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IMA Journal of Mathematical Control and Information 1990 7(4):317-338; doi:10.1093/imamci/7.4.317
© 1990 by Institute of Mathematics and its Applications
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On the Spectral-Lyapunov Approach to Parametric Optimization of Distributed-Parameter Systems

PIOTR GRABOWSKI

Institute of Automatics, Academy of Mining and Metallurgy al. Mickiewicza 30/B1, room 314, PL-30-059 Kraków, Poland

The paper is devoted to the discussion of the Riesz-bases application in the analysis of distributed-parameter systems controlled by a finite-dimensional or conventional controller. Both boundary control and boundary observation are allowed. The Riesz bases are constructed from a system of eigenfunctions of the closed-loop system operator. On the basis of the results obtained, they are expected to be an effective tool in proving that the closed-loop system is well-posed; i.e. they give rise to a C0-semigroup. These bases also enable us to construct Lyapunov functionals in the form of series expansions. The analysis is illustrated by a completely worked-out example where the proportional controller setting is optimized with respect to the ISE criterion. The controller is applied to a parabolic plant modelling a resistive—capacitative (noninductive) direct-current transmission line.


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