Download or read book Uncertainty Analysis of Optimal Dynamic Linear System Models written by Lee Mazurek and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear time invariant system models are insufficient for physical systems which have deterministic or stochastic time varying parameters. These parameters can be important to system performance, as in the case of a vehicle suspension, or safety, as in the case of a structural health monitoring problem. Time varying models are difficult to uniquely identify because they can have many parameters. For deterministic systems, researchers often assume input bases of variation or assume the bandwidth of variation. For stochastic systems, researchers often assume the correlation structure of the system parameters and the input. This thesis presents the novel application of matrix calculus methods which allow an analyst to choose the assumed portions of a system model's structure in order to find unknown system coefficients uniquely. These structured system identification methods are used to provide solutions for the time varying impulse response, or the novel solution for input-time variation of example systems. Traditional optimal and adaptive identification methods are also reproduced by this framework. Consistent methods are derived to evaluate the coherence and variance for any structured system model. The results presented in this thesis allow novel and traditional identification methods to be analyzed in a common structured identification framework. Traditional and novel model structures are compared using a suspension and structural health monitoring problem to show where novel methods improve prediction error and improve the understanding of model variance terms. Future work is expected to find additional useful model structures and solution methods based on this framework.
Download or read book Structural Sensitivity Analysis and Optimization 1 written by Kyung K. Choi and published by Springer Science & Business Media. This book was released on 2006-12-30 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Extensive numerical methods for computing design sensitivity are included in the text for practical application and software development. The numerical method allows integration of CAD-FEA-DSA software tools, so that design optimization can be carried out using CAD geometric models instead of FEA models. This capability allows integration of CAD-CAE-CAM so that optimized designs can be manufactured effectively.
Download or read book Robust Control of Uncertain Dynamic Systems written by Rama K. Yedavalli and published by Springer Science & Business Media. This book was released on 2013-12-05 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook aims to provide a clear understanding of the various tools of analysis and design for robust stability and performance of uncertain dynamic systems. In model-based control design and analysis, mathematical models can never completely represent the “real world” system that is being modeled, and thus it is imperative to incorporate and accommodate a level of uncertainty into the models. This book directly addresses these issues from a deterministic uncertainty viewpoint and focuses on the interval parameter characterization of uncertain systems. Various tools of analysis and design are presented in a consolidated manner. This volume fills a current gap in published works by explicitly addressing the subject of control of dynamic systems from linear state space framework, namely using a time-domain, matrix-theory based approach. This book also: Presents and formulates the robustness problem in a linear state space model framework. Illustrates various systems level methodologies with examples and applications drawn from aerospace, electrical and mechanical engineering. Provides connections between lyapunov-based matrix approach and the transfer function based polynomial approaches. Robust Control of Uncertain Dynamic Systems: A Linear State Space Approach is an ideal book for first year graduate students taking a course in robust control in aerospace, mechanical, or electrical engineering.
Download or read book Dynamics under Uncertainty written by Dragan Pamucar and published by MDPI. This book was released on 2021-09-08 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: The dynamics of systems have proven to be very powerful tools in understanding the behavior of different natural phenomena throughout the last two centuries. However, the attributes of natural systems are observed to deviate from their classical states due to the effect of different types of uncertainties. Actually, randomness and impreciseness are the two major sources of uncertainties in natural systems. Randomness is modeled by different stochastic processes and impreciseness could be modeled by fuzzy sets, rough sets, Dempster–Shafer theory, etc.
Download or read book Uncertainty Analysis in Engineering and Sciences Fuzzy Logic Statistics and Neural Network Approach written by Bilal M. Ayyub and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty has been of concern to engineers, managers and . scientists for many centuries. In management sciences there have existed definitions of uncertainty in a rather narrow sense since the beginning of this century. In engineering and uncertainty has for a long time been considered as in sciences, however, synonymous with random, stochastic, statistic, or probabilistic. Only since the early sixties views on uncertainty have ~ecome more heterogeneous and more tools to model uncertainty than statistics have been proposed by several scientists. The problem of modeling uncertainty adequately has become more important the more complex systems have become, the faster the scientific and engineering world develops, and the more important, but also more difficult, forecasting of future states of systems have become. The first question one should probably ask is whether uncertainty is a phenomenon, a feature of real world systems, a state of mind or a label for a situation in which a human being wants to make statements about phenomena, i. e. , reality, models, and theories, respectively. One cart also ask whether uncertainty is an objective fact or just a subjective impression which is closely related to individual persons. Whether uncertainty is an objective feature of physical real systems seems to be a philosophical question. This shall not be answered in this volume.
