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Optimal Control Of Dynamical Systems With Time Invariant Probabilistic Parametric Uncertainties
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Book Synopsis Optimal Control of Dynamical Systems with Time-invariant Probabilistic Parametric Uncertainties by : Dongying Erin Shen
Download or read book Optimal Control of Dynamical Systems with Time-invariant Probabilistic Parametric Uncertainties written by Dongying Erin Shen and published by . This book was released on 2018 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of taking model uncertainties into account during controller design is well established. Although this theory is well developed and quite mature, the worst-case uncertainty descriptions assumed in robust control formulations are incompatible with the uncertainty descriptions generated by commercial model identification software that produces time-invariant parameter uncertainties typically in the form of probability distribution functions. This doctoral thesis derives rigorous theory and algorithms for the optimal control of dynamical systems with time-invariant probabilistic uncertainties. The main contribution of this thesis is new feedback control design algorithms for linear time-invariant systems with time-invariant probabilistic parametric uncertainties and stochastic noise. The originally stochastic system of equations is transformed into an equivalent deterministic system of equations using polynomial chaos (PC) theory. In addition, the H2- and H[infinity symbol]-norms commonly used to describe the effect of stochastic noise on output are transformed such that the eventual closed-loop performance is insensitive to parametric uncertainties. A robustifying constant is used to enforce the closed-loop stability of the original system of equations. This approach results in the first PC-based feedback control algorithm with proven closed-loop stability, and the first PC-based feedback control formulation that is applicable to the design of fixed-order state and output feedback control designs. The numerical algorithm for the control design is formulated as optimization over bilinear matrix inequality (BMI) constraints, for which commercial software is available. The effectiveness of the approach is demonstrated in two case studies that include a continuous pharmaceutical manufacturing process. In addition to model uncertainties, chemical processes must operate within constraints, such as upper and lower bounds on the magnitude and rate of change of manipulated and/or output variables. The thesis also demonstrates an optimal feedback control formulation that explicitly addresses both constraints and time-invariant probabilistic parameter uncertainties for linear time-invariant systems. The H2-optimal feedback controllers designed using the BMI formulations are incorporated into a fast PC-based model predictive control (MPC) formulation. A numerical case study demonstrates the improved constraint satisfaction compared to past polynomial chaos-based formulations for model predictive control.
Book Synopsis Robustness of Dynamic Systems with Parameter Uncertainties by : Mohamed Mansour
Download or read book Robustness of Dynamic Systems with Parameter Uncertainties written by Mohamed Mansour and published by Birkhäuser. This book was released on 2012-12-06 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust Control is one of the fastest growing and promising areas of research today. In many practical systems there exist uncertainties which have to be considered in the analysis and design of control systems. In the last decade methods were developed for dealing with dynamic systems with unstructured uncertainties such as HOO_ and £I-optimal control. For systems with parameter uncertainties, the seminal paper of V. L. Kharitonov has triggered a large amount of very promising research. An international workshop dealing with all aspects of robust control was successfully organized by S. P. Bhattacharyya and L. H. Keel in San Antonio, Texas, USA in March 1991. We organized the second international workshop in this area in Ascona, Switzer land in April 1992. However, this second workshop was restricted to robust control of dynamic systems with parameter uncertainties with the objective to concentrate on some aspects of robust control. This book contains a collection of papers presented at the International Workshop on Robust Control held at the Centro Stefano Franscini, Monte Verita, Ascona, Switzer land on April 12-17, 1992 as well as a list of open problems presented during a dis cussion session at the workshop. Thirtyfive leading researchers from all over the world working in the area of robust control of dynamic systems with parameter uncertainties were invited to present their recent results and to discuss with their colleagues the recent advances in this field.
Book Synopsis Continuous Time Dynamical Systems by : B.M. Mohan
Download or read book Continuous Time Dynamical Systems written by B.M. Mohan and published by CRC Press. This book was released on 2018-10-08 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional. This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria. Illustrated throughout with detailed examples, the book covers topics including: Block-pulse functions and shifted Legendre polynomials State estimation of linear time-invariant systems Linear optimal control systems incorporating observers Optimal control of systems described by integro-differential equations Linear-quadratic-Gaussian control Optimal control of singular systems Optimal control of time-delay systems with and without reverse time terms Optimal control of second-order nonlinear systems Hierarchical control of linear time-invariant and time-varying systems
Book Synopsis Robust Control of Uncertain Dynamic Systems by : Rama K. Yedavalli
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.
