Nonlinear optimal tracking control with application to super-tankers for autopilot design

A new method is introduced to design optimal tracking controllers for a general class of nonlinear systems. A recently developed recursive approximation theory is applied to solve the nonlinear optimal tracking control problem explicitly by classical means. This reduces the nonlinear problem to a sequence of linear-quadratic and time-varying approximating problems which, under very mild conditions, globally converge in the limit to the nonlinear systems considered. The converged control input from the approximating sequence is then applied to the nonlinear system. The method is used to design an autopilot for the ESSO 190,000-dwt oil tanker. This multi-input-multi-output nonlinear super-tanker model is well established in the literature and represents a challenging problem for control design, where the design requirement is to follow a commanded maneuver at a desired speed. The performance index is selected so as to minimize: (a) the tracking error for a desired course heading, and (b) the rudder deflection angle to ensure that actuators operate within their operating limits. This will present a trade-off between accurate tracking and reduced actuator usage (fuel consumption) as they are both mutually dependent on each other. Simulations of the nonlinear super-tanker control model are conducted to illustrate the effectiveness of the nonlinear tracking controller.     

Hermite Polynomials for Iterative Output Replanning for Flat Systems Affected by Additive Noise

The paper considers the output tracking problem for nonlinear systems whose performance output is also a flat output of the system itself. A desired output signal is sought on the actual performance output by using a feedforward inverse input that is periodically updated with discrete‐time feedback of the sampled state of the system. The proposed method is based on an iterative output replanning that uses the desired output trajectory and the sampled state to replan an output trajectory whose inverse input helps in reducing the tracking error. This iterative replanning exploits the Hermite interpolating polynomials to achieve an overall arbitrarily smooth input and a tracking error that can be made arbitrarily small if the state sampling period is sufficiently small and mild assumptions are considered. Some simulation results are presented for the cases of a unicycle and a one‐trailer system affected by additive noise.     

Inverse Dyamics of Non-Minimum Phase Systems with Non-Zero Initial Conditions

A method is presented forcomputing the inverse dynamics of a linear non-minimum phasesystem with non-zero initial conditions. The method is also usedto change or correct a trajectory after it is already in motion,and consequently, it will allow for real time control by continuallyupdating the inverse dynamics computation.Frequency domain techniques are used to compute the input functionneeded to produce a desired output trajectory at a particulardegree of freedom. An output profile based on the differencebetween the desired trajectory and either a homogeneous responseor a forced response to a previous forcing function is used tocompute the required input function. The resulting input functionactively damps out initial conditions in the system and makesit track the desired trajectory.The method is applied to a non-collocated single-link flexiblerobot arm. The finite element method using Timoshenko beam theoryis used to discretize the equations of motion. Torque profilesare computed to control the tip displacement for several problems.The first problem is to control the tip to a desired trajectorywhen starting with non-zero initial conditions. The second problemis to change the desired trajectory while the previous desiredtrajectory is already in motion. The third problem is to correctthe trajectory after a disturbance is added to the system. Thefourth problem is to analyze sensitivity to errors in the modeland initial conditions. The last problem is to compare tip responsesfor rigid and flexible link assumptions in the inverse dynamicscomputation.     

Data-driven output-feedback fault-tolerant control for unknown dynamic systems with faults changing system dynamics

This paper studies the data-driven output-feedback fault-tolerant control (FTC) problem for unknown dynamic systems with faults changing system dynamics. In a framework of active FTC, two basic issues are addressed: the fault detection employing only the measured input–output information; the controller reconfiguration to achieve optimal output-feedback control in the presence of multiple faults. To detect faults and write the system state via the input–output data, an approach to data-driven design of a residual generator with a full-rank transformation matrix is presented. An output-feedback approximate dynamic programming method is developed to solve the optimal control problem under the condition that the unknown linear time-invariant discrete-time plant has multiple outputs. According to the above results and the proposed input–output data-based value function approximation structure of time-varying plants, a model-free output-feedback FTC scheme considering optimal performance is given. Finally, two numerical examples and a practical example of a DC motor control system are used to demonstrate the effectiveness of the proposed methods.     

