State transfer control of quantum systems on the Bloch sphere

The state transfer under control fields is analyzed based on the Bloch sphere representation of a single qubit. In order to achieve the target from an arbitrary initial state to a target state, the conditions that parameters should satisfy are deduced separately in two different requirements: One is in the case of the rotation angle around the x-axis being fixed and another is in the situation with a given evolution time. Several typical states trajectories are demonstrated by numerical simulations on the Bloch sphere. The relations between parameters and the trajectories are analyzed.     

任意初始状态下非正则系统的迭代学习控制设计

迭代学习控制已广泛应用于各种机器人控制系统,但目前的方法大多数都假设系统具有零初始误差。在实际工程应用中,迭代学习的初始状态往往会发生漂移,现有的学习算法不能正确地使用。针对具有非零初始误差的非正则线性离散系统,研究了其迭代学习算法,提出了两种新型的初始状态的学习方法,利用2 D系统理论,对迭代学习进行了2 D分析,以保证所提出算法的稳定性。由于不需要假设系统初始误差为零,该算法更符合工程实际,仿真验证了算法的有效性。     

Queue Size Distribution of Geo/G/1 Queue Under the Min(N,D)-Policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D,whichever occurs first(Min(N,D)-policy).By using renewal process theory and total probability decomposition technique,the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state,and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n~+.Meanwhile,the authors obtain the explicit expressions of the additional queue length distribution.Furthermore,the important relations between the steady state queue length distributions at different time epochs n~-,n and n~+ are also reported.Finally,the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution,and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

Performance evaluation for damping controllers of power systems based on multi-agent models

This paper proposes a multi-layer multi-agent model for the performance evaluation of power systems, which is different from the existing multi-agent ones. To describe the impact of the structure of the networked power system, the proposed model consists of three kinds of agents that form three layers: control agents such as the generators and associated controllers, information agents to exchange the information based on the wide area measurement system (WAMS) or transmit control signals to the power system stabilizers (PSSs), and network-node agents such as the generation nodes and load nodes connected with transmission lines. An optimal index is presented to evaluate the performance of damping controllers to the system's inter-area oscillation with respect to the information-layer topology. Then, the authors show that the inter-area information exchange is more powerful than the exchange within a given area to control the inter-area low frequency oscillation based on simulation analysis. This work was supported in part by the National Natural Science Foundation of China under Grants Nos. 50707035, 50595411, 60425307, 60221301, and 50607005, in part by the 111 project (B08013) and Program for Changjiang Scholars and Innovative Research Team in University (IRT0515) and in part by the Program for New Century Excellent Talents in University (NCET-05-0216).     

水面舰船动力定位系统ESO输入饱和控制

为解决现实服役海洋环境下,模型参数未知的水面舰船动力定位系统的控制问题,考虑执行器输入有界、舰船运动状态信号难测量等工程因素的限制,提出一种动力定位的状态观测饱和控制算法。首先,对非线性扩张状态观测器(extended state observer, ESO)在含有未知饱和控制输入结构下的状态观测能力进行分析,在原有假设条件的基础上制定一条附加假设条件,并分析该观测系统的合理性。接下来,将非线性ESO的特例(即线性ESO)应用于对舰船运动状态变量的实时观测,设计自适应律对模型的阻尼项和执行器不确定增益进行在线估计,进而得到各个执行器可变螺距形式的控制输入,引入动态辅助系统处理执行器的输入饱和限制。仿真结果表明:相比于传统的动力定位系统控制策略,所提出的控制策略在保证高定位精度和合理收敛速度要求的同时,更符合工程实际。     

任意初始状态下迭代学习控制的频域分析

针对广义受控对象G(s) ,提出了一种迭代学习控制器在频域中设计的思想 ,给出了在任意初始状态下迭代学习控制算法收敛的充分条件 ,证明了经过逐次迭代后系统实际输出信号对期望输出信号的逼近特性 ,输出跟踪误差将一致有界 ,且与期望状态及期望输入无关。进一步讨论了反馈控制在迭代学习控制器中的作用。仿真结果表明了该算法的有效性。     

On Minimum Norm Control for an Elastic Robot System

In this paper, we discuss a robot system formulated as a vibrating elastic system. By regarding the damping coefficient of structure as the control variable and adjudging its optimality by norm minimum, we have proved the existence, the uniqueness and the approximation of the optimal control element by utilizing space L2(0,L) 's the reflexivity, the smoothness and the strict convexity.     

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.     

基于2-D系统理论的变初始条件离散系统的迭代学习控制

对于具有重复运动特性的系统，迭代学习控制是一种简单有效的控制方法。为便于实时应用，所有迭代学习控制方案的设计必须在离散时间域进行。初始状态问题是学习控制设计中遇到的一个重要问题。针对具有变初始状态的离散时间系统，利用2-D线性连续．离散型系统理论设计了闭环迭代学习控制器，并给出了保证控制器收敛的充分必要条件。仿真结果证明了该方案的有效性。     

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.     