Book Synopsis Estimation and Control of Dynamical Systems by : Alain Bensoussan
Download or read book Estimation and Control of Dynamical Systems written by Alain Bensoussan and published by Springer. This book was released on 2018-05-23 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive presentation of classical and advanced topics in estimation and control of dynamical systems with an emphasis on stochastic control. Many aspects which are not easily found in a single text are provided, such as connections between control theory and mathematical finance, as well as differential games. The book is self-contained and prioritizes concepts rather than full rigor, targeting scientists who want to use control theory in their research in applied mathematics, engineering, economics, and management science. Examples and exercises are included throughout, which will be useful for PhD courses and graduate courses in general. Dr. Alain Bensoussan is Lars Magnus Ericsson Chair at UT Dallas and Director of the International Center for Decision and Risk Analysis which develops risk management research as it pertains to large-investment industrial projects that involve new technologies, applications and markets. He is also Chair Professor at City University Hong Kong.
Book Synopsis Control of Uncertain Dynamic Systems by : Shankar P. Bhattacharyya
Download or read book Control of Uncertain Dynamic Systems written by Shankar P. Bhattacharyya and published by CRC Press. This book was released on 2020-09-23 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of 34 papers presented by leading researchers at the International Workshop on Robust Control held in San Antonio, Texas in March 1991. The common theme tying these papers together is the analysis, synthesis, and design of control systems subject to various uncertainties. The papers describe the latest results in parametric understanding, H8 uncertainty, l1 optical control, and Quantitative Feedback Theory (QFT). The book is the first to bring together all the diverse points of view addressing the robust control problem and should strongly influence development in the robust control field for years to come. For this reason, control theorists, engineers, and applied mathematicians should consider it a crucial acquisition for their libraries.
Book Synopsis Uncertainty Propagation, Control and Estimation of Stochastic Dynamic Systems Using Generalized Polynomial Chaos Expansion by : Rajnish Bhusal
Download or read book Uncertainty Propagation, Control and Estimation of Stochastic Dynamic Systems Using Generalized Polynomial Chaos Expansion written by Rajnish Bhusal and published by . This book was released on 2022 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, uncertainty propagation has emerged as an important research area in the field of dynamical systems. The growing interest in this area arises out of the need to develop computationally efficient approaches to predict the evolution of a system subject to uncertainties. To this end, this dissertation is focused on developing computational frameworks for uncertainty propagation, control, and state estimation of stochastic dynamical systems using the generalized polynomial chaos (gPC) expansion technique.In the first part of this dissertation, the construction of gPC expansion is presented in general. The novelty of this dissertation lies in developing a mixed sparse grid quadrature technique to carry out computationally efficient uncertainty propagation in dynamical systems wherein the random variables are governed by different (or a mixture of) probability distribution types. Additionally, the proposed quadrature technique in the gPC expansion framework is utilized to study the sensitivity of the system output to the uncertain input variables. Subsequently, this work integrates the idea of uncertainty propagation with those of model data-fusion and optimal control theory for state estimation and robust control, respectively, of stochastic systems subject to parametric uncertainties. Furthermore, the stability margin of a group of cooperative unmanned vehicles is examined in a multi-agent system setting. In this regard, a unified framework is proposed to study the consensus of multi-agent systems with multiplicative uncertainties in the feedback path of agents. The proposed technique provides performance indices that measure the robustness of the networked group of agents to gain, phase, and input delay perturbations. Finally, the dissertation studies the consensus problems in multi-agent systems wherein the information exchange between the agents is affected by non-uniform time-varying delays in the network.The proposed frameworks are applied to various benchmark problems and real world applications, including the motion of satellites in low-Earth orbits, aeroelastic systems, hypersonic reentry of a spacecraft to Earth, synchronization in the states of short-period dynamics of aircraft, among others.
