On the Inherent Integration Structure of Nonlinear Systems

In this paper we characterize the inherent integration structureof affine nonlinear systems through a set of indices called—inanalogy with existing terminology for linear systems—theorders of the zeros at infinity. We show that our definitionencompasses earlier characterizations due to Hirschorn and Isidori.The discussion is entirely local in nature, so that we are ableto use recent results in the ‘geometric approach’to nonlinear system theory.     

Lead with closed-loop system compensation of a radically rotating elastic rod attached to a rigid body part II: Nonlinear system simulation and control

As was stated in Part I, the linear control models of a radically rotating elastic rod in all the analysis and design procedures for lead with closed-loop system compensation is presented. For a given linear system model, if the model is accurate, it will be accurate only over a very limit range of operation of the system. However, all the effort of design comes to be meaningful until it is tested using the nonlinear system model. On the other hand, the response of the nonlinear system model will not be as good as that of the linear model. In fact, some iterations on the design and on improving the design based-model are often needed before there is even a resemblance between the linear model response and the nonlinear system response. The present paper is a continuation of [1] and nonlinear control system simulation and a tuning process are presented. While almost all design procedures for physical system contain some tuning process, the development of an analytic design procedure for models of distributed-parameter control system can be evidently shown through this paper.     

Current algebra and the nonlinear σ-model

We present the current algebra of a particular form in the nonlinear σ-model. The algebra has a non-Abelian form with field-dependent structure functions. We comment on the connection of the model with noncommutative space. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 3, pp. 405–412, June, 2007.     

Existence and optimal control for periodic parabolic equations with nonlocal terms

Motivated by models which have been proposed for some problemsin mathematical biology and fisheries management and elsewhere,we consider a nonlinear periodic parabolic problem and an associatedcost functional J. A key feature of our problem is the presenceof a nonlocal term which—as we show by direct example—rendersthe standard mono-tonicity methods invalid. We therefore employtopological methods to deal both with existence of solutionsand of minima of J over the Control set. Some considerationsare also presented on related systems and on the question ofuniqueness.     

A delay-time-based maintenance model of a multi-component system

There is a well established literature on delay-time modelsof regular inspection policies where inspections may or maynotbe perfect, and where the initial point u of a defect arisesas a homogeneous Poisson process. This paper extends the modellingin two ways. The first is to include the observed practice wherethe multi-component system is inspected not only on a plannedbasis, but also when a component fails. The second extensionis to use a nonhomogeneous Poisson process to describe defectarrivals in the system. An inspection–replacement modelbased upon these two extensions is then developed for a multi-componentsystem. The total expected cost per unit time is minimized withrespect to theinspection intervals and the system replacementtime. The likelihood function of the time of failures and thenumber of defects found at inspections is established, in orderto estimate model parameters based upon routinely collectedmaintenance data. As a special case of the general model, aninspection model—based upon a homogeneous Poisson processof defects arising—is also proposed, which has a relativelysimple structure. Both simulated and real-life data of failuresand defects identified at inspections are used to test the modelsand parameter-estimating procedure.     

On the inversion problem for nonlinear systems

A new homology technique is applied to the inversion problemfor nonlinear systems, both in the input—output and state-spaceformulations.     

Optimal Petrov--Galerkin Methods through Approximate Symmetrization

^*Present address: Department of Mathematics, Imperial College, London SW7 2BZ. A technique of approximate symmetrization is used to derivea test space from a given trial space for a Petrov—Galerkinmethod. This is applied to one-dimensional diffusion—convectionproblems to give approximations which are near optimal in anenergy norm. Rigorous and precise error bounds are derived todemonstrate the uniformly good behaviour and near optimalityof the procedure over all values of the mesh Péclet number.     

有等待席位限制的基于终端区系统运行效能的枢纽机场最优跑道设计算法

根据枢纽机场实际终端区系统瓶颈和航空公司及旅客的关键需求,利用随机服务系统理论,分析了有等待席位限制的枢纽机场终端区的空域结构、飞行、管制状况,建立其运行模型,能根据相关参数计算航班滞留时间、队长和空闲跑道数等有用指标;再进一步应用系统运行效能理论,成功地建立了枢纽机场的最佳跑道设计算法,算法对枢纽机场跑道建设规划有较大的理论意义和参考应用价值,实践中已经得到应用.     

