Optimal control of a Vlasov–Poisson plasma by an external magnetic field

The aim of various technical applications (for example fusion research) is to control a plasma by magnetic fields in a desired fashion. In our model the plasma is described by the Vlasov–Poisson system that is equipped with an external magnetic field. We will prove that this model satisfies some basic properties that are necessary for calculus of variations. After that, we will analyze an optimal control problem with a tracking type cost functional with respect to the following topics: necessary conditions of first order for local optimality, derivation of an optimality system, sufficient conditions of second order for local optimality, uniqueness of the optimal control under certain conditions.     

A stable-manifold-based method for chaos control and synchronization

A stable-manifold-based method is proposed for chaos control and synchronization. The novelty of this new and effective method lies in that, once the suitable stable manifold according to the desired dynamic properties is constructed, the goal of control is only to force the system state to lie on the selected stable manifold because once the stable manifold is reached, the chaotic system will be guided towards the desired target. The effectiveness of the approach and idea is tested by stabilizing the Newton–Leipnik chaotic system which possesses more than one strange attractor and by synchronizing the unified chaotic system which unifies both the Lorenz system and the Chen system.     

Control design of the vibration reduction systems

The paper deals with an original control algorithm for semi-active and active suspension that are often used in automotive systems. The developed procedure assists in finding the structure of control system, which consists of the primary controller and calculates the desired active force. Then the desired force has to be approximately achieved by the semi-active or active element with calculated input signal using the inverse model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stochastic population dynamics under regime switching

In this paper we will develop a new stochastic population model under regime switching. Our model takes both white and color environmental noises into account. We will show that the white noise suppresses explosions in population dynamics. Moreover, from the point of population dynamics, our new model has more desired properties than some existing stochastic population models. In particular, we show that our model is stochastically ultimately bounded.     

Closed-loop suppression of chaos in nonlinear driven oscillators

Summary This paper discusses the suppression of chaos in nonlinear driven oscillators via the addition of a periodic perturbation. Given a system originally undergoing chaotic motions, it is desired that such a system be driven to some periodic orbit. This can be achieved by the addition of a weak periodic signal to the oscillator input. This is usually accomplished in open loop, but this procedure presents some difficulties which are discussed in the paper. To ensure that this is attained despite uncertainties and possible disturbances on the system, a procedure is suggested to perform control in closed loop. In addition, it is illustrated how a model, estimated from input/output data, can be used in the design. Numerical examples which use the Duffing-Ueda and modified van der Pol oscillators are included to illustrate some of the properties of the new approach.This work has been supported by CNPq (Brazil) under Grant 200597/90-6 and SERC (UK) under Grant GR/H 35286.     

Suboptimal shape control for quasi-static distributed-parameter systems

We propose an on-line control approach which will adjust the steady-state shape of a large antenna arbitrarily close to any achievable desired profile. The method makes use of distributed-parameter system theory and allows refocusing using a limited number of control actuators and sensors.The controller gains are calculated by approximating the solution to an infinite-dimensional optimal quasi-static control problem. The controller gain calculation is computationally simpler than that proposed in a companion paper. The Galerkin (finite element) approximation method is used for model reduction. We prove that both gain and state convergence can be achieved by using the proposed approximation scheme.This work was partially supported by the Air Force Office of Scientific Research, Grant No. AFOSR 83-0124, and by the National Aeronautics and Space Administration, Grant No. NAG-1-515.     

A Projection Model for Hierarchical Manpower Systems

This paper presents a projection model for a hierarchical manpower system, viz. a combined group of English County Police Constabularies. The model is designed to describe how observed wastage and promotion rates will shape the internal structure of the system should these persist. Employees in the system are classified according to rank and completed length of service. The model also determines recruitment rates necessary to achieve desired manning levels.     

Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems

In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, i.e., a predictor, a reference model and a controller. The predictor is designed to predict the system’s output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output and the reference system trajectories all converge to each other.     

A role for M -matrices in modelling population growth

Adopting a discrete-time cohort-type model to represent the dynamics of a population, the problem of achieving a desired total size of the population under a balanced growth (contraction) and the problem of maintaining the desired size, once achieved, are studied. Properties of positive-time systems and M-matrices are used to develop the results, which are illustrated using simple examples. The material is presented in a format that makes it appropriate as background material for interesting applications based modelling assignments on undergraduate programmes in the mathematical sciences, applied sciences, economics and technology. All relevant properties of both positive-time systems and M-matrices are presented and clarified at the outset.     

Flexible solutions to systems of linear inequalities

In this paper we present two methods for calculating solutions to a system of linear inequalities which have certain prescribed distance properties to the constraints (referred to as flexibility properties). The first method (based on the calculation of the centre of an inscribed sphere, which is a well-known problem in linear programming) allows changes in the solution in any direction over a certain distance without becoming infeasible. The second method consists in the calculation of a solution with flexibility properties with respect to a prescribed coordinate system. It comprises an iterative procedure inside the area of feasible solutions using simple arithmetic operations. The major part of the paper will be devoted to the second method, since it is new and has attractive properties. Both methods are particularly applicable to the analysis of linear programming models with uncertain and inaccurate constraint parameters and in cases where operational adjustments are desired.     

The Balance of Care Project: Modelling the Allocation of Health and Personal Social Services

The Balance of Care model was designed to predict from aggregate health and personal social service plans the care which will be received by different types of potential client. Planners can use the model to assess the implications of various competing strategies and hence choose the one which will yield a pattern of care closest to that desired. In order to predict the pattern of care inherent in a service strategy it is necessary to establish the priorities governing the allocation of services to clients. This paper concentrates on the structure of the model and the techniques developed to deduce priorities from the past behaviour of the health and personal social service system. Applications of the model are described more fully elsewhere.     

