01102924 - 426 must sample to reconstruct the original...

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426 IEEE TRANSACTIONS ON AUTOMATIC CONTROL. VOL. AC-27. NO. 2. APRIL 1982 must sample to reconstruct the original continuous time signal. It appears. however. that stability can be awmd provided only that samples are taken in manner which assures that temporary instabilities are obsenable in the error sequence cA. k 2 0. Practicallv speaking. however. if the sampling rate is too slow and the system is initially unstable. signals may quickly reach saturation levels. Remark 4: Although we have proven that the identification error e( I) converges to zero we have not shown that the parameter estimates O( r) converge to one of the optimal vectors 8:. In general this \vi11 only be the case if the external input is persistently exciting so that the conditiona of proposition I are met. Furthermore xve ha\e not guaranteed that the plant output converges to that of the model. Houever. simulation studies sce~n to indicate that this is the case. Remurk i: We have proposed the use of two alternative adJu>tnlent schemes of a prqection type. and a least-squares type. Although our simulations studies indicate considerably improved comergencs using the least-squares algorithm. it should be pointed out that care must be taken when implementing ths algorithm since PA must be assured to remain positive definite. VI. CONCLUDING REMARKS This report studied an alternative approach to the problem of applying discrete adaptation techniques for the control of continuous time proceseeb. For this approach stability results were derived which are independent of the average sampling rate. One important advantage of this approach over those proposed for continuous adaptive control of continuous processes is that this approach allows for use of the rapidly converging sequential least-squares estimation procedure. To control the rate of parameter convergence in continuous time adaptation prncedures one must resort to multiple equation error estimators [7]. [8]. These require implementation of considerably lugher order input and output filters. and lead tn conhid- erably- more complex control structures. The use of sequential least squares is also of great importance in extending these mults to the multivariable case. since as discussed in (51. there are many more parame- ters to adjust. Decentralized Control of Finite State Markov Processes K.41 HSU. MEllBER. IEEE. ASD STEVEN 1. MARCUS. MEMBER. IEEE A hsrracr -\Ye are concerned with the control of a particular class of d:nan~ic qstems-finite state Markov chainx The information pattern a\ailable is the so-called one step dela! sharing information pattern. Using this information pattern. the d!namic programming algorithm can be elplicitl! carried out to obtain the optimal polic). The problems are discussed under three different cost criteria-finite horiLon problem with expected total cost.
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This note was uploaded on 09/27/2010 for the course EE 229 taught by Professor R.srikant during the Spring '09 term at University of Illinois, Urbana Champaign.

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01102924 - 426 must sample to reconstruct the original...

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