Inverse data envelopment analysis model to preserve relative efficiency values: The case of variable returns to scale

This paper studies the inverse Data Envelopment Analysis (inverse DEA) for the case of variable returns to scale (inverse BCC). The developed inverse BCC model can preserve relative efficiency values of all decision making units (DMUs) in a new production possibility set composing of all current DMUs and a perturbed DMU with new input and output values. We consider the inverse BCC model for a resource allocation problem, where increases of some outputs and decreases of the other outputs of the considered DMU can be taken into account simultaneously. The inverse BCC problem is in the form of a multi-objective nonlinear programming model (MONLP), which is not easy to solve. We propose a linear programming model, which gives a Pareto-efficient solution to the inverse BCC problem. However, there exists at least an optimal solution to the proposed model if and only if the new output vector is in the set of current production possibility set. The proposed approach is illustrated via a case study of a motorcycle-part company.     

RBF neural networks for solving the inverse problem of backscattering spectra

This paper investigates a new method to solve the inverse problem of Rutherford backscattering (RBS) data. The inverse problem is to determine the sample structure information from measured spectra, which can be defined as a function approximation problem. We propose using radial basis function (RBF) neural networks to approximate an inverse function. Each RBS spectrum, which may contain up to 128 data points, is compressed by the principal component analysis, so that the dimensionality of input data and complexity of the network are reduced significantly. Our theoretical consideration is tested by numerical experiments with the example of the SiGe thin film sample and corresponding backscattering spectra. A comparison of the RBF method with multilayer perceptrons reveals that the former has better performance in extracting structural information from spectra. Furthermore, the proposed method can handle redundancies properly, which are caused by the constraint of output variables. This study is the first method based on RBF to deal with the inverse RBS data analysis problem.     

Optimal preview-based stable-inversion for output tracking of nonminimum-phase linear systems

In this article, a new approach to output tracking of nonminimum-phase systems is proposed. The proposed technique extends the preview-based stable-inversion method to optimally utilize finite-preview (in time) of the future desired output trajectory to find the feedforward input (called the inverse input) for achieving precision output tracking for nonminimum-phase systems. It has been shown that having a large enough preview time is critical to ensure the precision in the preview-based output tracking. The available preview time, however, can be limited due to the physical constraints, and more generally, the associated cost and/or hardware limits. Therefore, we propose obtaining the optimal preview-based inverse input by minimizing, within the preview time window, the predicted tracking error (under the preview-based inverse input) relative to the input energy. A simulation study on a piezoelectric actuator model is used to illustrate the proposed technique.     

Integrated design of fault detection systems in time-frequencydomain

Problems related to the integrated design of robust fault detection (FD) systems are studied. First, it is revealed that due to the time window introduced to realize the 2-norm based evaluation function, an optimal design of a FD system with the 2-norm based evaluation function may not ensure the expected optimal performance when the system is realized in real applications. To solve this problem, an integrated design method of FD systems using the absolute value of residual signal as evaluation function is then proposed. It leads to a residual generator which is much easier to be realized. Different from the usual 2-norm based approaches whose mathematical basis is the relationship between the energy of the output and input signals of a dynamic system, a relationship between the instant power of the output signal and the energy of the past input signal of a dynamic system is established and further used for FD system design. Another new kind of evaluation function based on the absolute value of wavelet transform of residual signal and the corresponding integrated design approach for FD systems are further proposed     

Exact,almost and optimal input decoupled (delayed) observers

The core of this paper deals with the construction of input-decoupled observers which seek asymptotic estimation of a desired output variable (a linear combination of state and input) of a time-invariant either continuous- or discrete-time system driven by unknown inputs and disturbances. Exact, almost, optimal (suboptimal) and constrained optimal estimation or filtering problems are formulated and studied. All the problems defined and studied here are inherently interconnected, and have a strong common thread of estimation and filtering in the face of the unknown input and external disturbance signals. They are interconnected from a variety of angles, e.g. they are motivated by one another, methods of obtaining the solvability conditions and their methods of solution rely on one another, etc. Thus, a hierarchy of problems and their solutions is built on top of one another. Some of the problems studied here are known in the literature but not in as general a form as is given here, while a majority of the problems studied here are new. A classical variation of all the above problems is also studied here by introducing an l-step delay in estimating the desired output from the measured output. The underlying philosophy throughout this work has been to study most if not all of the facets of estimation and filtering in one stretch under a single folder. Our study of all the above problems has been guided by three important perspectives: (1) obtaining the solvability conditions, both necessary and sufficient; (2) obtaining optimal performance whenever it applies; and (3) developing sound methodologies to design and construct appropriate observers or filters.     