Download or read book Dynamic Systems Control written by Robert E. Skelton and published by . This book was released on 1988 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text deals with matrix methods for handling, reducing, and analyzing data from a dynamic system, and covers techniques for the design of feedback controllers for those systems which can be perfectly modeled. Unlike other texts at this level, this book also provides techniques for the design of feedback controllers for those systems which cannot be perfectly modeled. In addition, presentation draws attention to the iterative nature of the control design process, and introduces model reduction and concepts of equivalent models, topics not generally covered at this level. Chapters cover mathematical preliminaries, models of dynamic systems, properties of state space realizations, controllability and observability, equivalent realizations and model reduction, stability, optimal control of time-variant systems, state estimation, and model error concepts and compensation. Extensive appendixes cover the requisite mathematics.
Download or read book Uncertain Models and Robust Control written by Alexander Weinmann and published by Springer Science & Business Media. This book was released on 1991 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: INHALT LANG: Introduction: Introductory Survey; Vector Norm. Matrix Norm. Matrix Measure; Functional Analysis, Function Norms and Control Signals.- Differential Sensitivity. Small-Scale Perturbation: Kronecker Calculus in Control Theory; Analysis Using Matrices and Control Theory; Eigenvalue and Eigenvector Differential Sensitivity; Transition Matrix Differential Sensitivity; Characteristic Polynomial Differential Sensitivity; Optimal Control and Performance Sensitivity; Desensitizing Control.- Robustness in the Time Domain: General Stability Bounds in Perturbed Systems; Robust Dynamic Interval Systems; Lyapunov-Based Methods for Perturbed Continuous-Time Systems; Lyapunov-Based Methods for Perturbed Discrete-Time Systems; Robust Pole Assignment; Models for Optimal and Interconnected Systems; Robust State Feedback Using Ellipsoid Sets; Robustness of Observers and Kalman-Bucy Filters; Initial Condition Perturbation, Overshoot and Robustness; Lnp-Stability and Robust Nonlinear Control.- Robustness in the Frequency Domain: Uncertain Polynomials. Interval Polynomials; Eigenvalues and Singular Values of Complex Matrices; Resolvent Matrix and Stability Radius; Robustness Via Singular-Value Analysis; Generalized Nyquist Stability of Perturbed Systems; Block-Structured Uncertainty and Structured Singular Value; Performance Robustness; Robust Controllers Via Spectral Radius Technique.- Coprime Factorization and Minimax Frequency Optimization: Robustness Based on the Internal Model Principle; Parametrization and Factorization of Systems; Hardy Space Robust Design.- Robustness Via Approximative Models: Robust Hyperplane Design in Variable Structure Control; SIngular Perturbaitons. Unmodelled High-Frequendy Dynamics; Control Using Aggregation Models; Optimum Control of Approximate and Nonlinear Systems; System Analysis via Orthogonal Functions; System Analysis Via Pulse Functions and Piecewise Linear Functions; Orthogonal Decomposition Applications.
