Stability analysis of the cell centered finite-volume M<Emphasis Type="SmallCaps">uscl</Emphasis> method on unstructured grids

The goal of this study is to apply the Muscl scheme to the linear advection equation on general unstructured grids and to examine the eigenvalue stability of the resulting linear semi-discrete equation. Although this semi-discrete scheme is in general stable on cartesian grids, numerical calculations of spectra show that this can sometimes fail for generalizations of the Muscl method to unstructured three-dimensional grids. This motivates our investigation of the influence of the slope reconstruction method and stencil on the eigenvalue stability of the Muscl scheme. A theoretical stability analysis of the first order upwind scheme proves that this method is stable on arbitrary grids. In contrast, a general theoretical result is very difficult to obtain for the Muscl scheme. We are able to identify a local property of the slope reconstruction that is strongly related to the appearance of unstable eigenmodes. This property allows to identify the reconstruction methods that are best suited for stable discretizations. The explicit numerical computation of spectra for a large number of two- and three-dimensional test cases confirms and completes the theoretical results.     

Some criteria for the global finite-time synchronization of two Lorenz–Stenflo systems coupled by a new controller

This paper investigates the global finite-time synchronization of two chaotic Lorenz–Stenflo systems coupled by a new controller called the generalized variable substitution controller. First of all, the generalized variable substitution controller is designed to establish the master–slave finite-time synchronization scheme for the Lorenz–Stenflo systems. And then, based on the finite-time stability theory, a sufficient criterion on the finite-time synchronization of this scheme is rigorously verified in the form of matrix and the corresponding estimation for the synchronization time is analytically given. Applying this criterion, some sufficient finite-time synchronization criteria under various generalized variable substitution controllers are further derived in the algebraic form. Finally, some numerical examples are introduced to compare the results proposed in this paper with those proposed in the existing literature, verifying the effectiveness of the criteria obtained.     

Spread spectrum communication and its circuit implementation using fractional-order chaotic system via a single driving variable

A one-driving-variable adaptive controller for synchronization of a kind of fractional order chaotic system is designed. Based on the theory of spread spectrum communication and the synchronization of one-driving-variable fractional order chaotic system, we propose a new scheme for general spread spectrum communication. Numerical simulation and circuit experiment results are provided to illustrate the effectiveness of the proposed scheme.     

Terminal repeller unconstrained subenergy tunneling (trust) for fast global optimization

A new method for unconstrained global function optimization, acronymedtrust, is introduced. This method formulates optimization as the solution of a deterministic dynamical system incorporating terminal repellers and a novel subenergy tunneling function. Benchmark tests comparing this method to other global optimization procedures are presented, and thetrust algorithm is shown to be substantially faster. Thetrust formulation leads to a simple stopping criterion. In addition, the structure of the equations enables an implementation of the algorithm in analog VLSI hardware, in the vein of artificial neural networks, for further substantial speed enhancement.This work was supported by the Department of Energy, Office of Basic Energy Sciences, Grant No. DE-A105-89-ER14086.     

Dual-Sampling-Rate Moving-Horizon Control of a Class of Linear Systems with Input Saturation and Plant Uncertainty

Moving-horizon control is a type of sampled-data feedback control in which the control over each sampling interval is determined by the solution of an open-loop optimal control problem. We develop a dual-sampling-rate moving-horizon control scheme for a class of linear, continuous-time plants with strict input saturation constraints in the presence of plant uncertainty and input disturbances. Our control scheme has two components: a slow-sampling moving-horizon controller for a nominal plant and a fast-sampling state-feedback controller whose function is to force the actual plant to emulate the nominal plant. The design of the moving-horizon controller takes into account the nonnegligible computation time required to compute the optimal control trajectory.We prove the local stability of the resulting feedback system and illustrate its performance with simulations. In these simulations, our dual-sampling-rate controller exhibits performance that is considerably superior to its single-sampling-rate moving-horizon controller counterpart.     