Book Synopsis Dynamics and Control by : George Leitmann
Download or read book Dynamics and Control written by George Leitmann and published by CRC Press. This book was released on 1999-08-19 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-authored volume presents selected papers from the Eighth Workshop on Dynamics and Control. Many of the papers represent significant advances in this area of research, and cover the development of control methods, including the control of dynamical systems subject to mixed constraints on both the control and state variables, and the development of a control design method for flexible manipulators with mismatched uncertainties. Advances in dynamic systems are presented, particularly in game-theoretic approaches and also the applications of dynamic systems methodology to social and environmental problems, for example, the concept of virtual biospheres in modeling climate change in terms of dynamical systems.
Book Synopsis Filtering for Stochastic Processes with Applications to Guidance by : Richard S. Bucy
Download or read book Filtering for Stochastic Processes with Applications to Guidance written by Richard S. Bucy and published by American Mathematical Soc.. This book was released on 2005 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition preserves the original text of 1968, with clarification and added references. From the Preface to the Second Edition: ``Since the First Edition of this book, numerous important results have appeared--in particular stochastic integrals with respect to martingales, random fields, Riccati equation theory and realization of nonlinear filters, to name a few. In Appendix D, an attempt is made to provide some of the references that the authors have found useful and tocomment on the relation of the cited references to the field ... [W]e hope that this new edition will have the effect of hastening the day when the nonlinear filter will enjoy the same popularity in applications as the linear filter does now.''
Book Synopsis Robust Stability Under Mixed Time Varying, Time Invariant and Parametric Uncertainty by :
Download or read book Robust Stability Under Mixed Time Varying, Time Invariant and Parametric Uncertainty written by and published by . This book was released on 1995 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robustness analysis is considered for systems with structured uncertainty involving a combination of linear time-invariant and linear time-varying perturbations, and parametric uncertainty. A necessary and sufficient condition for robust stability in terms of the structured singular value p is obtained, based on a finite augmentation of the original problem. The augmentation corresponds to considering the system at a fixed number of frequencies. Sufficient conditions based on scaled small-gain are also considered and characterized. A substantial amount of research in recent years has been devoted to analysis and synthesis of control systems o achieve robust stability and performance in the presence of structured uncertainty. This implies a decentralized nature of the uncertain perturbation, which is a reasonable modeling choice for complex systems, where uncertainty may be introduced at the subsystem level (see Safonov [17] and Doyle [5] for early treatments of this). In addition t o this "spatial" structure, different assumptions can be made on the dynamic properties of the uncertainty: real parametric, linear time invariant (LTI), linear time varying (LTV) or nonlinear perturbations. All these uncertainty classes arise naturally in modeling. Parametric uncertainty appears frequently in first principles models; LTI perturbations are well suited when.
Book Synopsis Model Reduction of Complex Dynamical Systems by : Peter Benner
Download or read book Model Reduction of Complex Dynamical Systems written by Peter Benner and published by Springer Nature. This book was released on 2021-08-26 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume presents some of the latest research related to model order reduction of complex dynamical systems with a focus on time-dependent problems. Chapters are written by leading researchers and users of model order reduction techniques and are based on presentations given at the 2019 edition of the workshop series Model Reduction of Complex Dynamical Systems – MODRED, held at the University of Graz in Austria. The topics considered can be divided into five categories: system-theoretic methods, such as balanced truncation, Hankel norm approximation, and reduced-basis methods; data-driven methods, including Loewner matrix and pencil-based approaches, dynamic mode decomposition, and kernel-based methods; surrogate modeling for design and optimization, with special emphasis on control and data assimilation; model reduction methods in applications, such as control and network systems, computational electromagnetics, structural mechanics, and fluid dynamics; and model order reduction software packages and benchmarks. This volume will be an ideal resource for graduate students and researchers in all areas of model reduction, as well as those working in applied mathematics and theoretical informatics.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Synthesis and Parametric Study of the Optimal Control of Second Order Linear Time Invariant Systems with a Parameterized Cost Functional by : Arun Kanti Guha
Download or read book Synthesis and Parametric Study of the Optimal Control of Second Order Linear Time Invariant Systems with a Parameterized Cost Functional written by Arun Kanti Guha and published by . This book was released on 1969 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Control of Stochastic Hybrid Systems based on Probabilistic Reachable Set Computation by : Leonhard Asselborn
