Adaptive Control of Periodic Systems: (English)

Adaptive Control of Periodic Systems: (English)

          
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About the Book

Adaptive control is needed to cope with parametric uncertainty in dynamical systems. The adaptive control of LTI systems in both discrete and continuous time has been studied for four decades and the results are currently used widely in many different fields. In recent years, interest has shifted to the adaptive control of time-varying systems. It is known that the adaptive control of arbitrarily rapidly time-varying systems is in general intractable, but systems with periodically time-varying parameters (LTP systems) which have much more structure, are amenable to mathematical analysis. Further, there is also a need for such control in practical problems which have arisen in industry during the past twenty years. This thesis is the first attempt to deal with the adaptive control of LTP systems. Adaptive Control involves estimation of unknown parameters, adjusting the control parameters based on the estimates, and demonstrating that the overall system is stable. System theoretic properties such as stability, controllability, and observability play an important role both in formulating of the problems, as well as in generating solutions for them. For LTI systems, these properties have been studied since 1960s, and algebraic conditions that have to be satisfied to assure these properties are now well established. In the case of LTP systems, these properties can be expressed only in terms of transition matrices that are much more involved than those for LTI systems. Since adaptive control problems can be formulated only when these properties are well understood, it is not surprising that systematic efforts have not been made thus far for formulating and solving adaptive control problems that arise in LTP systems. Even in the case of LTI systems, it is well recognized that problems related to adaptive discrete-time system are not as difficult as those that arise in the continuous-time systems. This is amply evident in the solutions that were derived in the 1980s and 1990s for all the important problems. These differences are even more amplified in the LTP case; some problems in continuous time cannot even be formulated precisely. This thesis consequently focuses primarily on the adaptive identification and control of discrete-time systems, and derives most of the results that currently exist in the literature for LTI systems. Based on these investigations of discrete-time adaptive systems, attempts are made in the thesis to examine their continuous-time counterparts, and discuss the principal difficulties encountered. The dissertation examines critically the system theoretic properties of LTP systems in Chapter 2, and the mathematical framework provided for their analysis by Floquet theory in Chapter 3. Assuming that adaptive identification and control problems can be formulated precisely, a unified method of developing stable adaptive laws using error models is treated in Chapter 4. Chapter 5 presents a detailed study of the adaptation in SISO discrete-time LTP systems, and represents the core of the thesis. The important problems of identification, stabilization, regulation, and tracking of arbitrary signals are investigated, and practically implementable stable adaptive laws are derived. The dissertation concludes with a discussion of continuous-time adaptive control in Chapter 6 and discrete multivariable systems in Chapter 7. Directions for future research are indicated towards the end of the dissertation.


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Product Details
  • ISBN-13: 9781243716118
  • Publisher: Proquest, Umi Dissertation Publishing
  • Publisher Imprint: Proquest, Umi Dissertation Publishing
  • Height: 246 mm
  • No of Pages: 174
  • Series Title: English
  • Weight: 322 gr
  • ISBN-10: 1243716118
  • Publisher Date: 01 Sep 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Spine Width: 9 mm
  • Width: 189 mm


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