Thesis (Ph. D.)--University of Wisconsin--Madison, 1981. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references.

by T. L. Johnson. / Bibliography: .18. / Research supported by the Air Force Office of Scientific Research under Grant AFOSR 72-2273.

The closed-loop control of processes over networks has in recent years become an increasingly popular research topic. This is a very viable solution for a wide variety of applications due to the rapid developments in communication network technologies and the widespread expansion of network devices and users. The convergence of communication networks technologies and advanced control methods do have a great potential to replace traditional control systems. The research programme presented in this thesis led to a development of networked predictive control algorithms over wired local area networks, general packet radio service wireless networks and wireless local area networks. Since the network is taken as a part of a control system, the network-induced time delay and data dropout are unavoidable. How to compensate for these issues is the main challenge in designing control methodologies for networked control systems. Five solutions were presented in this thesis to address these problems and were termed as recursive predictive control method I, inner loop predictive control method, outer loop predictive control method, modified generalised predictive control method and recursive predictive control method II. Irrespective of the different implementations of the networked control methods used, there is a common structure for each method which consists of a predictive control generator, a network delay compensator, a buffer and a plant output predictor. The predictive control generator and network delay compensator were used to compensate for the network delay and data dropout in the forward channel. The network delay and data dropout in the feedback channel was compensated for by using the plant output predictor, buffer and network delay compensator. The relationship between the sampling rate, packet size, network delay and data dropout were examined by using a round trip time delay method. Two network delay measurement methods were also presented and analysed in this thesis. The results of the real-time measurement of the network delay were used in an offline simulation. A networked servo system was built to test the system performance for an approximately linear, open-loop stable system and a networked inverted pendulum system was used to illustrate the system performance for an open-loop unstable system. The stability of each method was also considered. In order to simplify the software development, the Matlab/Simulink/Real-time workshop integrated development suit was used in the practical control system. The simulation block diagram in the Simulink environment was translated to the standard C language by using the real-time workshop. The ARMLINUX-GCC 3.4.4 was used to compile the generated C language file into the executable file running on an embedded board. In order to monitor the status of the control system and change the parameters of the controller, a network-based supervisory program was also developed using Microsoft Visual C++ 6.0.

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University of Macau / Faculty of Science and Technology / Department of Mathematics

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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. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Problems in the theory of economic dynamics are tackled both by theoretical arguments and by use of specific examples. The work is divided into three essays. The first treats optimal control theory from an economic point of view, giving an exposition of the mathematical theory in terms of economic concepts. The idea of the marginal worth of time is introduced and found to be useful in a variety of problems. An interpretation is given of the phase planes of optimal control problems as demand-and-supply diagrams. The second essay makes use of the techniques developed in the first to solve the problem of when and how a firm faced with adverse economic circumstances will choose to go out of business if its operations depend on a stock of some fixed asset that depreciates over time. A straightforward catalogue is presented of different possible outcomes. The third essay deals with a model of urban housing. It contains two main sections. In the first, an equilibrium state is described in which demand by tenants for housing is met by supply from landlords who act as profit maximisers over the whole period of time that their property exists. The rent paid for any particular dwelling is assumed to depend on its state of upkeep, which in turn depends on how much is spent by a landlord on maintenance. The equilibrium is found by a procedure analogous to that regularly used in general equilibrium theory, namely by finding a fixed point of a mapping in a (here infinite-dimensional) vector space. In the second section of the essay, it is assumed that some externality arises which adversely affects urban life and which provokes people to move out to suburbs. The consequences of this are studied and two different kinds of dynamical evolution can be distinguished. One, in which house construction in the suburbs is slow enough to make it necessary for new construction to continue in the city, tends not to be disastrous for the city; the other, in which all urban construction stops when the externality arises, usually leads to complete decay of the city. Throughout the thesis there is an emphasis on the differences in approach between static or quasistatic problems and dynamic ones. / Arts, Faculty of / Vancouver School of Economics / Graduate

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