H Infinity Optimization And Robust Multivariable Control

The loop-shaping approach consists of obtaining a specification in relation to the open loop of the control from specifications regarding various closed loop transfers, because it is easier to work on a single transfer (in addition to the open loop) than on a multitude of transfers (various loopings such as set point/error, disturbance/error, disturbance/control, etc.). The simplicity and flexibility of the approach make it very well adapted to the industrial context. This book presents the loop-shaping approach in its entirety, starting with the declension of high-level specifications into a loop-shaping specification. It then shows how it is possible to fully integrate this approach for the calculation of robust and efficient correctors with the help of existing techniques, which have already been industrially tried and tested, such as H-infinity synthesis. The concept of a gap metric (or distance between models) is also presented along with its connection with the prime factors of a set of systems shaping a ball of models, as well as its connections with robust synthesis by loop-shaping, in order to calculate efficient and robust correctors. As H-infinity loop-shaping is often demanding in terms of the order of correctors, the author also looks at loop-shaping synthesis under an ordering constraint. Two further promising lines of research are presented, one using stochastic optimization, and the other non-smooth optimization. Finally, the book introduces the concept of correction with two degrees of freedom via the formalism of prime factorization. Avenues for future work are also opened up by the author as he discusses the main drawbacks to loop-shaping synthesis, and how these issues can be solved using modern optimization techniques in an increasingly competitive industrial context, in accordance with ever more complex sets of functional specifications, associated with increasingly broad conditions of usage. Contents Introduction 1. The Loop-shaping Approach 2. Loop-shaping H-infinity Synthesis 3. Two Degrees-of-Freedom Controllers 4. Extensions and Optimizations Appendix 1. Demonstrative Elements on the Optimization of Robust Stabilization with Order Constraint Appendix 2. Establishment of Real LMIs for the Quasi-Convex Problem of Optimization of the Weighting Functions About the Authors Philippe Feyel is an R&D Engineer for the high-tech company Sagem Défense Sécurité, part of the defence and security business of the SAFRAN group, in Paris, France.

A Generalized Framework of Linear Multivariable Control proposes a number of generalized models by using the generalized inverse of matrix, while the usual linear multivariable control theory relies on some regular models. The book supports that in H-infinity control, the linear fractional transformation formulation is relying on the inverse of the block matrix. If the block matrix is not regular, the H-infinity control does not apply any more in the normal framework. Therefore, it is very important to relax those restrictions to generalize the classical notions and models to include some non-regular cases. This book is ideal for scholars, academics, professional engineer and students who are interested in control system theory. Presents a comprehensive set of numerical procedures, algorithms, and examples on how to deal with irregular models Provides a summary on generalized framework of linear multivariable control that focuses on generalizations of models and notions Introduces a number of generalized models by using the generalized inverse of matrix

New methods are presented for analysis and synthesis of control systems subject to structured uncertainties. The technical approach involves the structured singular value, as an analysis tool and H infinity as a synthesis tool. Alternative formulations are compared with the H infinity approach, extensions of mu to handle real parameter problems are presented, and the issue of the convergence of mu synthesis to a global optimum is studied. A comprehensive solution for the synthesis of general optimal controllers is given for linear lumped time-invariant systems. The existence of an optimal solution for H inifinity optimization is proved, and some properties of this solution are discovered. The method called Euler's constant iteration is presented and its convergence properties are established. A new algorithm for solving a class of algebraic riccati equations is obtained Explicit error bounds for model reduction in the synthesis process are derived. The constructions use standard matrix operations and linear algebra applied to state-space representations of linear systems.

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The Encyclopedia of Systems and Control collects a broad range of short expository articles that describe the current state of the art in the central topics of control and systems engineering as well as in many of the related fields in which control is an enabling technology. The editors have assembled the most comprehensive reference possible, and this has been greatly facilitated by the publisher’s commitment continuously to publish updates to the articles as they become available in the future. Although control engineering is now a mature discipline, it remains an area in which there is a great deal of research activity, and as new developments in both theory and applications become available, they will be included in the online version of the encyclopedia. A carefully chosen team of leading authorities in the field has written the well over 250 articles that comprise the work. The topics range from basic principles of feedback in servomechanisms to advanced topics such as the control of Boolean networks and evolutionary game theory. Because the content has been selected to reflect both foundational importance as well as subjects that are of current interest to the research and practitioner communities, a broad readership that includes students, application engineers, and research scientists will find material that is of interest.