A maximum principle for general backward stochastic differential equation

In this paper, the authors consider a stochastic control problem where the system is governed by a general backward stochastic differential equation. The control domain need not be convex, and the diffusion coefficient can contain a control variable. The authors obtain a stochastic maximum principle for the optimal control of this problem by virtue of the second-order duality method.     

Stochastic maximum principle for mixed regular-singular control problems of forward-backward systems

This paper considers a stochastic optimal control problem of a forward-backward system with regular-singular controls where the set of regular controls is not necessarily convex and the regular control enters the diffusion coefficient. This control problem is difficult to solve with the classical method of spike variation. The authors use the approach of relaxed controls to establish maximum principle for this stochastic optimal control problem. Sufficient optimality conditions are also investigated.     

A Maximum Principle for Fully Coupled Forward-Backward Stochastic Control System Driven by Lvy Process with Terminal State Constraints

This paper is concerned with a fully coupled forward-backward stochastic optimal control problem where the controlled system is driven by L′evy process, while the forward state is constrained in a convex set at the terminal time. The authors use an equivalent backward formulation to deal with the terminal state constraint, and then obtain a stochastic maximum principle by Ekeland's variational principle. Finally, the result is applied to the utility optimization problem in a financial market.     

On optimal mean-field control problem of mean-field forward-backward stochastic system with jumps under partial information

This paper considers the problem of partially observed optimal control for forward-backward stochastic systems driven by Brownian motions and an independent Poisson random measure with a feature that the cost functional is of mean-field type. When the coefficients of the system and the objective performance functionals are allowed to be random, possibly non-Markovian, Malliavin calculus is employed to derive a maximum principle for the optimal control of such a system where the adjoint process is explicitly expressed. The authors also investigate the mean-field type optimal control problem for the system driven by mean-field type forward-backward stochastic differential equations (FBSDEs in short) with jumps, where the coefficients contain not only the state process but also its expectation under partially observed information. The maximum principle is established using convex variational technique. An example is given to illustrate the obtained results.     

Stochastic maximum principle for optimal control problems of forward-backward delay systems involving impulse controls

This paper is concerned with the optimal control problems of forward-backward delay systems involving impulse controls. The authors establish a stochastic maximum principle for this kind of systems. The most distinguishing features of the proposed problem are that the control variables consist of regular and impulsive controls, both with time delay, and that the domain of regular control is not necessarily convex. The authors obtain the necessary and sufficient conditions for optimal controls, which have potential applications in mathematical finance.     

The maximum principle for partially observed optimal control of forward-backward stochastic systems with random jumps

This paper studies the problem of partially observed optimal control for forward-backward stochastic systems which are driven both by Brownian motions and an independent Poisson random measure. Combining forward-backward stochastic differential equation theory with certain classical convex variational techniques, the necessary maximum principle is proved for the partially observed optimal control, where the control domain is a nonempty convex set. Under certain convexity assumptions, the author also gives the sufficient conditions of an optimal control for the aforementioned optimal optimal problem. To illustrate the theoretical result, the author also works out an example of partial information linear-quadratic optimal control, and finds an explicit expression of the corresponding optimal control by applying the necessary and sufficient maximum principle.     

Maximum principle for partially-observed optimal control problems of stochastic delay systems

This paper is concerned with partially-observed optimal control problems for stochastic delay systems. Combining Girsanov’s theorem with a standard variational technique, the authors obtain a maximum principle on the assumption that the system equation contains time delay and the control domain is convex. The related adjoint processes are characterized as solutions to anticipated backward stochastic differential equations in finite-dimensional spaces. Then, the proposed theoretical result is applied to study partially-observed linear-quadratic optimal control problem for stochastic delay system and an explicit observable control variable is given.     

