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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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A digital motor controller for student lab use is designed, built, and tested. The controller uses an encoder for position measurement, and an H-bridge to drive the electromechanical plant. A user interface is created to enhance usability of the device. The user interface is able to display key parameters of the control algorithm as well as the state of the system. It is also used to modify the gains and sample rate of the control algorithm. The design of the system is refined, and 10 units are built for the EE472 Digital Controls Lab. The lab manuals for the first 4 experiments are revised to match and support the new system. The possible future for the project is described with some suggestions for improving the system.

In recent years, multi-robot systems have been widely used in many applications such as warehouse inventory tracking and automatic search and rescue operations. Probability roadmap (PRM) is a typical path planning algorithm that can determine an optimal trajectory once the robot start and goal positions are specified. However, when the number of robots in the system increases, it converges slowly and may even fail to find the solution. In this thesis, a fuzzy inference system is proposed and combined with the probability roadmap algorithm for robot path planning. Computer simulation results in five different environments show this approach is very effective to reduce computation cost in most cases for multi-robot systems of various sizes. It is able to reduce the number of collision checks by at least 27% with a trade off of increased average path length of 12% at the most. It is also noticed that the proposed fuzzy system is not advantageous when combined with the sub-dimension expansion algorithm. More research will be conducted in the future to further improve the performance of the proposed fuzzy inference system.

This thesis investigates the broad theme of guaranteeing the stability of nonlinear control systems. In the first section, we describe the application of discrete controller for the stabilization of certain nonlinear stochastic control systems subject to unavailability of state measurements. In the second section, we consider input constrained nonlinear systems and characterize the region from which stabilization to the origin is possible. We then use this information to design a controller which stabilizes everywhere in this set. / Thesis / Master of Applied Science (MASc)

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A new decentralized nonlinear controller for Robot Manipulators is presented in this thesis. Based on concepts of Lyapunov stability theory and some control ideas proposed in [3]-[7], we obtain continuous nonlinear decentralized control laws which guarantee position and velocity tracking to within an arbitrarily small error. Assumptions based on physical constraints of manipulators are made to guarantee the existence of the controller and asymptotic stability of the closed loop system. Simulations show how well this rather simple control scheme works on two of the links of the Puma 560 Manipulator. The main contribution of this thesis is that it extends the results of a class of complex centralized control algorithms to the decentralized robust control of interconnected nonlinear subsystems like robot manipulators. / Graduation date: 1992