Stochastic Optimal Control Problem in Advertising Model with Delay

This paper investigates the optimal control problem arising in advertising model with delay. The authors reformulate the problem in Hilbert space by stochastic evolution equation and consider the optimal control problem of controlled stochastic evolution system. The necessary and sufficient optimality conditions of the control are established. The proposed approach is different from most existing studies of optimal advertising policy problem with delay. These results are applied to the optimal advertising policy problem under two different structures and the optimal advertising strategies are obtained.     

Stochastic stabilization analysis of networked control systems

Considering the stochastic delay problems existing in networked control systems, a new control mode is proposed for networked control systems whose delay is longer than a sampling period. Under the control mode, the mathematical model of such a system is established. A stochastic stabilization condition for the system is given. The maximum delay can be derived from the stabilization condition.     

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.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied.When data are transmitted over network,the stochastic data packet dropout process can be described by a two-state Markov chain.The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes.The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality.The state feedback controller can be constructed via the solution of a set of linear matrix inequalities.An example is given to verify the effectiveness of the method proposed.     

Stabilization of Continuous-Time Systems Against Stochastic Network Uncertainties: Fundamental Variance Bounds

This paper studies the stabilizability and stabilization of continuous-time systems in the presence of stochastic multiplicative uncertainties. The authors consider multi-input, multi-output(MIMO) linear time-invariant systems subject to multiple static, structured stochastic uncertainties,and seek to derive fundamental conditions to ensure that a system can be stabilized under a mean-square criterion. In the stochastic control framework, this problem can be considered as one of optimal control under state-or input-dependent random noises, while in the networked control setting, a problem of networked feedback stabilization over lossy communication channels. The authors adopt a mean-square small gain analysis approach, and obtain necessary and sufficient conditions for a system to be meansquare stabilizable via output feedback. For single-input, single-output(SISO) systems, the condition provides an analytical bound, demonstrating explicitly how plant unstable poles, nonminimum phase zeros, and time delay may impose a limit on the uncertainty variance required for mean-square stabilization. For MIMO minimum phase systems with possible delays, the condition amounts to solving a generalized eigenvalue problem, readily solvable using linear matrix inequality optimization techniques.     

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.     

Robust H∞ control for networked control systems

The robust H∞ control for networked control systems with both stochastic network-induced delay and data packet dropout is studied. When data are transmitted over network, the stochastic data packet dropout process can be described by a two-state Markov chain. The networked control systems with stochastic network-induced delay and data packet dropout are modeled as a discrete time Markov jump linear system with two operation modes. The sufficient condition of robust H∞ control for networked control systems stabilized by state feedback controller is presented in terms of linear matrix inequality. The state feedback controller can be constructed via the solution of a set of linear matrix inequalities. An example is given to verify the effectiveness of the method proposed.     

Simulation of a class of delay stochastic system with distributed parameter

1.INTRODUCTION It systemisoneofthemostimportantstochastic systems[1～3].Linearstochasticsystemwithreaction diffusiontermsusuallyappearsinstudyofdiffusion ofparticle[4,5].ItissignificanttostudylinearIt systemwithdistributedparameter.Mostofsystems discussedinliteraturesarewithoutIt termordis tributedparameter.AndsimulationoflineardelayIt systemwithdistributedparameterarenotgiv en[1～3,6～14].Inthispaper,partialdifferentialequa tionistransferredintoordinarydifferentialequation.Differential…     

Robust H∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality(BMI),which ensures a prescribed stochastic robust H∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.     

飞行器最优时滞反馈控制器设计

在设计飞行器最优反馈控制时,针对系统具有控制时滞的特性,采用连续状态变换思想,将具有时滞的控制系统转化为无时滞的控制系统,求使得无时滞控制系统性能指标最小的解,利用这个解去求原系统的状态函数,进而得到时滞反馈控制与状态变换后最优控制之间的关系,求出最优时滞反馈控制的增益。对某型无人直升机实验所得的悬停数据进行仿真验证,仿真结果证明了所提方法的有效性。     

White noise estimation for discrete-time systems with random delay and packet dropout

This paper is concerned with the optimal and suboptimal deconvolution problems for discrete-time systems with random delayed observations. When the random delay is known online, i.e., time stamped, the random delayed system is reconstructed as an equivalent delay-free one by using measurement reorganization technique, and then an optimal input white noise estimator is presented based on the stochastic Kahnan filtering theory. However, tb_e optimal white-noise estimator is timevarying, stochastic, and doesn＇t converge to a steady state in general. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criteria. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.     

Robust H∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H∞ control for uncertain neutral stochastic systems with time-varying delay is discussed. The parameter uncertaintie is assumed to be time varying norm-bounded. First, the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method. Then, a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality (BMI), which ensures a prescribed stochastic robust H∞ performance level for the resulting closed loop system with nonzero disturbance input and for all admissible uncertainties. An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.     

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.     

Worst-Case Investment Strategy with Delay

This paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state(crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.     

FORWARD-BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS, LINEAR QUADRATIC STOCHASTIC OPTIMAL CONTROL AND NONZERO SUM DIFFERENTIAL GAMES

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.     

State Estimation of Discrete Stochastic Singular System

1　 IntroductionIn the area of singular systems control much work has been done recently. The basictheory of singular systems has been proposed. A lot of results are obtained fordeterministic singluar systems[1～ 2 ] . However,only a few results are from stochasticsingular systems[3～ 5] ,in which attention is paid to time-invariant stochastic singularsystems. The state estimation and observation problems of time-invariant stochasticsingular systems have been discussed in[3 ] .The state estim…     

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.     

Controllability and observability of networked control systems with time-varying delays

The controllability and observability of networked control systems are studied. Aiming at the networked control system with time-varying delay, the sufficient and necessary conditions for complete controllability and complete observability of the system are presented, respectively. Because of Markov characteristic of the network-induced delay, in terms of stochastic theory, a sufficient and necessary condition for completely mean value controllability of networked control systems is obtained. Further, the conditions that the controllability and observability of networked control systems are equivalent to the initial time-invariant system are given. Controllability and observability realization indexes are also discussed, respectively. The numerical example demonstrates the effectiveness of the proposed theory.     

Decentralized Control of Discrete-Time System with Delay in Mean Field LQR Problem

This paper studies the decentralized optimal control of discrete-time system with input delay,where a large number of agents with the identical decoupling dynamical equations and the coupling cost function through the mean field are considered.The decentralized and centralized optimal controllers are proposed by the optimal tracking control of LQR problem with delay.They are proved that the optimal controllers and the optimal cost function of the centralized and decentralized solutions are equivalent for the optimal control problem.An illustrative example is given to show the efficiency of the decentralized optimal controllers.     

一种随机滑模变结构制导律的设计

针对导弹在目标拦截过程中的特点,考虑到系统的状态噪声和观测噪声等随机因素的影响,以随机滑模变结构控制理论为基础,设计了一种随机滑模变结构制导律.此制导律考虑导弹在目标拦截过程中滤波器和控制器的相互联系,综合了最优制导律视线角速度收敛和滑模变结构制导律鲁棒性强的优点,通过理论分析证明闭环系统在随机意义下的滑模次可达性.最后通过仿真验证了设计方法的正确性.