Control of Uncertain Systems: A Linear Programming Approach 1st Edition by Munther A. Dahleh (PDF)

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A textbook for a first or second year graduate course in control theory. Presents a computational theory for robust control that highlights the fundamental limitation and capabilities of linear controller design for plants with uncertainty. Annotation copyright Book News, Inc. Portland, Or.

User’s Reviews

Editorial Reviews: From the Publisher A state-of-the-art approach to the most recent developments in the field of robust control. From the Back Cover Key Benefit: In tackling the problem of robust controller design from a unique perspective, this volume brings together three branches of mathematics: operator theory, optimization theory, and algebraic theory of rational matrix functions. Together, these techniques enable readers to capture the fundamental limitations of design in a quantitative way, and provide computable methods for analysis and synthesis of control systems. Content is presented rigorously — with intuitive explanations of the results and examples that highlight the utility of those results. Key Topics: Formulates general design problems that involve time-domain specification, and bounded, but persistent, disturbances. Surveys the background, problem definitions and set-up, parametrization of controllers and closed loop maps, and a general robustness set-up, all for MIMIO systems. Presents a very powerful theory in optimization — duality theory. Explains the detailed solution of the synthesis problem — with an emphasis is on l…à performance and robustness. Includes many examples. Market: For engineers involved in robust controller design.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I think that the other reviews posted here do not give a fair evaluation of the book. (These reviews are also so similar that one wonders why the second reviewer felt it necessary to post…) It is true that the L1 method has not received as much attention as other robust control techniques, such as the H-infinity theory, but it is a viable alternative, and has been used to design real-life controllers, such as those for high-purity distillation columns. One of the merits of this approach, as J. Ball noted in his review of this book for SIAM Review (Vol.41, No.4) is that it is easier to incorporate time-domain constraints (e.g., overshoot, settling time, maximum deviation from desired tracking) than in some other robust control approaches. Other features of controller performance can be analyzed as well, because the design approach is amenable to detailed analysis. This book is not meant to be a treatise on linear programming or on functional analysis, and shouldn’t be criticized on those grounds. Contrary to the statements of the earlier reviewers, the material of this book should be of some interest to researchers: there are open problems in this area that are discussed in an article by Bamieh and Dahleh in the book “Open Problems in Mathematical Systems and Control Theory” (Springer, 1999), and articles on the relationship of infinite-dimensional convex analysis with this area have been recently published in IEEE Trans. Auto. Control. Potential readers should compare this book with the later “Computational methods for controller design” (Springer, 1998) by Elia and Dahleh, which covers some of the same topics.

⭐This book is primarily about one approach to the control of plants with uncertainties: The L1 (ell one) theory. Unfortunately it is not a very useful book: there is probably not one real life plant that carriers a controller designed by this method. This is not surprising since the L1 objective is of little interest in general.The book is essentially a watered down version of a few topics in infinite dimensional optimization and functional analysis. The L1 theory is simply an application of the Hahn Banach theorem to an idealized formulation of the control problem. The problem is then reduced to an infinite dimensional linear program, which, with truncation is reduced to a finite dimensional one. The objective function, however, is not very useful. One can simply use the constraints to obtain a feasible solution to the LP, but the resulting design is difficult to comprehend, and it is difficult to specify margins with this method.So for the control engineer, the book is not very useful. For the mathematicians, it gives little insight into control issues, and talks only of known mathematics.

⭐With the exception of one chapter, this book is about a narrow and unproven approach to control system design: The L1 theory. There is almost surely no real life plant that carries a controller based on this design. Additionally, the authors present a mathematical treatment of an engineering subject, but the treatment fails to give the experienced control engineer any insight.From the point of view of mathematical control theory, the book is simply a watered down version of a few topics in infinite dimensional optimization and functional analysis. It is based on an application of the Hahn Banach theorem to a formulation of the control problem. It also contains a lot of mathematical facts, but it does not tie them well to control theory. So the mathematician will get little insight into the subject of control.Here we have a book that is neither useful to the engineer, nor to the mathematician.

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