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作者： Akhtar, Imran Borggaard, Jeff Stoyanov, Miroslav Zietsman, Lizette Interdisciplinary Center for Applied Mathematics Virginia Tech Blacksburg VA 24061 United States

ISBN: (纸本)9781600867453

Design of feedback controls for distributed parameter systems in fluid flows remains a formidable task for researchers. One popular approach is "reduce-then-contol" which has been successfully implemented by first developing a reduced-order model and then applying the control theory. However, this approach has several drawbacks, such as ensuring the unknown feedback functional gains are well represented in the reduced-basis. Control of vortex shedding past a circular cylinder has become a canonical problem to test or validate a flow control design. Control of the von Karman vortex street has many applications, e.g. when designing ocean platforms-as the vortex shedding induces an oscillatory fatigue load on structural components. In this paper, we follow "control-then-reduce" approach to control von Kármán vortex street (periodic shedding) in a channel using cylinder rotation as the actuation. The approach is to linearize the Navier-Stokes equations about the desired (unstable) steady-state flow and design the control for the regulator problem using distributed parameter control theory. The Oseen equations are discretized using finite element methods and the resulting LQR control problem requires the solution to algebraic Riccati equations with very high rank. The feedback gains are computed using model reduction in a "control-then-reduce" framework. Model reduction is used to efficiently solve both Chandrasekhar and Lyapunov equations. The reduced Chandrasekhar equations are used to produce a stable initial guess for a Kleinman-Newton iteration. The high-rank Lyapunov equations associated with Kleinman-Newton iterations are solved by applying a novel model reduction strategy. numerical results for a 2-D cylinder wake problem at a Reynolds number of 100 demonstrate that this approach works when perturbations from the steady-state solution are small enough. In this study, we map the functional gains computed for the flow past a cylinder in a channel onto an exterior f

关键词： Circular cylinders

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Quantitative Nonlinear Analysis of Autocatalytic Pathways with applications to Glycolysis

Quantitative Nonlinear Analysis of Autocatalytic Pathways wi...

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American Control conference

作者： Gentian Buzi Ufuk Topcu John C. Doyle Control and Dynamical Systems California Institute of Technology Pasadena CA 91125 USA

ISBN: (纸本)9781424474264

Autocatalytic pathways are frequently encountered in biological networks. One such pathway, the glycolytic pathway, is of special importance and has been studied extensively. Using tools from linear systems theory, our previous work on a simple two dimensional model of glycolysis demonstrated that autocatalysis can aggravate control performance and contribute to instability. Here, we expand this work and study properties of nonlinear autocatalytic pathway models (of which glycolysis is an example). Changes in the concentration of metabolites and catalyzing enzymes during the lifetime of the cell can perturb the system from the nominal operating point of the pathway. We investigate effects of such perturbations through the estimation of invariant subsets of the region of attraction around nominal operating conditions (i.e., a measure of the set of perturbations from which the cell recovers). numerical experiments demonstrate that systems that are robust with respect to perturbations in parameter space have easily "verifiable" region of attraction properties in terms of proof complexity.

关键词： glycolysis perturbation region of attraction Pathway Autocatalysis Workstations NONlinear ANALYSIS Operating conditions control performance Cells parameter space methods

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Discretising effectively a linear singular differential system by choosing an appropriate sampling period

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IET CONTROL theory AND applications 2009年第7期3卷 823-833页

作者： Kalogeropoulos, G. I. Karageorgos, A. D. Pantelous, A. A. Univ Athens Dept Math GR-10679 Athens Greece

Two main goals are to discretise the solution of an autonomous linear singular continuous-time system and to compare the discretised with the continuous solution at fixed time moments. Practically speaking, we are interested in such kind of systems, since they are inherent in many physical, economical and engineering phenomena. The complex Kronecker canonical form decomposes the singular system into five sub-systems, whose solutions are obtained. Moreover, in order for the norm of the difference between the two solutions to be smaller than a fully pre-defined, acceptable bound, the sampling period should be arranged in a particular interval. A numerical example is also available.

