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State estimation and optimization with application to adaptive control of Linear Distributed Parameter Systems

University of British Columbia

This thesis is concerned with estimation and control of linear distributed parameter systems. For the estimation of linear deterministic continuous-time distributed parameter systems, a linear deterministic distributed parameter filter that yields the state estimate based on noiseless linear measurements available over the complete occupied spatial domain is derived by consideration of a Lyapunov type of stability. The general results are then specialized to the case when noiseless linear measurements are available at only several points in the spatial domain. A numerical example illustrates its use in an overall control scheme. For the estimation of linear stochastic discrete-time distributed parameter systems, a linear discrete-time distributed parameter filter having a predictor-corrector structure, that yields the minimum-variance estimate of the state based on noise-corrupted linear measurements assumed available at only several spatial locations, is derived. The filtered estimate and the filtering error are shown to satisfy an orthogonal projection lemma, whence a Wiener-Hopf equation is derived. The filter is implementable on-line and a numerical example illustrates its use. The optimal pointwise regulation control problem for linear stochastic discrete-time distributed parameter systems is treated through application of dynamic programming. The separation of the complete control scheme into the estimation and control subsystems is shown. Its usefulness is illustrated in a numerical example. By first expanding Green's function and then considering the limiting behaviour of the corresponding discrete-time results on estimation and control obtained previously, solutions of the continuous-time linear minimum-variance filtering estimation and optimal pointwise regulation control problems for linear stochastic continuous-time distributed parameter systems are obtained. Further, a separation theorem is obtained and Kalman's duality theorem extended. For the pointwise regulation control problem of linear stochastic discrete-time distributed parameter systems, the case of unknown noise characteristics is treated. Based on an examination of the open-loop-optimal feedback control approach, a suboptimal control scheme is proposed. A filter that is adaptively selected on-line based on minimizing an instantaneous cost functional so derived from the original one as to realize a trade-off between control and estimation costs is put forward. A numerical example shows the effectiveness of the suboptimal control scheme in comparison with the optimal one.

Text

2010-01-29

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http://hdl.handle.net/2429/19316

Electrical and Computer Engineering

University of British Columbia

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