On a Moving Boundary Solution to the Fokker-Planck Equation for Particle Transport in Turbulent Flows with Absorbing Boundaries

A Fokker—Planck equation describing the transport of particlesin turbulent flows is considered. The initial value problemwith perfectly absorbing boundary conditions on the wall issolved by introducing a characteristic line in phase space.It is found that the solution domain in phase space decomposesinto three regions which are connected by two moving boundaries,and the moving boundaries can be found explicitly. For Gaussian-typeinitial conditions, the solution of the Fokker—Planckequation can be obtained in each of the three regions by solvinga diffusion equation. An approximation procedure for the generalinitial value problem is established and the approximate solutionsequence is shown to be convergent in a certain Hilbert space.     

Linearized control systems and small-time reachable sets

Using linear approximations of nonlinear systems has long beena practice to design control laws. In this paper, an analysisis given involving linear approximation of the nonlinear controlsystem and small-time reachable sets in R². A useful concept,the swing–out, which is a measure of nonlinearity, isdefined. This is used to examine the relationship between thesmall-time reachable sets of the nonlinear control system andits linear approximation. Behaviour of the nonlinear systemunder a control law is examined within this context. More factsare given about the swing-out for some special cases.     

Performance analysis of automatic assembly systems with in-line parallel stations

An automatic assembly system—a key tool for mass production—isgenerally composed of a number of workstations and a transportsystem. One common problem associated with automatic assemblysystems is that some assembly operations may have relativelylong cycle times. As a consequence, productivity, which is determinedby the operations with the longest cycle time, can be reducedsignificantly. Therefore a special form of parallel workstationknown as an in-line parallel (tandem-gated) station was developedto improve the performance of an automatic assembly system.In this design, stations working in parallel are installed ina serial structure and perform identical operations. Thus, morethan one assembly may be processed simultaneously—a typeof design especially beneficial when a stage requires a longoperation cycle time. A typical example is a computer assemblysystem which performs long inspection operations to ensure thatthe quality level of each product is up to the acceptance level. In this paper, we describe a simulation study of the performancecharacteristics of this type of system, with a statistical analysisof each decision factor. Phenomena affecting the performanceof in-line parallel stations, identified by the assistance ofthe computer graphical display, will then be discussed. An analyticalmodel based on these phenomena identified is then developed.The results generated by the analytical model developed arevalidated by comparisons with the simulation results. Finally,guidelines for optimization of buffer size are presented.     

Semi-Markov models for human-resource modelling

For human-resource modelling, models of wastage—such asthe lognormal model—ignore the variations in leaving ratesbetween grades, while models of the grade, structuresuch asthe Markov model—ignore duration dependence inthe ratesof movement to other grades or leaving. The semi-Markov approachallows us to combine a flexible means of modelling durationdependentstay in a grade with a transition matrix of movements betweengrades. We may therefore describe the whole system and predictits future development. We discuss the use of semi-Markov models for human resourcemanagement and provide a means of estimating the parameters.The use of the model to assess promotion patterns is also considered.     

An optimal control model and algorithm for the deviated well’s trajectory planning

This paper presents a nonlinear piecewise smooth dynamical system of the trajectory of deviated wells according to engineering background. An optimal control model is established and the necessary conditions for optimality are proved via maximum principle. The optimal control problem is solved by a revised Hooke–Jeeves algorithm. The uniform design technique has been incorporated into the revised Hooke–Jeeves algorithm to handle the multimodal function. Computer simulation is used for this paper, and the numerical example illustrates the validity and efficiency of the algorithm. The procedure demonstrates its advantages in practical applications in Liaohe Oil Field.     