Fixed-Time Leader-Following Formation Control of Fully-Actuated Underwater Vehicles Without Velocity Measurements

This paper is concerned with formation control of fully-actuated underwater vehicles (FUVs), focusing on improving system convergence speed and overcoming velocity measurement limitation. By employing the fixed-time control theory and command filtering technique, a full state feedback formation algorithm is proposed, which makes the follower track the leader in a given time with all signals in the system globally practically stabilized in fixed time. To avoid degraded control performance due to inaccurate velocity measurement, a fixed-time convergent observer is designed to estimate the velocity of FUVs. Then the authors give an observer-based fixed-time control method, with which acceptable formation performance can be achieved in fixed time without velocity measurement. The effectiveness and performance of the proposed method are demonstrated by numerical simulations.

     

Queue size distribution of Geo/G/1 queue under the Min(<Emphasis Type="Italic">N,D</Emphasis>)-policy

This paper considers a discrete-time Geo/G/1 queue under the Min(N,D)-policy in which the idle server resumes its service if either N customers accumulate in the system or the total backlog of the service times of the waiting customers exceeds D, whichever occurs first (Min(N,D)-policy). By using renewal process theory and total probability decomposition technique, the authors study the transient and equilibrium properties of the queue length from the beginning of the arbitrary initial state, and obtain both the recursive expression of the z-transformation of the transient queue length distribution and the recursive formula for calculating the steady state queue length at arbitrary time epoch n ⁺. Meanwhile, the authors obtain the explicit expressions of the additional queue length distribution. Furthermore, the important relations between the steady state queue length distributions at different time epochs n ^-, n and n ⁺ are also reported. Finally, the authors give numerical examples to illustrate the effect of system parameters on the steady state queue length distribution, and also show from numerical results that the expressions of the steady state queue length distribution is important in the system capacity design.     

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.     

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.     

多起点多讫点公共交通系统早高峰乘车均衡模型、算法与变动票价管理

分析早高峰时段多起点多讫点公共交通系统乘客乘车行为,考虑乘客的乘车时间成本、车票价格、拥挤成本和误时成本,区分有无座位情况,建立固定交通需求下的用户均衡模型和系统最优模型,针对模型建立有效算法,比较各模型导出系统最优的变动票价管理方案.数值算例结果验证了模型、算法和变动票价管理方案的有效性.对计算结果分析中,发现误时成本较小车次上,短途乘客对于长途乘客存在"挤出效应".     

Optimal Output Tracking Control and Stabilization of Networked Control Systems with Packet Losses

This paper studies the optimal output tracking control and stabilization for networked control systems with packet losses via output feedback control. Both finite-horizon and infinite-horizon cases are considered. For the finite-horizon case, the authors introduce an augmented system according to the state variable and the reference trajectory for the first time. Based on a set of difference Riccati equations, an optimal output feedback tracking controller is proposed by applying the stochastic maximum principle. And an optimal estimator is presented. For the infinite-horizon case, a necessary and sufficient condition for the stabilization of the system is provided. And an optimal output feedback stabilizing tracking controller is obtained by establishing a set of algebraic Riccati equations. Finally,numerical examples are given to verify the proposed results.     

Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations

This paper presents a new model of discrete time Geo/Geo/1 repairable queueing system with pseudo-fault, negative customers and multiple working vacations. The authors assume that system service may be interrupted by breakdown or pseudo-fault, this system may become disabled only when it is in a regular busy period, and negative customers adopt two types of typical killing strategies. In this paper, the authors know that the evolution of the system can be described by a two-dimensional Markov chain, and the two-dimensional Markov chain satisfies the condition of quasi birth and death chains. Based on the method of matrix-geometric solution, the authors obtain distributions for the stationary queue length in RCH and RCE strategy, respectively. Moreover, the reliability of the system is analyzed and the number of customers and waiting time of a customer in the system in steady state are obtained. The authors analyze the impact of two killing strategies on the system comparatively.This paper studies the individually and socially optimal behaviors of positive customers, and presents a pricing policy for positive customers, therefore, the authors obtain the socially optimal arrival rate.Various numerical results are provided to show the change of performance measures.     

Optimal pricing and inventory policy with order cancelations under the cash-on-delivery payment scheme

Considering a periodic review system where the online seller allows the customers to pay when the products are delivered to them（referred as cash-on-delivery payment scheme in this paper）,the authors investigate the seller＇s joint pricing and inventory control policy with a finite planning horizon.In particular,the authors incorporate the customers＇ possible order cancellation behavior with the cash-on-delivery scheme.It can be proven that the base-stock list price policy is optimal under mild conditions.The authors also analyze the impact of the customers＇ forward looking behavior on the optimal policy.     

Finite element approximation for a class of parameter estimation problems

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.     

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.