Download or read book Control of Stochastic Hybrid Systems based on Probabilistic Reachable Set Computation written by Leonhard Asselborn and published by kassel university press GmbH. This book was released on 2018-09-17 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes an algorithmic controller synthesis based on the computation of probabilistic reachable sets for stochastic hybrid systems. Hybrid systems consist in general of a composition of discrete and continuous valued dynamics, and are able to capture a wide range of physical phenomena. The stochasticity is considered in form of normally distributed initial continuous states and normally distributed disturbances, resulting in stochastic hybrid systems. The reachable sets describe all states, which are reachable by a system for a given initialization of the system state, inputs, disturbances, and time horizon. For stochastic hybrid systems, these sets are probabilistic, since the system state and disturbance are random variables. This thesis introduces probabilistic reachable sets with a predefined confidence, which are used in an optimization based procedure for the determination of stabilizing control inputs. Besides the stabilizing property, the controlled dynamics also observes input constraints, as well as, so-called chance constraints for the continuous state. The main contribution of this thesis is the formulation of an algorithmic control procedure for each considerd type of stochastic hybrid systems, where different discrete dynamics are considered. First, a control procedure for a deterministic system with bounded disturbances is introduced, and thereafter a probabilistic distribution of the system state and the disturbance is assumed. The formulation of probabilistic reachable sets with a predefined confidence is subsequently used in a control procedure for a stochastic hybrid system, in which the switch of the continuous dynamics is externally induced. Finally, the control procedure based on reachable set computation is extended to a type of stochastic hybrid systems with autonomously switching of the continuous dynamics.
Book Synopsis Set-Theoretic Methods in Control by : Franco Blanchini
Download or read book Set-Theoretic Methods in Control written by Franco Blanchini and published by Birkhäuser. This book was released on 2015-07-02 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second edition of this monograph describes the set-theoretic approach for the control and analysis of dynamic systems, both from a theoretical and practical standpoint. This approach is linked to fundamental control problems, such as Lyapunov stability analysis and stabilization, optimal control, control under constraints, persistent disturbance rejection, and uncertain systems analysis and synthesis. Completely self-contained, this book provides a solid foundation of mathematical techniques and applications, extensive references to the relevant literature, and numerous avenues for further theoretical study. All the material from the first edition has been updated to reflect the most recent developments in the field, and a new chapter on switching systems has been added. Each chapter contains examples, case studies, and exercises to allow for a better understanding of theoretical concepts by practical application. The mathematical language is kept to the minimum level necessary for the adequate formulation and statement of the main concepts, yet allowing for a detailed exposition of the numerical algorithms for the solution of the proposed problems. Set-Theoretic Methods in Control will appeal to both researchers and practitioners in control engineering and applied mathematics. It is also well-suited as a textbook for graduate students in these areas. Praise for the First Edition "This is an excellent book, full of new ideas and collecting a lot of diverse material related to set-theoretic methods. It can be recommended to a wide control community audience." - B. T. Polyak, Mathematical Reviews "This book is an outstanding monograph of a recent research trend in control. It reflects the vast experience of the authors as well as their noticeable contributions to the development of this field...[It] is highly recommended to PhD students and researchers working in control engineering or applied mathematics. The material can also be used for graduate courses in these areas." - Octavian Pastravanu, Zentralblatt MATH
Book Synopsis Dynamical Systems by : Albert C. J. Luo
Download or read book Dynamical Systems written by Albert C. J. Luo and published by Springer Science & Business Media. This book was released on 2010-07-17 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dynamical Systems: Discontinuous, Stochasticity and Time-Delay provides an overview of the most recent developments in nonlinear dynamics, vibration and control. This book focuses on the most recent advances in all three areas, with particular emphasis on recent analytical, numerical and experimental research and its results. Real dynamical system problems, such as the behavior of suspension systems of railways, nonlinear vibration and applied control in coal manufacturing, along with the multifractal spectrum of LAN traffic, are discussed at length, giving the reader a sense of real-world instances where these theories are applied. Dynamical Systems: Discontinuous, Stochasticity and Time-Delay also contains material on time-delay systems as they relate to linear switching, dynamics of complex networks, and machine tools with multiple boundaries. It is the ideal book for engineers and academic researchers working in areas like mechanical and control engineering, as well as applied mathematics.
Download or read book Applied Mechanics Reviews written by and published by . This book was released on 1972 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt:
