Robust Stabilization Of Uncertain Systems And H Optimal Control

This book reports on the latest advances in adaptive critic control with robust stabilization for uncertain nonlinear systems. Covering the core theory, novel methods, and a number of typical industrial applications related to the robust adaptive critic control field, it develops a comprehensive framework of robust adaptive strategies, including theoretical analysis, algorithm design, simulation verification, and experimental results. As such, it is of interest to university researchers, graduate students, and engineers in the fields of automation, computer science, and electrical engineering wishing to learn about the fundamental principles, methods, algorithms, and applications in the field of robust adaptive critic control. In addition, it promotes the development of robust adaptive critic control approaches, and the construction of higher-level intelligent systems.

This monograph presents the fundamentals of global stabilization and optimal control of nonlinear systems with uncertain models. It offers a unified view of deterministic disturbance attenuation, stochastic control, and adaptive control for nonlinear systems. The book addresses researchers in the areas of robust and adaptive nonlinear control, nonlinear H-infinity stochastic control, and other related areas of control and dynamical systems theory.

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.

Robust stability conditions obtained through generalization of the notion of energy dissipation in physical systems are discussed in this report. Linear time-invariant (LTI) systems which dissipate energy corresponding to quadratic power functions are characterized in the time-domain and the frequency-domain, in terms of linear matrix inequalities (LMls) and algebraic Riccati equations (ARE's). A novel characterization of strictly dissipative LTI systems is introduced in this report. Sufficient conditions in terms of dissipativity and strict dissipativity are presented for (1) stability of the feedback interconnection of dissipative LTI systems, (2) stability of dissipative LTI systems with memoryless feedback nonlinearities, and (3) quadratic stability of uncertain linear systems. It is demonstrated that the framework of dissipative LTI systems investigated in this report unifies and extends small gain, passivity, and sector conditions for stability. Techniques for selecting power functions for characterization of uncertain plants and robust controller synthesis based on these stability results are introduced. A spring-mass-damper example is used to illustrate the application of these methods for robust controller synthesis. Gupta, Sandeep Langley Research Center...

This volume is the second of the three volume publication containing the proceedings of the 1989 International Symposium on the Mathemat ical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989 The International Symposia MTNS focus attention on problems from system and control theory, circuit theory and signal processing, which, in general, require application of sophisticated mathematical tools, such as from function and operator theory, linear algebra and matrix theory, differential and algebraic geometry. The interaction between advanced mathematical methods and practical engineering problems of circuits, systems and control, which is typical for MTNS, turns out to be most effective and is, as these proceedings show, a continuing source of exciting advances. The second volume contains invited papers and a large selection of other symposium presentations in the vast area of robust and nonlinear control. Modern developments in robust control and H-infinity theory, for finite as well as for infinite dimensional systems, are presented. A large part of the volume is devoted to nonlinear control. Special atten tion is paid to problems in robotics. Also the general theory of nonlinear and infinite dimensional systems is discussed. A couple of papers deal with problems of stochastic control and filterina. vi Preface The titles of the two other volumes are: Realization and Modelling in System Theory (volume 1) and Signal Processing, Scattering and Operator Theory, and Numerical Methods (volume 3).

This paper presents a linear quadratic regulator approach to the robust stabilization, robust performance, and disturbance attenuation of uncertain linear systems. The state-feedback designed systems provide both robust stability with optimal performance and disturbance attenuation with H infinity-norm bounds. The proposed approach can be applied to matched and/or mismatched uncertain linear systems. For a matched uncertain linear system, it is shown that the disturbance-attenuation robust-stabilizing controllers with or without optimal performance always exist and can be easily determined without searching; whereas, for a mismatched uncertain linear system, the introduced tuning parameters greatly enhance the flexibility of finding the disturbance- attenuation robust-stabilizing controllers. Control theory, Adaptive control, Robust control, Algorithms, Digital control, Multivariable systems.

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.

This book provides a unified collection of important, recent results for the design of robust controllers for uncertain systems. Most of the results presented are based on H? control theory, or its stochastic counterpart, risk sensitive control theory.Central to the philosophy of the book is the notion of an uncertain system. Uncertain systems are considered using several different uncertainty modeling schemes. These include norm bounded uncertainty, integral quadratic constraint (IQC) uncertainty and a number of stochastic uncertainty descriptions. In particular, the authors examine stochastic uncertain systems in which the uncertainty is outlined by a stochastic version of the IQC uncertainty description.For each class of uncertain systems covered in the book, corresponding robust control problems are defined and solutions discussed.