Download or read book Applied Research in Uncertainty Modeling and Analysis written by Bilal M. Ayyub and published by Springer Science & Business Media. This book was released on 2007-12-29 with total page 547 pages. Available in PDF, EPUB and Kindle. Book excerpt: The application areas of uncertainty are numerous and diverse, including all fields of engineering, computer science, systems control and finance. Determining appropriate ways and methods of dealing with uncertainty has been a constant challenge. The theme for this book is better understanding and the application of uncertainty theories. This book, with invited chapters, deals with the uncertainty phenomena in diverse fields. The book is an outgrowth of the Fourth International Symposium on Uncertainty Modeling and Analysis (ISUMA), which was held at the center of Adult Education, College Park, Maryland, in September 2003. All of the chapters have been carefully edited, following a review process in which the editorial committee scrutinized each chapter. The contents of the book are reported in twenty-three chapters, covering more than . . ... pages. This book is divided into six main sections. Part I (Chapters 1-4) presents the philosophical and theoretical foundation of uncertainty, new computational directions in neural networks, and some theoretical foundation of fuzzy systems. Part I1 (Chapters 5-8) reports on biomedical and chemical engineering applications. The sections looks at noise reduction techniques using hidden Markov models, evaluation of biomedical signals using neural networks, and changes in medical image detection using Markov Random Field and Mean Field theory. One of the chapters reports on optimization in chemical engineering processes.
Download or read book Modeling Estimation and Control of Systems with Uncertainty written by G.B. DiMasi and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the papers that have been presented at the Conference on Modeling and Control of Uncertain Systems held in Sopron, Hungary on September 3-7, 1990, organised within the framework of the activities of the System and Decision Sciences Program of IIASA - the International Institute for Applied Systems Analysis. The importance of the subject has drawn the attention of researchers all over the world since several years. In fact, in most actual applications the knowledge about the system under investigation presents aspects of uncertainty due to measurement errors or poor understanding of the rele vant underlying mechanisms. For this reason models that take into account these intrinsic uncertainties have been used and techniques for the analysis of their behavior as well as for their estimation and control have been devel oped. The main ways to deal with uncertainty consist in its description by stochastic processes or in terms of set-valued dynamics and this volume col lects relevant contributions in both directions. However, in order to avoid undesirable distinctions between these approaches, but on the contrary to stress the unity of ideas, we decided to organize the papers according to the alphabetical order of their authors. We should like to take this opportunity to thank IIASA for supporting the Conference and the Hungarian National Member Organization for the kind hospitality in Sopron. Finally we would like to express our gratitude to Ms. Donna Huchthausen for her valuable secretarial assistance. Vienna, February 20, 1991 GIOVANNI B.
Download or read book Sensitivity Analysis in Linear Systems written by Assem Deif and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: A text surveying perturbation techniques and sensitivity analysis of linear systems is an ambitious undertaking, considering the lack of basic comprehensive texts on the subject. A wide-ranging and global coverage of the topic is as yet missing, despite the existence of numerous monographs dealing with specific topics but generally of use to only a narrow category of people. In fact, most works approach this subject from the numerical analysis point of view. Indeed, researchers in this field have been most concerned with this topic, although engineers and scholars in all fields may find it equally interesting. One can state, without great exaggeration, that a great deal of engineering work is devoted to testing systems' sensitivity to changes in design parameters. As a rule, high-sensitivity elements are those which should be designed with utmost care. On the other hand, as the mathematical modelling serving for the design process is usually idealized and often inaccurately formulated, some unforeseen alterations may cause the system to behave in a slightly different manner. Sensitivity analysis can help the engineer innovate ways to minimize such system discrepancy, since it starts from the assumption of such a discrepancy between the ideal and the actual system.