Passivity-based control for Hopfield neural networks using convex representation

This paper considers the problem of passivity-based controller design for Hopfield neural networks. By making use of a convex representation of nonlinearities, a feedback control scheme based on passivity and Lyapunov theory is presented. A criterion for existence of the controller is given in terms of linear matrix inequality (LMI), which can be easily solved by a convex optimization problem. An example and its numerical simulation are given to show the effectiveness of the proposed method.     

An entropy satisfying MUSCL scheme for systems of conservation laws

Summary. For the high-order numerical approximation of hyperbolic systems of conservation laws, we propose to use as a building principle an entropy diminishing criterion instead of the familiar total variation diminishing criterion introduced by Harten for scalar equations. Based on this new criterion, we derive entropy diminishing projections that ensure, both, the second order of accuracy and all of the classical discrete entropy inequalities. The resulting scheme is a nonlinear version of the classical Van Leer's MUSCL scheme. Strong convergence of this second order, entropy satisfying scheme is proved for systems of two equations. Numerical tests demonstrate the interest of our theory. Received March 28, 1995 / Revised version received June 17, 1995     

On the „bayesification“ of the minimax principle

Summary The term Bayesification is introduced as meaning the adoption of criteria, that keep the Bayes type of solution as far as the knowledge of the probability distribution over the states of nature extends. A general decision model in Wald's sense is developed, Bayes and minimax solution are defined and reasons are given for the Bayesification. Neither the Bayes nor the minimax criterion per se allow Bayesification. In order to get a Bayesification in the above sense the Bayes type of solution is extended to a certain combination of Bayes and minimax type of solution. This extension is generalized in order to provide a mechanism that allows the decision maker to incorporate into the decision criterion any a priori information available. It is shown that special cases of the generalized criterion are Bayes solution, minimax solution, and a solution analogous to that ofHodges andLehmann. Another special case of the generalized criterion is shown as a special case of a criterion proposed bySchneeweiss.

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Zusammenfassung Der Begriff Bayesifikation wird als eine bestimmte Verhaltensweise bei der Wahl von Kriterien eingeführt. Bayesifikation bedeutet das Verhalten, das den Bayes'schen Lösungstyp solange beibehält, wie die Kenntnis der Wahrscheinlichkeitsverteilung über den Zuständen der Realität reicht. Ein allgemeines Entscheidungsmodell im Sinne Walds wird entwickelt, die Bayes'sche und die Minimax-Lösung werden definiert, und es werden Gründe für die Bayesifikation angegeben. Weder das Bayes'sche noch das Minimax-Kriterium gestatten von sich aus die Bayesifikation. Um zur Bayesifikation im obigen Sinne zu gelangen, wird der Bayes'sche Lösungstyp zu einer bestimmten Kombination aus Bayestyp und Minimaxtyp erweitert. Diese Erweiterung wird verallgemeinert, um einen Mechanismus zu schaffen, der dem Entscheidenden erlaubt, jede verfügbare a-priori-Information dem Entscheidungskriterium zu inkorporieren. Es wird gezeigt, daß die Bayes'sche Lösung, die Minimax-Lösung und die Lösung vonHodges undLehmann Sonderfälle dieses verallgemeinerten Kriteriums sind. Ein anderer Sonderfall des verallgemeinerten Kriteriums wird als Sonderfall des vonSchneeweiss vorgeschlagenen Kriteriums dargelegt.

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Diese Studie ist im Rahmen eines Forschungsauftrags des Bundesministeriums der Verteidigung entstanden. Eine erste Fassung hat der Verfasser am 1. März 1965 als Gastvortrag an der University of Alberta, Edmonton (Alberta), die vorliegende Fassung am 5. April auf der Conference on Game Theory an der Princeton University, Princeton (New Jersey) vorgetragen.

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Vorgel. v.:W. Krelle.     

Adaptive timestep control for the contact-stabilized Newmark method

The aim of this paper is to devise an adaptive timestep control in the contact-stabilized Newmark method (ContacX) for dynamical contact problems between two viscoelastic bodies in the framework of Signorini’s condition. In order to construct a comparative scheme of higher order accuracy, we extend extrapolation techniques. This approach demands a subtle theoretical investigation of an asymptotic error expansion of the contact-stabilized Newmark scheme. On the basis of theoretical insight and numerical observations, we suggest an error estimator and a timestep selection which also cover the presence of contact. Finally, we give a numerical example.     