面向互动式网络场景再现的流速控制系统与方法

互动式网络场景再现是一种重要的真实网络流量产生方法.然而,由于流量产生过程的复杂性,基于精确的数学模型对该过程产生流速进行控制是一个较为困难的新问题.文中设计实现了一个面向互动式网络场景再现的流速控制系统,并将网络场景再现过程中的流速控制问题转化为目标跟踪控制问题进行求解.该系统采用一种基于函数近似器的流速控制方法,利用函数近似器对系统的输入输出关系进行描述,通过动态调整系统输入流量来对回放过程输出流量进行跟踪.最后,利用真实网络流量实验考察了文中系统和方法在不同丢包、传输延迟以及会话阻断环境下的实际控制效果,并从收敛时间、产生输入输出、控制误差等角度对系统的控制性能进行了分析.     

Developing a novel inverse data envelopment analysis (DEA) model for evaluating after-sales units

This paper proposes a novel model of inverse data envelopment analysis (IDEA) based on the slack-based measure (SBM) approach. The developed inverse SBM model can maintain relative efficiency of decision making units (DMUs) with new input and output. This model can also measure the input and output volumes when a decision maker (DM) increases efficiency score. The inverse SBM model is a kind of multi-objective non-linear programming (MONLP) problem, which is not easy to solve. Therefore, we suggest a linear programming model for solving inverse SBM model. In this model efficiency score of DMU under evaluation remains unchanged. Furthermore, we suggest an optimal combination of inputs and outputs in the production possibility set (PPS). A case study is presented to demonstrate the efficacy of our proposed model.     

一种热连轧活套多变量控制方法及仿真分析

针对双输入双输出耦合活套控制系统,提出了一种新的多变量控制方法。该方法将活套控制问题视为双输入双输出随动系统渐近跟踪问题,通过建立活套控制系统状态空间模型,采用多变量极点配置方法配置活套控制系统的期望闭环极点,以实现期望性能指标。该方法计算简单,物理概念清晰,克服了常规解耦控制器设计复杂,计算繁琐的弱点。仿真结果表明,系统不仅具有较好的动态性能和稳态性能,而且有很强的鲁棒稳定性。     

Inverse modeling technology for parameter estimation

Computational simulation models are extensively used in the development, design, and analysis of an aircraft engine and its components to represent the physics of an underlying phenomenon. The use of such a model-based simulation in engineering often necessitates the need to estimate model parameters based on physical experiments or field data. This class of problems, referred to as inverse problems (Woodbury KA 2003 Inverse engineering handbook. CRC, Boca Raton) in the literature, can be classified as well-posed or ill-posed depending on the quality (uncertainty) and quantity (amount) of data that are available to the engineer. The development of a generic inverse modeling solver in a probabilistic design system (PEZ version 2.6 user-manual. Probabilistic design system at General Electric Aviation, Cincinnati) requires the ability to handle diverse characteristics in various models. These characteristics include (a) varying fidelity in model accuracy with simulation times from a couple of seconds to many hours; (b) models being black-box, with the engineer having access to only the input and output; (c) nonlinearity in the model; and (d) time-dependent model input and output. This paper demonstrates methods that have been implemented to handle these features, with emphasis on applications in heat transfer and applied mechanics. A practical issue faced in the application of inverse modeling for parameter estimation is ill-posedness, which is characterized by instability and nonuniqueness in the solution. Generic methods to deal with ill-posedness include (a) model development, (b) optimal experimental design, and (c) regularization methods. The purpose of this paper is to communicate the development and implementation of an inverse method that provides a solution for both well-posed and ill-posed problems using regularization based on the prior values of the parameters. In the case of an ill-posed problem, the method provides two solution schemes—a most probable solution closest to the prior, based on the singular value decomposition (SVD), and a maximum a posteriori probability (MAP) solution. The inverse problem is solved as a finite dimensional nonlinear optimization problem using the SVD and/or MAP techniques tailored to the specifics of the application. The objective of the paper is to demonstrate the development and validation of these inverse modeling techniques in several industrial applications, e.g., heat transfer coefficient estimation for disk quenching in process modeling, material model parameter estimation, sparse clearance data modeling, and steady state and transient engine high-pressure compressor heat transfer estimation.     