Download or read book Numerical Methods for Uncertainty Analysis in Dynamical Systems written by Kyungeun Kim and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The current methods for uncertainty analysis in dynamical systems are restricted in terms of computational cost and evaluation domain since they either use grid points or work only along trajectories. To break through these problems we present a new method: the Rothe & maximum-entropy method which follows the steps below. A deterministic dynamical system with initial value uncertainties can be analyzed via the uncertainty propagation which is based on the Liouville equation in the form of the first-order linear partial differential equation. On this equation we conduct a semi-discretization in time via A-stable rational approximations of consistency order k and this yields the stationary spatial problem. This spatial problem now can be solved by the spatial discretization scheme: we propose the maximum-entropy approximation which provides unbiased interpolations even with fewer numbers of scattered points. Through these steps we finally obtain a system of linear equations for the evolution of the probability density function ut, which can be easily solved in several ways. This method can provide more efficiency in terms of computation time thanks to using fewer numbers of scattered points instead of grid points. Also, it enables the constant tracking of probability density functions in a specific fixed domain of interest and this is especially effective for switched systems. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/151898
Download or read book Model Validation and Uncertainty Quantification Volume 3 written by H. Sezer Atamturktur and published by Springer Science & Business Media. This book was released on 2014-04-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data
Download or read book Linear Dynamical Systems written by Mircea D. Grigoriu and published by Springer Nature. This book was released on 2021-01-30 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a concise, clear, and rigorous presentation of the dynamics of linear systems that delivers the necessary tools for the analysis and design of mechanical/ structural systems, regardless of their complexity. The book is written for senior undergraduate and first year graduate students as well as engineers working on the design of mechanical/structural systems subjected to dynamic actions, such as wind/earthquake engineers and mechanical engineers working on wind turbines. Professor Grigoriu's lucid presentation maximizes student understanding of the formulation and the solution of linear systems subjected to dynamic actions, and provides a clear distinction between problems of practical interest and their special cases. Based on the author's lecture notes from courses taught at Cornell University, the material is class-tested over many years and ideal as a core text for a range of classes in mechanical, civil, and geotechnical engineering, as well as for self-directed learning by practitioners in the field.
Download or read book Uncertain Dynamic Systems written by Fred C. Schweppe and published by Prentice Hall. This book was released on 1973 with total page 588 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modelling Optimization and Control of Biomedical Systems written by Efstratios N. Pistikopoulos and published by John Wiley & Sons. This book was released on 2017-10-26 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shows the newest developments in the field of multi-parametric model predictive control and optimization and their application for drug delivery systems This book is based on the Modelling, Control and Optimization of Biomedical Systems (MOBILE) project, which was created to derive intelligent computer model-based systems for optimization of biomedical drug delivery systems in the cases of diabetes, anaesthesia, and blood cancer. These systems can ensure reliable and fast calculation of the optimal drug dosage without the need for an online computer—while taking into account the specifics and constraints of the patient model, flexibility to adapt to changing patient characteristics and incorporation of the physician’s performance criteria, and maintaining the safety of the patients. Modelling Optimization and Control of Biomedical Systems covers: mathematical modelling of drug delivery systems; model analysis, parameter estimation, and approximation; optimization and control; sensitivity analysis & model reduction; multi-parametric programming and model predictive control; estimation techniques; physiologically-based patient model; control design for volatile anaesthesia; multiparametric model based approach to intravenous anaesthesia; hybrid model predictive control strategies; Type I Diabetes Mellitus; in vitro and in silico block of the integrated platform for the study of leukaemia; chemotherapy treatment as a process systems application; and more. Introduces readers to the Modelling, Control and Optimization of Biomedical Systems (MOBILE) project Presents in detail the theoretical background, computational tools, and methods that are used in all the different biomedical systems Teaches the theory for multi-parametric mixed-integer programming and explicit optimal control of volatile anaesthesia Provides an overview of the framework for modelling, optimization, and control of biomedical systems This book will appeal to students, researchers, and scientists working on the modelling, control, and optimization of biomedical systems and to those involved in cancer treatment, anaesthsia, and drug delivery systems.