Optimal Switching Integrity Attacks on Sensors in Industrial Control Systems

In this article, an optimal switching integrity attack problem is investigated to study the response of feedback control systems under attack. The authors model the malicious attacks on sensors as additive norm bounded signals. The authors consider an attacker who is only capable of launching attacks to limited number of sensors once a time and changing the combinations of attacked sensors all over the time. The objective of this paper is to find the optimal switching sequence of these combinations and the optimal attack input. The authors solve this problem by transforming it into a traditional optimal control problem with new control variables vary continuously in the range [0, 1]. The optimal solutions of the new control variables are of bang-bang-type. Therefore, an algebraic switching condition and an optimal attack input can be obtained. Finally, numerical results are provided to illustrate the effectiveness of the methods.     

科普教育及媒体报道对于不实信息传播的影响

本文研究突发事件发生后不实信息的传播与扩散问题,首先,基于系统动力学的思想,提出了不实信息的动态传播模型,刻画了科普教育以及媒体报道对于不实信息传播的影响,分析了模型的稳定性态. 为了克服静态决策的局限性,论文基于最优控制理论的方法,构建了社会效用最大化的控制模型,利用庞特里亚金最大值原理,进一步探讨得出了不实信息传播的动态最优控制策略. 最后,基于模型推导结论和数据模拟,说明了最优控制的优势所在,提出了在应急管理中不实信息的控制建议与思考,为应急管理奠定了理论基础和决策依据.     

连续边界条件系统的最优控制

本文研究连续边界条件系统的最优控制问题，给出了最优控制存在的必要条件，证明了该类最优控制仍有最大值原理成立。     

MAXIMUM PRINCIPLE FOR OPTIMAL CONTROLPROBLEM OF FULLY COUPLEDFORWARD-BACKWARD STOCHASTIC SYSTEMS

1.IntroductionLet(fi,F,P)beaprobabilityspaceand{Bt}tZobead-dimensionalBrownianmotioninthisspace.Let{R}tZobethenaturalfiltrationofthisBrownianmotion.Weconsiderthefollowingfullycoupledforward-backwardstochasticsystems:where(x,y,z)takesvaluesinR"xacxRTnxd.LetUbeanonemptyconvexsubsetofR',Anelementofadiscalledanadmissiblecontrol.Wecandefinethefollowingcostfunction:TheoptimalcontrolproblemistominimizethecostfunctionJ(v(.))overadmissiblecontrols.Anadmissiblecontrolu(.)iscalledanoptimalcontrol…     

MAXIMUM PRINCIPLE FOR THE OPTIMAL CONTROL OF AN ABLATION-TRANSPIRATION COOLING SYSTEM

This paper is concerned with an optimal control problem of an ablationtranspiration cooling control system with Stefan-Signorini boundary condition. The existence of weak solution of the system is considered. The Dubovitskii and Milyutin approach is adopted in the investigation of the Pontryagin‘s maximum principle of the system. The optimality necessary condition is presented for the problem with fixed final horizon and phase constraints.     

基于变阶长迭代动态规划的聚合物驱方案动态优化

聚合物驱是一种重要的提高原油采收率技术. 针对聚合物驱的注入方案优化问题, 建立了聚合物驱最优控制模型. 该模型以利润最大为性能指标, 以聚合物驱的渗流力学方程为支配方程, 并以聚合物最大用量约束和聚合物注入浓度的上下限约束为不等式约束条件. 各段塞间的注入浓度、段塞尺寸及驱油结束时间为该最优控制问题的优化变量. 对于该分布参数最优控制问题, 提出了一种变阶长迭代动态规划算法. 首先引入标准化的时间变量, 将原自由终端时间的聚合物驱最优控制问题转化为固定终端时间问题, 然后采用经典的迭代动态规划算法求解, 实现了注入浓度、段塞尺寸及驱油结束时间的同时优化, 最后通过实例验证了所提出算法的有效性.     

含直觉模糊弹性约束的模糊线性规划求解

本文基于模糊结构元方法构建并讨论了一类含有直觉模糊弹性约束的新型模糊线性规划问题. 通过引入模糊数的加权特征数, 定义了一种序关系并拓展了Verdegay的模糊线性规划方法, 将新型模糊线性规划问题转化成两个等价的含参数约束条件的清晰线性规划模型, 给出了此类线性规划模型对比最优可行解的求法. 最后通过一个数值实例来说明此类问题的一般求解方法.     

