Thesis (Ph. D.)--University of Wisconsin--Madison, 1972. / Typescript. Vita. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin, 1966. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliography.

Thesis (Ph. D.)--University of Wisconsin, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

Thesis (Ph. D.)--University of Wisconsin--Madison, 1965. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 181-185).

Thesis (M.S.)--University of Wisconsin--Madison, 1984. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 171-176).

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This thesis describes discrete robust adaptive control methods based on using slow sampling and slow adaptation. For the stability analysis, we consider that the plant model order is not exactly known and assume that the estimation model order is lower than the plant model order. A stability condition is derived with a given upper limit for the adaptation gain which is related to a strictly positive real operator. Discussion of the relation between sampling and stability condition is then given. For the robust adaptive control design, we study slow adaptation and predictive control. For the slow adaptation, the main idea is to use only good estimates and use a compensation filter. Some frequency domain information on the plant is necessary for this method. For predictive control, we discuss the relationship between the extended control horizon and the critical sampling. For a simple case, it is shown that the larger extended control horizon brings more robust adaptive control. The purpose of this thesis is to provide robust discrete adaptive controller design guidelines, especially in such cases as using slow sampling frequency, slow adaptation rate. It is true that in practice, for various discrete adaptive control algorithms, slow sampling and slow adaptation rate will bring more robustness. The use of slow sampling and slow adaptation rate is simple and economic, thus a careful choice of sampling rate and adaptation rate is highly recommended. This thesis provides such guidelines for choosing proper sampling rate and adaptation rate for robust discrete adaptive control. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Many communication channels have a power-to-noise ratio (PNR) which is not constant in time, producing a time-varying error probability. If a feedback channel is available, the receiver can request changes in certain transmitter parameters in response to the changing channel conditions. In this thesis a scheme for adaptively changing the data rate by varying the duration of the transmitted pulses in order to compensate for this fluctuating PNR is described and analyzed. Implicit equations for the optimum rate request as a function of past and current instantaneous PNR have been derived for an arbitrary probability density function of the PNR. The effects of a bandwidth constraint, of time delay in the feedback link, and of time and amplitude discrete rate requests have been included in the analysis. Application of adaptive rate control to the Rayleigh fading channel can produce an enormous reduction in required transmitter power over a fixed rate non-diversity system, up to 50 db for typical values of error probability. For the same values of bandwidth, data rate, and error probability, and for typical values of feedback delay, the variable rate system can still effect a power reduction in the range 15-18 db, or a factor of 30-60, over the best alternative scheme, known as maximal-ratio predetection combined frequency diversity. A method is given which allows tradeoffs between power, bandwidth and data rate for two-way communication over Rayleigh fading channels to be examined graphically. Adaptive rate control on multi-user channels produces a smaller improvement. For the range of parameters considered likely, there is a maximum of about 1.7 db improvement over a fixed rate system. Although the magnitude of the improvement introduced by adaptive rate control is strongly dependent on the probability density function of the PNR, it has been shown that for at least one commonly occurring class of time-varying channels the savings are well worth the cost of implementation. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The broad theory of adaptive control is introduced, with m o t i v a t i o n for using such techniques. The two mos t popu l a r techniques, the Model Re f er e n c e A d a ptive C o n t r o l l e r s (MRAC) and the Self Tuning C o n t r o l l e r s (STC) are studied in more d e t a i l . The MRAC and the STC often lead to identical solutions. The c on d i t i o n s for which these two techni q u e s are e q u i v a l e n t are discussed. P a r a m e t e r Adap t a ti o n A l go r i t h m s (PAA) are required by both the MRA a n : the STC. For this reason the PAA is e x a m i ne d in some det.ai . This is i n itiated by de r i v i ng an o f f - l i n e lea; -squares PAA. This is then c o n v e r t e d into a r ec u r s i v e on-l in e estimator. Using intuitive arguments, the various choices of gain p a r a m e t e r as well as the v a r ia t i o n s of the nasic form o f the a l g o r i t h m are discussed. This i n c l ud e s a w a r n in g as to w here the p i tf a l l s of such a l g o r i t h m s may lie. In order to examine the s t a b il i t y of these a lgorithms, the H y p e r s t a b i l i t y theorem is introduced. This requires k n o w l e d g e of the Popov i n e q ua l i t y and Stric t l y P o s itive Real (SPR) functions. This is intro d u c ed initially using i n t u i t i v e ene i g y concepts after which the r i g o r ou s m a t h e m a t i c a l representa* ion is d e r i v e d . The H y p e r s t a b i l i t y T h e o r e m is then used to exam i n e the s t a b i l i t y condition for various forms of the PAA.