Der plastische Grenzzustand in der schiefen ebenen Erd- oder Schneeschicht

Summary On the basis of recent articles byD. C. Drucker, W. Prager, R. T. Shield andH. Ziegler, the author establishes general relations for the state of plane flow in an idealized soil. A simple geometric interpretation of the relation between the stresses and the strain rates is given. The condition that the dissipation rate associated with an admissible state of motion cannot be negative is transformed into a new criterion, which in many cases facilitates the decision as to whether a state of motion is compatible with a prescribed state of stress or not. As an example, a study is made of the plastic state of an inclined plane layer. Particular emphasis is paid to a comparison of layers of equal inclination but of different cohesion and internal friction. Layers of variable density are also considered.     

Linear preselective policies for stochastic project scheduling

In the context of stochastic resource-constrained project scheduling we introduce a novel class of scheduling policies, the linear preselective policies. They combine the benefits of preselective policies and priority policies; two classes that are well known from both deterministic and stochastic scheduling. We study several properties of this new class of policies which indicate its usefulness for computational purposes. Based on a new representation of preselective policies as and/or precedence constraints we derive efficient algorithms for computing earliest job start times and state a necessary and sufficient dominance criterion for preselective policies.  A computational experiment based on 480 instances empirically validates the theoretical findings.     

Robust H{infty} control of uncertain systems with time-varying state and control input delays

In this paper, a new method for robust H controller of uncertainsystems with time-varying state and control input delays isproposed. A sufficient condition, which is dependent on themaximum value of the time derivative of time-varying delay,is also presented for the existence of H controller. The proposedcontroller not only stabilizes closed-loop uncertain systemsbut also guarantees a prescribed H norm bound of the closed-looptransfer matrix from the disturbance to controlled output. Furthermore,we propose a new robust stability criterion to decide the allowedmaximum bound of plant uncertainty which still can be stabilizedby proposed robust controller. An example given illustratesthe availability of the proposed design method.     

Quadratic optimal synchronization of uncertain chaotic systems

This paper investigates the quadratic optimal synchronization of uncertain chaotic systems with parameter mismatch, parametric perturbations and external disturbances on both master and slave systems. A robust control scheme based on Lyapunov stability theory and quadratic optimal control approach is derived to realize chaotic synchronization. The sufficient criterion for stability condition is formulated in a linear matrix inequality (LMI) form. The effect of uncertain parameters and external disturbance is suppressed to an H_∞ norm constraint. An adaptive algorithm is proposed to adjust the uncertain bound in the robust controller avoiding the chattering phenomena. The simulation results for synchronization of the Chua’s circuit system and the Lorenz system demonstrate the effectiveness of the proposed scheme.     

A Hybrid Robust Adaptive Sliding Mode Controller for partially modelled systems: Discrete-time Lyapunov stability analysis and application

This work presents a new discrete-time Hybrid Robust Adaptive Sliding Mode Controller, developed from the union of a Robust Model Reference Adaptive Controller, an Adaptive Sliding Mode Controller, and an Adaptive One Sample Ahead Preview Controller in an unique control structure. Robust Model Reference Adaptive Controller is an adequate direct adaptive control strategy to control partially known plants, but can present slow closed-loop response to ensure global stability. Therefore, an adaptive One Sample Ahead Preview controller is incorporated to accelerate transient regimes, once it tries to track reference signal in one sample. Furthermore, an adaptive Sliding Mode Controller is also merged in the controller structure to help controller performance in transient regime and it also improves relevantly the steady state response in a scenario of several unmodelled dynamics Stability analysis of this controller using Lyapunov criterion and its robustness proof are provided, considering the plant subjected to unmodelled dynamics, which provides controller design constraints. These proofs show the controller is globally stable, and the tracking error tends to a residual set in steady state, even in the presence of matched and unmatched dynamics. Numerical simulations of the Hybrid Robust Adaptive Sliding Mode Controller applied on an unstable nonminimum-phase plant are presented, where only part of the overall plant is take into consideration for controller design. Results corroborate the feasibility and robustness of the developed control strategy and the performance superiority when compared to an adaptive One Sample Ahead Preview controller, with a 75% tracking error reduction in a scenario of several unmodelled dynamics.     