Adaptive Numerical Approach for Optimal Control of a Single Train

This paper considers the optimal control problem of a single train, which is formulated as an optimal control problem of nonlinear systems with switching controller. The switching sequence and the switching time are decision variables to be chosen optimally. Generally speaking, it is very difficult to solve this problem analytically due to its nonlinear nature, the complexity of the controller,and the existence of system state and control input constraints. To obtain the numerical solution, by introducing binary functions for every value of the control input, relaxing the binary functions, and imposing a penalty function on the relaxation, the problem is transformed into a parameter optimization problem, which can be efficiently solved by using any gradient-based numerical approach. Then, the authors propose an adaptive numerical approach to solve this problem. Convergence results indicate that any optimal solution of the parameter optimization problem is also an optimal solution of the original problem. Finally, an optimal control problem of a single train illustrates that the adaptive numerical approach proposed by us is less time-consuming and obtains a better cost function value than the existing approaches.     

CRITICAL BIRTH ORDER RATIO CONTROL AND ATTAINABLE SET OF A DISCRETE AGE－DEPENDENT PARITY PROGRESSION POPULATION SYSTEM

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Optimal Reinsurance Under Distortion Risk Measures and Expected Value Premium Principle for Reinsurer

This paper discusses optimal reinsurance strategy by minimizing insurer’s risk under one general risk measure:Distortion risk measure.The authors assume that the reinsurance premium is determined by the expected value premium principle and the retained loss of the insurer is an increasing function of the initial loss.An explicit solution of the insurer’s optimal reinsurance problem is obtained.The optimal strategies for some special distortion risk measures,such as value-at-risk(VaR) and tail value-at-risk(TVaR),are also investigated.     

Study on Pollution Cost Control Model under Asymmetric Information Based on Principal Agent

Pollution cost control is key to solve pollution problem. The paper takes pollution control cost of pollution control contract between management authority and pollutant discharge enterprise as research object, considers pollution control quality level, pollution control quality inspection and pollution control cost model, and establishes pollution control cost model of management authority and pollutant discharge enterprise, including rational constraints of pollutant discharge enterprise. And it analyzes principal-agent relationship between the two under condition of asymmetric information, and un-observability of pollution control level is shown as hiding information of sewage enterprises. In essence, it is problem of adverse selection in principal-agent. Pollution control cost of management is objective function. The first order condition of pollution control cost of sewage enterprise is transformed into state space equation, and optimal control of problem is solved by using maximum principle. In particular, management authority, as principal, uses pollution control provisions to reward, punish and encourage pollutant discharge enterprises as agents.     

Optimal pricing,production, and sales policies for new product under supply constraint

This paper considers a firm that sells a durable product with a given market potential. The purpose of the firm is to maximize its profit by determining how much capacity to install before the sales horizon, how many products to produce in accordance with the capacity, and how many products to sell by pricing. Appealing to Pontryagin maximum principle in control theory, the authors obtain the closed-forms of all optimal decisions the firm should make. Furthermore, the optimal production rate and optimal sales rate are both equal to the demand rate, which is caused by the optimal pricing policy during the whole horizon, and the optimal pricing path is increasing with the cost of installing a unit of capacity. Furthermore, numerical analysis reveals the visual impression of the relationship of the parameters.     

基于Branch ＆Bound方法MIQP问题的求解及应用

研究基于Branch＆Bound(B＆B)方法的混合整数二次规划(Mixed Integer Quadratic Programming，MQP)问题的求解，以及在一类混杂系统优化控制中的应用。B＆B算法求解MIQP问题的过程，可视为对于一个二叉树的搜索。影响B＆B算法寻优效率的两个主要方面是：分支变量的选择规则，以及树搜索策略。通过设定控制变量QPmax，用以限制寻优过程求解QP问题的最大数目，可以在较短的时间内获得MIQP问题的满足整数约束条件次优解。利用MATLAB编制MIQP问题的求解程序，并在混杂系统优化控制中的应用，做了仿真计算。