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1979•International Journal of ControlRequires access

Lower and upper bounds for the quadratic cost of linear regulators

Armin Hoffmann, G. Langholz

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Abstract

Lower and upper bounds for the quadratic cost functional of linear regulators are derived. These bounds are explicitly expressed in terms of some system parameters, arc independent of the initial conditions and are rather easy to compute. The results are based on a previous work by the authors concerning the lower bound. In this paper, the upper bound established is used to improve the lower bound, both being calculated by an iterative procedure to any degree of accuracy which is dependent on the number of iterations only.

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What this paper is about

Lower and upper bounds for the quadratic cost functional of linear regulators are derived. These bounds are explicitly expressed in terms of some system parameters, arc independent of the initial conditions and are rather easy to compute. The results are based on a previous work by the authors concerning the lower bound. In this paper, the upper bound established is used to improve the lower bound, both being calculated by an iterative procedure to any degree of accuracy which is dependent on the number of iterations only.

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Available abstract

Lower and upper bounds for the quadratic cost functional of linear regulators are derived. These bounds are explicitly expressed in terms of some system parameters, arc independent of the initial conditions and are rather easy to compute. The results are based on a previous work by the authors concerning the lower bound. In this paper, the upper bound established is used to improve the lower bound, both being calculated by an iterative procedure to any degree of accuracy which is dependent on the number of iterations only.

Key concepts: Upper and lower bounds, Mathematics, Quadratic equation, Arc (geometry), Work (physics), Applied mathematics, Linear system, Mathematical optimization

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