Generic pole assignability,structurally constrained controllers and unimodular completion

In this paper we assume dynamical systems are represented by linear differential-algebraic equations (DAEs) of order possibly higher than one. We consider a structured system of DAEs for both the to-be-controlled plant and the controller. We model the structure of the plant and the controller as an undirected and bipartite graph and formulate necessary and sufficient conditions on this graph for the structured controller to generically achieve arbitrary pole placement. A special case of this problem also gives new equivalent conditions for structural controllability of a plant. Use of results in matching theory, and in particular, ‘admissibility’ of edges and ‘elementary bipartite graphs’, make the problem and the solution very intuitive. Further, our approach requires standard graph algorithms to check the required conditions for generic arbitrary pole placement, thus helping in easily obtaining running time estimates for checking this. When applied to the state space case, for which the literature has running time estimates, our algorithm is faster for sparse state space systems and comparable for general state space systems.     

Indecomposable quasi‐characteristics scheme on pyramidal stencil and its application for numerical simulation of two‐phase flows through heterogeneous porous medium

A new high‐resolution indecomposable quasi‐characteristics scheme with monotone properties based on pyramidal stencil is considered. This scheme is based on consideration of two high‐resolution numerical schemes approximated governing equations on the pyramidal stencil with different kinds of dispersion terms approximation. Two numerical solutions obtained by these schemes are analyzed, and the final solution is chosen according to the special criterion to provide the monotone properties in regions where discontinuities of solutions could arise. This technique allows to construct the high‐order monotone solutions and keeps both the monotone properties and the high‐order approximation in regions with discontinuities of solutions. The selection criterion has a local character suitable for parallel computation. Application of the proposed technique to the solution of the time‐dependent 2D two‐phase flows through the porous media with the essentially heterogeneous properties is considered, and some numerical results are presented. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 44–55, 2002     

Adaptive anti control of chaos for robot manipulators with experimental evaluations

Roughly speaking, anti control of chaos consists in injecting a chaotic behavior to a system by means of a control scheme. This note introduces a new scheme to solve the anti control of chaos for robot manipulators. The proposed controller uses an adaption law to estimate the robot parameters on line. Thus, the controller does not require any knowledge of the physical parameters of the manipulator, such as masses, lengths of the links, moments of inertia, etc. The new scheme is based in the velocity field control paradigm, hence the specification of a chaotic system to define a desired velocity field is required. Experimental results in a two degrees-of-freedom direct-drive robot illustrate the practical feasibility of the introduced theory. In order to achieve anti control of chaos of our experimental system, two different chaotic attractors are used: the Genesio-Tesi system and a Jerk-type system. Results showed that the controller is able to inject the chaotic behavior to the robot while the robot parameters are estimated on line.     

Modeling aspects and numerical analysis of offshore systems

There is a strong effort to improve the efficiency of renewable energy systems in order to reduce the CO₂ emissions. This paper addresses an approach to increase the efficiency of an ocean wave energy plant with a model based predictive controller. For this controller it is necessary to have a prediction of the ocean waves and a model of the whole system. The future development of the ocean waves is predicted by an AR-model. A system identification yields the model of the energy plant. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

Output feedback control for MIMO nonlinear systems using factorization

A new output feedback adaptive control scheme for multi-input and multi-output (MIMO) nonlinear systems is presented based on the high frequency gain matrix factorization and the backstepping approach with vector form. The only required prior knowledge about the high frequency gain matrix of the linear part of the system is the signs of its leading principal minors. The proposed controller is a dynamic one that only needs the measurement of the system output, and the observer and the filters are introduced in order to construct a virtual estimate of the unmeasured system states. The global stability of the closed-loop systems is guaranteed through this control scheme, and the tracking error converges to zero. Finally, the numerical simulation results illustrate the effectiveness of the proposed scheme.