Synthesis of Dissipative and Stabilizing Systems of Adaptive Control

  • Vladimir Yu. Tertychny-Dauri
Part of the Mathematics and Its Applications book series (MAIA, volume 538)


The second part of the book contains four chapters that the author’s own work on development of the method of adaptive integral transforms. The material was partially given in [313–326] and was substantially revised and expanded in the present version. The method of integral transforms (IT) applies to the problems of MS control and adaptation and involves filtration of higher derivatives. The solutions of built-in stable filters lead to integral dependencies in the feedback adaptive contour. In spite of the fact that certain tedious analytical constructions result from the IT method, adaptive control algorithms allow diverse objective conditions to be effectively realized, optimally stabilized testing included. It is probable that all possible continuous problems of control and adaptation can be solved most fully and explicitly with the help of integral, and especially integro-differential, equations. Such a judjement is supported by the argument that the given types of equations have been properly generalized from records of the solutions of input differential equations.


Lyapunov Function Adaptive System Adaptive Algorithm Dissipative System Integral Transformation 
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Copyright information

© Springer Science+Business Media New York 2002

Authors and Affiliations

  • Vladimir Yu. Tertychny-Dauri
    • 1
  1. 1.Institute of Fine Mechanics and OpticsTechnical UniversitySt PetersburgRussia

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