Functional expansions in bilinear system analysis Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/pk02cd065

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  • Bilinear systems, encountered in many important applications of engineering, biological and socio-economic systems, represent the logical step in complexity between the linear systems which are inadequate in the modeling of various dynamic processes and the difficult realm of nonlinear systems. This dissertation studies two functional expansions in bilinear system analysis- - the Volterra series approach and the Walsh-function approach. The Volterra series for bilinear systems is developed by means of the Reversion technique. The uniform convergence of the series is provedand estimates on the bound of the output of the system and on the error due to the truncation of the series are obtained. The above development leads to a direct synthesis of the Volterra kernels which characterize the bilinear system. This result is related to Bush's canonic forms and it is shown that synthesized kernels facilitate the computation of the Volterra transfer functions. The notions of "weakly" bilinear, which are systems that can be represented by a finite Volterra series, and "strongly" bilinear, which cannot be so represented, are introduced. A method is proposed to estimate the parameters of the system using discrete Volterra kernels. A neutron kinetics model is included as an application of the method. In the second approach, a finite orthonormal set of functions is used in the expansion of input/output functions for parameter estimation and input/parameter functions for output computation of deterministic systems. Walsh functions form the basis of the expansions as a consequence of their group properties with respect to binary algebra and of their relationship with the integrals of Walsh functions. This method is applicable to time-variant bilinear systems and to systems with polynomial type nonlinearities as well. The effectiveness of the proposed method for parameter estimation of deterministic systems subject to modeling and measurement noise is examined. Several computational examples are presented to demonstrate the accuracy of the method.
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