An inverse analysis method for design optimization with both statistical and fuzzy uncertainties

If the statistical data for the input uncertainties are sufficient to construct the distribution function, the input uncertainties can be treated as random variables to use the reliability-based design optimization (RBDO) method; otherwise, the input uncertainties can be treated as fuzzy variables to use the possibility-based design optimization (PBDO) method. However, many structural design problems include both input uncertainties with sufficient and insufficient data. This paper proposes a new mixed-variable design optimization (MVDO) method using the performance measure approach (PMA) for such design problems. For the inverse analysis, this paper proposes a new most probable/possible point (MPPP) search method called maximal failure search (MFS), which is an integration of the enhanced hybrid mean value method (HMV+) and maximal possibility search (MPS) method. This paper also improves the HMV+ method using an angle-based interpolation. Mathematical and physical examples are used to demonstrate the proposed inverse analysis method and MVDO method.     

Optimization of a proton exchange membrane fuel cell membrane electrode assembly

A computational framework for fuel cell analysis and optimization is presented as an innovative alternative to the time consuming trial-and-error process currently used for fuel cell design. The framework is based on a two-dimensional through-the-channel isothermal, isobaric and single phase membrane electrode assembly (MEA) model. The model input parameters are the manufacturing parameters used to build the MEA: platinum loading, platinum to carbon ratio, electrolyte content and gas diffusion layer porosity. The governing equations of the fuel cell model are solved using Netwon’s algorithm and an adaptive finite element method in order to achieve near quadratic convergence and a mesh independent solution respectively. The analysis module is used to solve the optimization problem of finding the optimal MEA composition for maximizing performance. To solve the optimization problem a gradient-based optimization algorithm is used in conjunction with analytical sensitivities. By using a gradient-based method and analytical sensitivities, the framework presented is capable of solving a complete MEA optimization problem with state-of-the-art electrode models in approximately 30 min, making it a viable alternative for solving large-scale fuel cell problems.     

Kalman filtering in extended noise environments

This note introduces an extended environment for Kalman filtering that considers also the presence of additive noise on input observations in order to solve the problem of optimal (minimal variance) estimation of noise-corrupted input and output sequences. This environment includes as subcases both errors-in-variables filtering (optimal estimate of inputs and outputs from noisy observations) and traditional Kalman filtering (optimal estimate of state and output in presence of state and output noise). A Monte Carlo simulation shows that the performance of this extended filtering technique leads to the expected minimal variance estimates.     

Tracking control of a two-wheeled mobile robot using input–output linearization

This paper discusses the tracking control of two-wheeled mobile robots that have more outputs than inputs. If the number of inputs and the number of outputs are not the same, the inverse of the decoupling matrix in the input–output linearization does not exist. Therefore, a modified input–output linearization method is proposed, to solve the problem by means of a generalized inverse that provides a least-squares solution. The experimental results show that the tracking of posture, position and orientation (the 3-output case) has advantages over position tracking (the 2-output case) from the viewpoint of input power efficiency, because smoother responses can be obtained by considering the orientation.     

A New Well-Solvable Class of PNS Problems

A manufacturing system consists of operating units which convert their input materials into their output materials. In the problem of designing a process network, we have to find a suitable network of operating units which produces the desired products from the given raw materials. If we consider this process network design problem from a structural point of view, then we obtain a combinatorial optimization problem called the Process Network Synthesis or (PNS) problem. It is known that the PNS problem is NP-complete. Here, a new method is presented to reduce the solution of some more difficult PNS problems to the solution of simpler ones, and using this method, a new well-solvable class of PNS problems is established. Received February 12, 1999; revised October 24, 2000     

基于信息融合估计的离散系统最优跟踪控制

针对期望输出和未来干扰无预见的离散线性系统最优跟踪问题,提出一种基于信息融合最优估计的控制方法.若将当前给定值和可测干扰值分别看作系统未来输出和干扰的预见值,则跟踪控制问题可转化为具有无限预见步数的预见控制问题,并将无限预见信息融合成一步等效预见信息,进而获得近似最优融合控制律.对线性直流电机系统和宏观经济系统的仿真结果均验证了该控制器在提高系统跟踪精度和抑制干扰等方面的有效性.     

输入约束不确定系统的点对点迭代学习控制与优化

为解决工业过程中机械臂等特殊重复运行系统的输出在有限时间内无需实现全轨迹跟踪,仅需跟踪期望轨迹上某些特殊关键点的控制问题,针对线性时不变离散系统提出一种基于范数最优的点对点迭代学习控制算法.通过输入输出时间序列矩阵模型变换构建综合性多目标点性能指标函数,求解二次型最优解得到优化迭代学习控制律,同时给出模型标称和不确定情形下最大奇异值形式鲁棒控制算法收敛的充分条件,并进一步推广得到输入约束系统优化控制算法的收敛性结果,最后在三轴龙门机器人模型上验证算法的有效性.