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Applications of analytic centers for the numerical solution of semiinfinite, convex programs arising in control theory

  • Optimal Control
  • Conference paper
  • First Online:
System Modelling and Optimization

Part of the book series: Lecture Notes in Control and Information Sciences ((LNCIS,volume 143))

Abstract

Generalizing the notion of the analytic center of a finite system of linear (convex, analytic) inequalities — which proved to be of central importance for the resurging theory of interior point methods in linear (convex) programming — we define an analytic center for convex sets K in R n defined as feasible sets, corresponding to a smooth, p parameter family of convex, quadratic (e.g. linear) inequalities 1≤p≤n−1. Connections to the theory of (central solutions of) the classical moment and related operator extension problems as well as to relevant notions of affine differential and integral geometry are briefly discussed. We show by several theorems that the proposed centre c(K) provides a nice (low complexity, stable, easy to update,...) two sided ellipsoidal approximation for K, which in turns can be used to find (suboptimal) solutions of important problems of observation and control in dynamic uncertain systems. For example we construct dynamic observers and feedback controls guaranting, i.e. associated to (extremal) invariant sets in linear differential (or difference) games with momentaneously bounded controls (disturbances) and measurement errors.

On leave from Inst. of Math. Eötvös Univ. Budapest, Hungary.

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Authors and Affiliations

  1. Inst. für Angewandte Mathematik, Univ. Würzburg Am Hubland, D8700, Würzburg

    G. Sonnevend

Authors
  1. G. Sonnevend
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H. -J. Sebastian K. Tammer

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© 1990 International Federation for Information Processing

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Sonnevend, G. (1990). Applications of analytic centers for the numerical solution of semiinfinite, convex programs arising in control theory. In: Sebastian, H.J., Tammer, K. (eds) System Modelling and Optimization. Lecture Notes in Control and Information Sciences, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0008393

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  • DOI: https://doi.org/10.1007/BFb0008393

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52659-9

  • Online ISBN: 978-3-540-47095-3

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