Boundary Integral Equation Solution of Non-linear Plane Potential Problems

This paper presents the boundary integral equation (BIE) formulation,and numerical solution procedure for two-dimensional problemsgoverned by Laplac's equation and subject to non-linear boundaryconditions. The introduction of non-linear terms constitutesa fundamental extension of the BIE method, as previous applicationshave been restricted entirely to linear problems. Furthermore,non-linearities necessitate the use of iterative solution techniqueswhich present the conceptual disadvantage that a solution isnot guaranteed. However, such difficulties were not encounteredwith the Newton—Raphson method employed in this study.The various features of the BIE technique are illustrated bythe application to a physical problem which is of significancein heat exchanger design.     

An Approach to the Design of Nonlinear Control Systems

A method is proposed for the design of nonlinear systems with an additive control input. The method is based on the Alekseev integral equation and a design procedure developed by the present author, which has been used previously for nonlinear, time-dependent endpoint systems.     

Equivalents of the finitary non-deterministic inductive definitions

We present statements equivalent to some fragments of the principle of non-deterministic inductive definitions (NID) by van den Berg (2013), working in a weak subsystem of constructive set theory CZF. We show that several statements in constructive topology which were initially proved using NID are equivalent to the elementary and finitary NIDs. We also show that the finitary NID is equivalent to its binary fragment and that the elementary NID is equivalent to a variant of NID based on the notion of biclosed subset. Our result suggests that proving these statements in constructive topology requires genuine extensions of CZF with the elementary or finitary NID.     

Asymptotic efficient estimation in semiparametric nonlinear regression models

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Multivariable identification and controller design of an integrated flight control system

This paper investigates the multivariable identification and controller design for the longitudinal channel of a Boeing 747 transport. The transfer function matrix of the system is identified using the prediction error (PE) identification method with multivariable ARX model. An ellipsoidal parametric uncertainty set is constructed from the covariance matrix of the identified parameters. It contains the parameters of actual system at a certain probability level. The identified models and the associated uncertainty sets are validated by measuring the worst-case ν-gap and then compared with the maximum value of the generalized stability margin. In automatic flight control system or autopilots, multiple specifications criteria are needed to be satisfied concurrently, such as good holding (small static altitude holding error), fast response, smooth transition (less oscillation, overshoot). The design of a Multiple Simultaneous Specifications (MSS) controller effectively and practically is a very significant and challenging job. Liu and Mills [H.H.T. Liu, J.K. Mills, Multiple specification design in flight control system, in: Proceedings of the American Control Conference, Chicago, Illinois, 2000, pp. 1365–1369] proposed a MSS controller design method using a convex combination approach. In this paper, we apply the method [H.H.T. Liu, J.K. Mills, Multiple specification design in flight control system, in: Proceedings of the American Control Conference, Chicago, Illinois, 2000, pp. 1365–1369; H.H.T. Liu, Design combination in integrated flight control, in: Proceedings of the American Control Conference, Arlington, Virginia, 2001, pp. 494–499; H.H.T. Liu, Multi-objective design for an integrated flight control system: a combination with model reduction approach, in: Proceedings of IEEE International Symposium on Computer Aided Control System Design, Glasgow, 2002, pp. 21–26] to design a MSS controller based on the identified models of the Boeing 747 transport aircraft longitudinal channel. The controllers are also validated by simulation using the true plant transfer functions.     

Optimization-based design of plant-friendly multisine signals using geometric discrepancy criteria

System identification is an important means for obtaining dynamical models for process control applications; experimental testing represents the most time-consuming step in this task. The design of constrained, “plant-friendly” multisine input signals that optimize a geometric discrepancy criterion arising from Weyl’s Theorem is examined in this paper. Such signals are meaningful for data-centric estimation methods, where uniform coverage of the output state-space is critical. The usefulness of this problem formulation is demonstrated by applying it to a linear problem example and to the nonlinear, highly interactive distillation column model developed by Weischedel and McAvoy. The optimization problem includes a search for both the Fourier coefficients and phases in the multisine signal, resulting in an uniformly distributed output signal displaying a desirable balance between high and low gain directions. The solution involves very little user intervention (which enhances its practical usefulness) and has great benefits compared to multisine signals that minimize crest factor. The constrained nonlinear optimization problems that are solved represent challenges even for high-performance optimization software.