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Nonlinear and Optimal Control Theory pp 61–161Cite as

Lecture Notes on Logically Switched Dynamical Systems

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Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1932))

The subject of logically switched dynamical systems is a large one which overlaps with many areas including hybrid system theory, adaptive control, optimal control, cooperative control, etc. Ten years ago we presented a lecture, documented in [1], which addressed several of the areas of logically switched dynamical systems which were being studied at the time. Since then there have been many advances in many directions, far to many too adequately address in these notes. One of the most up to date and best written books on the subject is the monograph by Liberzon [2] to which we refer the reader for a broad but incisive perspective as well an extensive list of references.

In these notes we will deal with two largely disconnected topics, namely switched adaptive control (sometimes called supervisory control) and “flocking” which is about the dynamics of reaching a consensus in a rapidly changing environment. In the area of adaptive control we focus mainly on one problem which we study in depth. Our aim is to give a thorough analysis under realistic assumptions of the adaptive version of what is perhaps the most important design objective in all of feedback control, namely set-point control of a singleinput, single output process admitting a linear model. While the non-adaptive version the set-point control problem is very well understood and has been so for more than a half century, the adaptive version still is not because there is no credible counterpart in an adaptive context of the performance theories which address the non-adaptive version of the problem. In fact, even just the stabilization question for the adaptive version of the problem did not really get ironed out until ten years ago, except under unrealistic assumptions which ignored the effects of noise and/or un-modeled dynamics.

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Authors and Affiliations

  1. Department of Electrical Engineering, Yale University, 208267, 06520-8284, New Haven, CT, USA

    A. Stephen Morse

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  1. A. Stephen Morse
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Editors and Affiliations

  1. Dipartimento di Ingegneria dell'Informazione, Università di Siena, via Roma 56, 53100, Siena, Italy

    Paolo Nistri

  2. Dipartimento di Matematica Applicata “G. Sansone”, Università di Firenze, via di S. Marta 3, 50139, Firenze, Italy

    Gianna Stefani

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Morse, A.S. (2008). Lecture Notes on Logically Switched Dynamical Systems. In: Nistri, P., Stefani, G. (eds) Nonlinear and Optimal Control Theory. Lecture Notes in Mathematics, vol 1932. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77653-6_2

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