关键词： matrix pencil theory linear systems differential equations autonomous linear singular continuous-time system Differential equations (numerical analysis) Other topics in statistics Probability theory, stochastic processes, and statistics linear algebra (numerical analysis) sampling methods complex Kronecker canonical form matrix decomposition sampling period linear singular differential system discretisation continuous time systems numerical approximation and analysis

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A Review of Vector Convergence Acceleration methods, With applications to linear algebra Problems

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INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY 2009年第8期109卷 1631-1639页

作者： Brezinski, C. Redivo-Zaglia, M. Univ Padua Dipartimento Matemat Pura & Applicata I-35121 Padua Italy Univ Sci & Tech Lille Flandres Artois CNRS UFR Math Pures & Appl Lab Paul PainleveUMR 8524 F-59655 Villeneuve Dascq France

In this article, in a few pages, we will try to give an idea of convergence acceleration methods and extrapolation procedures for vector sequences, and to present some applications to linear algebra problems and to the treatment of the Gibbs phenomenon for Fourier series in order to show their effectiveness. The interested reader is referred to the literature for more details. In the bibliography, due to space limitation, we will only give the more recent items, and, for older ones, we refer to Brezinski and Redivo-Zaglia, Extrapolation methods. (Extrapolation methods. theory and practice, North-Holland, 1991). This book also contains, on a magnetic support, a library (in Fortran 77 language) for convergence acceleration algorithms and extrapolation methods. (C) 2008 Wiley Periodicals, Inc. Int J Quantum Chem 109: 1631-1639, 2009

关键词： extrapolation projection sequence transformations linear algebra linear systems regularization Fourier series Gibbs phenomenon

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Adaptive H_∞ control for a class of non-linear systems using neural networks

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IET CONTROL theory AND applications 2009年第7期3卷 813-822页

作者： Liu, Y. Jia, Y. M. Beihang Univ Res Div 7 Beijing 100191 Peoples R China

An adaptive H-infinity controller is designed for a class of non-linear dynamical systems by using neural networks (NNs) to approximate the unknown system function. It is shown that under bounded initial conditions, the H-infinity performance from the external disturbance to the controlled output is achieved with a prescribed attenuation level. A systematic design procedure is then developed for the synthesis of the adaptive H-infinity controller by solving two linear matrix inequalities (LMIs). Finally, a numerical example is included to demonstrate the effectiveness of the proposed controller.

关键词： H∞ control adaptive control neural network systematic design procedure neurocontrollers function approximation control system synthesis linear matrix inequality Control system analysis and synthesis methods Nonlinear control systems system function approximation linear algebra (numerical analysis) adaptive H∞ controller synthesis Self-adjusting control systems nonlinear control systems Interpolation and function approximation (numerical analysis) Neurocontrol Optimal control linear matrix inequalities nonlinear dynamical systems nonlinear dynamical system

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Memory state feedback controller design for singular systems with multiple internal constant point delays

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IET CONTROL theory AND applications 2009年第6期3卷 631-641页

作者： Xie, Y. F. Gui, W. H. Wang, Y. L. Jiang, Z. H. Ding, S. X. Cent S Univ Sch Informat Sci & Engn Changsha 410083 Peoples R China Univ Duisburg Essen Inst Automat Control & Complex Syst D-47057 Duisburg Germany

The problem of delay-dependent stabilisation for singular linear continuous-time systems with multiple internal incommensurate constant point delays is investigated. The condition when a singular system subject to point delays is regular independent of time delays is given and it can be easily tested with numerical or algebraic methods. Based on the Lyapunov-Krasovskii functional approach and the descriptor integral-inequality lemma, a sufficient condition for delay-dependent stability is obtained. The main idea is to design multiple memory state feedback control laws such that the resulting closed-loop system is regular independent of time delays, impulse free and stable via solving matrix inequality problem. An explicit expression for the desired memory state feedback control law is also given. Finally, a numerical example is presented to illustrate the effectiveness and the availability for the proposed method.

关键词： matrix inequality problem multiple internal constant point time delay Lyapunov-Krasovskii functional approach algebraic method stability control system synthesis Stability in control theory Control system analysis and synthesis methods state feedback closed loop systems matrix algebra linear systems linear algebra (numerical analysis) Lyapunov methods delays delay-dependent stability continuous time systems closed-loop system memory state feedback controller design singular linear continuous-time system Distributed parameter control systems descriptor integral-inequality lemma

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Repetitive control by output error for a class of uncertain time-delay systems

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IET CONTROL theory AND applications 2009年第9期3卷 1283-1292页

作者： Quan, Q. Yang, D. Cai, K. -Y. Jiang, J. Beijing Univ Aeronaut & Astronaut Dept Automat Control Beijing 100191 Peoples R China Chinese Acad Space Technol Beijing 100094 Peoples R China

The problem of designing output error controllers to track periodic reference signals for a class of uncertain linear time-delay systems subject to periodic disturbances is addressed. A repetitive controller, which is a type of output error controller, is developed for these systems and a sufficient condition for stability of the closed-loop system is derived by applying the Lyapunov-Krasovskii functional and linear matrix inequalities (LMIs). In order to relax the stability condition, the theory of the modified repetitive control ( RC) system is extended to the systems represented by irrational transfer functions. Based on the extended theory of the modified RC system, a modified repetitive controller, another type of output error controller, is developed for these systems and sufficient conditions for stability of the closed-loop system are derived in terms of a frequency-domain criterion and LMI. numerical simulations are presented to demonstrate the effectiveness of the proposed controllers.