Determination of optimal penalties for antitrust violations in a dynamic setting

We analyze a differential game describing the interactions between a firm that might be violating competition law and the antitrust authority. The objective of the authority is to minimize social costs (loss in consumer surplus) induced by an increase in prices above marginal costs. It turns out that the penalty schemes which are used now in EU and US legislation appear not to be as efficient as desired from the point of view of minimization of consumer loss from price-fixing activities of the firm. In particular, we prove that full compliance behavior is not sustainable as a Nash Equilibrium in Markovian strategies over the whole planning period, and, moreover, that it will never arise as the long-run steady-state equilibrium of the model. We also investigate the question which penalty system enables us to completely deter cartel formation in a dynamic setting. We found that this socially desirable outcome can be achieved in case the penalty is an increasing function of the degree of offence and is negatively related to the probability of law enforcement.     

A Nonlinear Control Concept for Rolling Mills

This contribution is concerned with the nonlinear control of a temper rolling mill based on the exact input/output linearization method. The considered subsystem of the temper rolling plant consists of a four‐high mill stand with a hydraulic adjustment system, and bridle rolls in the entry and the exit section. The demand on the temper rolling process is to establish a certain elongation of the steel strip under the action of the roll force and certain predefined backward and forward strip tensions in order to achieve the desired material characteristics and surface properties of the rolled product. The nonlinear control concept to be presented is characterized by the fact that the torques of the bridle rolls are intended as control inputs for the elongation and master speed control, whereas the hydraulic adjustment system and the main mill drive are used to take effect on the strip tensions. After a brief review of the mathematical model of the mill we will focus on the multi‐input nonlinear tension control.     

An extended and tractable approach on the convergence problem of the mixed push-pull manpower model

In this paper, the asymptotic behavior of the time-homogeneous mixed push-pull manpower model is studied under the assumption that the desired stock vector and the recruitment policy are fixed over time. In the mixed push-pull manpower model, the internal mobility of a personnel system can be regulated by both pull and push transitions. Based on those characteristics, we express and examine the dynamics of the personnel system by formulating the mixed push-pull manpower model by means of particular transition matrices, which we demonstrate to have interesting properties. We show that under certain conditions the stock vector converges. An explicit analytical form for this limiting personnel stock vector is found.     

永磁同步电机伺服系统的有限时间位置控制

研究了永磁同步电机伺服系统的位置跟踪问题.利用反馈线性化的思想,对永磁同步电机的数学模型进行分析,实现了电机模型的精确线性化和解耦.首先,将永磁同步电机位置跟踪系统采用反馈线性化技术变换为两个线性子系统,分别对其设计相应的基于连续状态反馈线性化的有限时间控制器,并设计了有限时间负载观测器来观测估计外部负载扰动.对永磁同步电机位置跟踪的闭环系统进行了稳定性的分析.与对应的渐近稳定控制的方案相比,基于有限时间的控制方案实现了永磁同步电机对期望信号的有限时间跟踪,获得了更好的动态响应和抗扰动性能.仿真结果表明了该控制方案的有效性.     

School redistricting: embedding GIS tools with integer programming

The paper deals with a school redistricting problem in which blocks of a city must be assigned to schools according to diverse criteria. Previous approaches are reviewed and some desired properties of a good school districting plan are established. An optimization model together with a geographic information system environment are then proposed for finding a solution that satisfies these properties. A prototype of the system is described, some implementation issues are discussed, and two real-life examples from the city of Philadelphia are studied, one corresponding to a relatively easy to solve problem, and the other to a much harder one. The trade-offs in the solutions are analysed and feasibility questions are discussed. The results of the study strongly suggest that ill-defined spatial problems, such as school redistricting, can be addressed effectively by an interaction between objective analysis and subjective judgement.     

Higher Order Continuum Modelling for Predicting the Mechanical Behaviour of Solid Foams

A higher order continuum model is presented, which is able to capture size effects and regularize softening in rotational, shearing and especially compressive settings. It is shown that with a minimal setting of 3 additional constitutive parameters the model has all desired properties. For parameter identification an example system of a honeycomb structure is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic server allocation for unstable queueing networks with flexible servers

This paper is concerned with the dynamic assignment of servers to tasks in queueing networks where demand may exceed the capacity for service. The objective is to maximize the system throughput. We use fluid limit analysis to show that several quantities of interest, namely the maximum possible throughput, the maximum throughput for a given arrival rate, the minimum arrival rate that will yield a desired feasible throughput, and the optimal allocations of servers to classes for a given arrival rate and desired throughput, can be computed by solving linear programming problems. We develop generalized round-robin policies for assigning servers to classes for a given arrival rate and desired throughput, and show that our policies achieve the desired throughput as long as this throughput is feasible for the arrival rate. We conclude with numerical examples that illustrate the points discussed and provide insights into the system behavior when the arrival rate deviates from the one the system is designed for.     

Controlled Deployment of a Tethered Satellite System

The deployment of a tethered satellite system undoubtedly represents one of the most critical phases in a tether mission: due to its complicated dynamics, high amplitude oscillations are likely to rise in the system, and it will take a long time to reach the desired stable radial equilibrium state. Based on a viscoelastic space billiard model, a targeting strategy is developed in this paper, which makes use of the system's chaotic nature and allows to steer the system into its equilibrium faster and more efficiently compared to conventional strategies.     

一类复杂水资源系统最优化问题的随机方法分析

对一类复杂水资源系统的最优化规划问题 ,在考虑天然来水这一随因素影响的情况下如何进行运行分析是十分重要的 ,文中对多个变量的非线性规划数学模型 ,运用随机分析方法得到了最优设计方案 ,具有现实意义 .