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Computation of peak output for inputs restricted in L 2 and L ∞ norms using finite difference schemes and convex optimization

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Abstract

Control systems designed by the principle of matching gives rise to problems of evaluating the peak output. This paper proposes a practical method for computing the peak output of linear time-invariant and non-anticipative systems for a class of possible sets that are characterized with many bounding conditions on the two- and/or the infinity-norms of the inputs and their derivatives. The original infinite-dimensional convex optimization problem is approximated as a large-scale convex programme defined in a Euclidean space, which are associated with sparse matrices and thus can be solved efficiently in practice. The numerical results show that the method performs satisfactorily, and that using a possible set with many bounding conditions can help to reduce the design conservatism and thereby yield a better match.

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Authors and Affiliations

  1. Control Systems Research Laboratory, Department of Electrical Engineering, Chulalongkorn University, Bangkok, 10330, Thailand

    Warit Silpsrikul & Suchin Arunsawatwong

Authors
  1. Warit Silpsrikul
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  2. Suchin Arunsawatwong
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Corresponding author

Correspondence to Suchin Arunsawatwong.

Additional information

Warit Silpsrikul received the B.Eng. and M.Eng. degrees in electrical engineering from Chulalongkorn University, Thailand, in 1996 and 2000, respectively. He is currently a Ph. D. student at the Department of Electrical Engineering, Chulalongkorn University.

His research interest includes the application of the method of inequalities and the principle of matching to engineering problems.

Suchin Arunsawatwong received the B.Eng. and M.Eng. degrees in electrical engineering from Chulalongkorn University, Thailand, in 1985 and 1988, respectively, and Ph.D. degree in control engineering from the Control Systems Centre, University of Manchester Institute of Science and Technology, UK, in 1995. He is currently an assistant professor at the Department of Electrical Engineering, Chulalongkorn University.

His research interests include stability of delay differential systems, numerical solution of differential equations, and control systems design by the method of inequalities and the principle of matching

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Silpsrikul, W., Arunsawatwong, S. Computation of peak output for inputs restricted in L 2 and L ∞ norms using finite difference schemes and convex optimization. Int. J. Autom. Comput. 6, 7–13 (2009). https://doi.org/10.1007/s11633-009-0007-9

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  • DOI: https://doi.org/10.1007/s11633-009-0007-9

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