关键词： error statistics Other topics in statistics periodic reference signal repetitive control frequency-domain criterion time-varying systems Lyapunov-Krasovskii function Time-varying control systems stability control system synthesis Stability in control theory linear matrix inequality Control system analysis and synthesis methods closed loop systems uncertain time-delay system linear systems linear algebra (numerical analysis) delays Lyapunov methods output error uncertain systems linear matrix inequalities closed-loop system Distributed parameter control systems periodic control

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Non-fragile dynamic output feedback control for linear systems with time-varying delay

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IET CONTROL theory AND applications 2009年第8期3卷 995-1005页

作者： Li, L. Jia, Y. Beihang Univ Dept Syst & Control Beijing 100191 Peoples R China

This paper is devoted to the problems of non-fragile H-infinity and L-2-L-infinity control for a class of linear systems with time-varying state delay. The purpose is to design a dynamic output feedback controller with additive gain variations such that the closed-loop system is asymptotically stable while satisfying a prescribed H-infinity (or L-2-L-infinity) performance level. By using linear matrix inequality approach, a delay-dependent stability criterion is obtained by introducing a new type of Lyapunov-Krasovskii functional. Based on the obtained criterion, sufficient conditions for the existence of desired controllers are derived, and the corresponding stabilisation dynamic output feedback controller design algorithm is proposed. numerical examples are included to illustrate the benefit and effectiveness of the proposed method.

关键词： H∞ control nonfragile L2-L∞ control time-varying systems Lyapunov-Krasovskii functional linear matrix inequality approach Time-varying control systems Stability in control theory control system synthesis Control system analysis and synthesis methods time-varying state delay closed loop systems linear systems feedback linear algebra (numerical analysis) delays Lyapunov methods nonfragile H∞ control additive gain variation delay-dependent stability criterion Optimal control linear matrix inequalities asymptotically stable closed-loop system linear system nonfragile dynamic output feedback controller design Distributed parameter control systems asymptotic stability

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H_∞-filtering and state feedback control for discrete-time switched descriptor systems

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IET CONTROL theory AND applications 2009年第6期3卷 661-670页

作者： Koenig, D. Marx, B. Inst Natl Polytech Grenoble CNRS INPG UJF UMR 5216 Gipsa Lab F-38402 St Martin Dheres France Nancy Univ CRAN UMR 7039 CNRS F-54516 Vandoeuvre Les Nancy France

The problem of H-infinity filtering for a class of discrete-time switched systems with unknown inputs is investigated. By using a switched Lyapunov function, sufficient conditions for the solution of this problem are obtained in terms of linear matrix inequalities. Filtering is envisaged both with proportional and proportional integral observers. In addition, the results obtained in observer design are transposed to the controller design for switched descriptor systems. The control of a switched uncertain descriptor system is also treated. A numerical example is given to illustrate the presented results.

关键词： H∞ control Signal processing theory filtering theory proportional integral observer PI control time-varying systems Time-varying control systems Stability in control theory control system synthesis linear matrix inequality Control system analysis and synthesis methods state feedback state feedback control H∞-filtering Lyapunov function discrete-time switched descriptor system linear algebra (numerical analysis) Lyapunov methods uncertain systems linear matrix inequalities Discrete control systems Optimal control uncertain system observers discrete time systems

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Stability and robust stabilisation for uncertain discrete stochastic hybrid singular systems with time delay

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IET CONTROL theory AND applications 2009年第9期3卷 1217-1225页

作者： Ma, S. Boukas, E. K. Shandong Univ Sch Math Jinan 250100 Peoples R China Ecole Polytech Dept Mech Engn Stn Ctr Ville Montreal PQ H3C 3A7 Canada

The stochastic stability and robust stochastic stabilisation for time-delay discrete Markovian jump singular systems with parameter uncertainties are discussed. Based on stochastic Lyapunov functional, a delay-dependent linear matrix inequalities (LMIs) condition for the time-delay discrete Markovian jump singular systems to be regular, causal and stochastically stable is given. With this condition, the problem of robust stochastic stabilisation is solved. A numerical example to illustrate the effectiveness of the method is given.

关键词： stochastic systems discrete systems robust stochastic stabilisation Time-varying control systems Stability in control theory stochastic Lyapunov functional stochastic stability uncertain discrete stochastic hybrid singular system robust control delay-dependent linear matrix inequalities linear algebra (numerical analysis) delays Lyapunov methods time delay discrete Markovian jump singular system uncertain systems Discrete control systems linear matrix inequalities Markov processes Distributed parameter control systems

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