational Principle ◽  
The State ◽  
Ekeland's Variational Principle ◽  
Near Optimality

In this paper, we introduce a stochastic predator-pray system with Markov switching. We establish the necessary conditions of near-optimal control for this system. The proof of the main results are based on Ito's formula, Ekeland's variational principle and some estimates on the state and the adjoint process with respect to the control variable.

scholarly journals Pontryagin’s Maximum Principle for Optimal Control of Stochastic SEIR Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Ruimin Xu ◽  
Rongwei Guo
Keyword(s):  
Optimal Control ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Hamiltonian Function ◽  
Model System ◽  
Seir Model ◽  
Verification Theorem ◽  
Explicit Formulation ◽  
Adjoint Variables ◽  
Sufficient Conditions For Optimality

In this paper, we study the necessary conditions as well as sufficient conditions for optimality of stochastic SEIR model. The most distinguishing feature, compared with the well-studied SEIR model, is that the model system follows stochastic differential equations (SDEs) driven by Brownian motions. Hamiltonian function is introduced to derive the necessary conditions. Using the explicit formulation of adjoint variables, desired necessary conditions for optimal control results are obtained. We also establish a sufficient condition which is called verification theorem for the stochastic SEIR model.

scholarly journals Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks

2021 ◽  
Vol 18 (5) ◽  
pp. 6452-6483
Author(s):  
Keguo Ren ◽  
◽  
Xining Li ◽  
Qimin Zhang ◽  
Keyword(s):  
Optimal Control ◽  
Avian Influenza ◽  
Complex Networks ◽  
Sufficient Conditions ◽  
Hamiltonian Function ◽  
Threshold Dynamics ◽  
Threshold Behavior ◽  
Necessary And Sufficient ◽  
Theoretical Results ◽  
Near Optimality

<abstract><p>Near-optimization is as sensible and important as optimization for both theory and applications. This paper concerns the near-optimal control of an avian influenza model with saturation on heterogeneous complex networks. Firstly, the basic reproduction number $ \mathcal{R}_{0} $ is defined for the model, which can be used to govern the threshold dynamics of influenza disease. Secondly, the near-optimal control problem was formulated by slaughtering poultry and treating infected humans while keeping the loss and cost to a minimum. Thanks to the maximum condition of the Hamiltonian function and the Ekeland's variational principle, we establish both necessary and sufficient conditions for the near-optimality by several delicate estimates for the state and adjoint processes. Finally, a number of examples presented to illustrate our theoretical results.</p></abstract>

scholarly journals Dynamical Analysis and Optimal Control for a SEIR Model Based on Virus Mutation in WSNs

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 929
Author(s):  
Guiyun Liu ◽  
Jieyong Chen ◽  
Zhongwei Liang ◽  
Zhimin Peng ◽  
Junqiang Li
Keyword(s):  
Optimal Control ◽  
Rapid Development ◽  
Hamiltonian Function ◽  
Propagation Model ◽  
Dynamical Analysis ◽  
Optimal Control Strategy ◽  
Epidemic Dynamics ◽  
Optimization Control ◽  
The Cost ◽  
The Pontryagin Maximum Principle

With the rapid development of science and technology, the application of wireless sensor networks (WSNs) is more and more widely. It has been widely concerned by scholars. Viruses are one of the main threats to WSNs. In this paper, based on the principle of epidemic dynamics, we build a SEIR propagation model with the mutated virus in WSNs, where E nodes are infectious and cannot be repaired to S nodes or R nodes. Subsequently, the basic reproduction number R0, the local stability and global stability of the system are analyzed. The cost function and Hamiltonian function are constructed by taking the repair ratio of infected nodes and the repair ratio of mutated infected nodes as optimization control variables. Based on the Pontryagin maximum principle, an optimal control strategy is designed to effectively control the spread of the virus and minimize the total cost. The simulation results show that the model has a guiding significance to curb the spread of mutated virus in WSNs.

Sign in / Sign up

Export Citation Format

Share Document