Download or read book The nth Order Comprehensive Adjoint Sensitivity Analysis Methodology Volume I written by Dan Gabriel Cacuci and published by Springer Nature. This book was released on 2022-07-19 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The computational models of physical systems comprise parameters, independent and dependent variables. Since the physical processes themselves are seldom known precisely and since most of the model parameters stem from experimental procedures which are also subject to imprecisions, the results predicted by these models are also imprecise, being affected by the uncertainties underlying the respective model. The functional derivatives (also called “sensitivities”) of results (also called “responses”) produced by mathematical/computational models are needed for many purposes, including: (i) understanding the model by ranking the importance of the various model parameters; (ii) performing “reduced-order modeling” by eliminating unimportant parameters and/or processes; (iii) quantifying the uncertainties induced in a model response due to model parameter uncertainties; (iv) performing “model validation,” by comparing computations to experiments to address the question “does the model represent reality?” (v) prioritizing improvements in the model; (vi) performing data assimilation and model calibration as part of forward “predictive modeling” to obtain best-estimate predicted results with reduced predicted uncertainties; (vii) performing inverse “predictive modeling”; (viii) designing and optimizing the system. This 3-Volume monograph describes a comprehensive adjoint sensitivity analysis methodology, developed by the author, which enables the efficient and exact computation of arbitrarily high-order sensitivities of model responses in large-scale systems comprising many model parameters. The qualifier “comprehensive” is employed to highlight that the model parameters considered within the framework of this methodology also include the system’s uncertain boundaries and internal interfaces in phase-space. The model’s responses can be either scalar-valued functionals of the model’s parameters and state variables (e.g., as customarily encountered in optimization problems) or general function-valued responses. Since linear operators admit bona-fide adjoint operators, responses of models that are linear in the state functions (i.e., dependent variables) can depend simultaneously on both the forward and the adjoint state functions. Hence, the sensitivity analysis of such responses warrants the treatment of linear systems in their own right, rather than treating them as particular cases of nonlinear systems. This is in contradistinction to responses for nonlinear systems, which can depend only on the forward state functions, since nonlinear operators do not admit bona-fide adjoint operators (only a linearized form of a nonlinear operator may admit an adjoint operator). Thus, Volume 1 of this book presents the mathematical framework of the nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Response-Coupled Forward/Adjoint Linear Systems (abbreviated as “nth-CASAM-L”), which is conceived for the most efficient computation of exactly obtained mathematical expressions of arbitrarily-high-order (nth-order) sensitivities of a generic system response with respect to all of the parameters underlying the respective forward/adjoint systems. Volume 2 of this book presents the application of the nth-CASAM-L to perform a fourth-order sensitivity and uncertainty analysis of an OECD/NEA reactor physics benchmark which is representative of a large-scale model comprises many (21,976) uncertain parameters, thereby amply illustrating the unique potential of the nth-CASAM-L to enable the exact and efficient computation of chosen high-order response sensitivities to model parameters. Volume 3 of this book presents the “nth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviation: nth-CASAM-N) for the practical, efficient, and exact computation of arbitrarily-high order sensitivities of responses to model parameters for systems that are also nonlinear in their underlying state functions. Such computations are not feasible with any other methodology. The application of the nth-CASAM-L and the nth-CASAM-N overcomes the so-called “curse of dimensionality” in sensitivity and uncertainty analysis, thus revolutionizing all of the fields of activities which require accurate computation of response sensitivities. Since this monograph includes many illustrative, fully worked-out, paradigm problems, it can serve as a textbook or as supplementary reading for graduate courses in academic departments in the natural sciences and engineering.
Download or read book Dynamic Feature Space Modelling Filtering and Self Tuning Control of Stochastic Systems written by Pieter W. Otter and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The literature on systems seems to have been growing almost expo nentially during the last decade and one may question whether there is need for another book. In the author's view, most of the literature on 'systems' is either technical in mathematical sense or technical ifF engineering sense (with technical words such as noise, filtering etc. ) and not easily accessible to researchers is other fields, in particular not to economists, econometricians and quantitative researchers in so cial sciences. This is unfortunate, because achievements in the rather 'young' science of system theory and system engineering are of impor tance for modelling, estimation and regulation (control) problems in other branches of science. State space mode~iing; the concept of ob servability and controllability; the mathematical formulations of sta bility; the so-called canonical forms; prediction error e~timation; optimal control and Kalman filtering are some examples of results of system theory and system engineering which proved to be successful in practice. A brief summary of system theoretical concepts is given in Chapter II where an attempt has been made to translate the concepts in to the more 'familiar' language used in econometrics and social sciences by means of examples. By interrelating concepts and results from system theory with those from econometrics and social sciences, the author has attempted to narrow the gap between the more technical sciences such as engi neering and social sciences and econometrics, and to contribute to either side.
