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2012 | OriginalPaper | Buchkapitel

4. Iterative Optimization

verfasst von : Alexandre Sanfelice Bazanella, Lucíola Campestrini, Diego Eckhard

Erschienen in: Data-Driven Controller Design

Verlag: Springer Netherlands

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Abstract

In many practical cases the theoretical conditions required by the “one-shot” solutions are not met. Moreover, operational constraints of the process often require that only small adjustments to existing parameter settings can be made, which precludes the application of VRFT in these situations. In such cases the data-driven control design must be performed through iterative procedures in which each iteration requires collecting more data, each time with a different controller in the loop. In Chap. 4 a general review of basic optimization theory is given, setting the stage for the chapters to follow. The basic convergence properties of the basic optimization algorithms—steepest descent and Newton-Raphson in particular—are analyzed. Some robustness properties, that is, convergence under imprecise information, of these algorithms are also demonstrated.

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Fußnoten
1
Of course similar definitions can be made for maxima.
 
2
Note that the Hessian is symmetric and thus all its eigenvalues are real.
 
3
This second constraint is not present when the algorithm is an autonomous system.
 
4
For a more complete proof the reader is referred to standard optimization books. Such proofs get somewhat technical, so we prefer to give here only a sketch that provides insight into the convergence mechanisms.
 
Literatur
1.
Zurück zum Zitat A.S. Bazanella, M. Gevers, L. Mišković, B.D.O. Anderson, Iterative minimization of H 2 control performance criteria. Automatica 44(10), 2549–2559 (2008) MathSciNetMATHCrossRef A.S. Bazanella, M. Gevers, L. Mišković, B.D.O. Anderson, Iterative minimization of H 2 control performance criteria. Automatica 44(10), 2549–2559 (2008) MathSciNetMATHCrossRef
2.
Zurück zum Zitat J.R. Blum, Multidimensional stochastic approximation methods. Ann. Math. Stat. 25(4), 737–744 (1954) MATHCrossRef J.R. Blum, Multidimensional stochastic approximation methods. Ann. Math. Stat. 25(4), 737–744 (1954) MATHCrossRef
4.
Zurück zum Zitat D. Eckhard, A.S. Bazanella, Data-based controller tuning: Improving the convergence rate, in Decision and Control (CDC), 2010 49th IEEE Conference on, (2010), pp. 4801–4806 CrossRef D. Eckhard, A.S. Bazanella, Data-based controller tuning: Improving the convergence rate, in Decision and Control (CDC), 2010 49th IEEE Conference on, (2010), pp. 4801–4806 CrossRef
6.
Zurück zum Zitat M. Vidyasagar, Nonlinear Systems Analysis, 2nd edn. (Prentice Hall, New York, 1992) MATH M. Vidyasagar, Nonlinear Systems Analysis, 2nd edn. (Prentice Hall, New York, 1992) MATH
Metadaten
Titel
Iterative Optimization
verfasst von
Alexandre Sanfelice Bazanella
Lucíola Campestrini
Diego Eckhard
Copyright-Jahr
2012
Verlag
Springer Netherlands
DOI
https://doi.org/10.1007/978-94-007-2300-9_4

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