| The ability of biological systems to make intelligent control decisions based on pattern recognition is well known. However, due to the complex and diverse nature of the problems, the study of pattern recognition and control within a systems theoretic framework is extremely difficult. In this thesis pattern recognition and control problems are considered when the patterns of interest are restricted to the state space, the parameter space, or the command space of the system. The control decisions are also confined to the choice of the control input, the controller, and the reference trajectory respectively, as we consider each of these three spaces. Most, if not all, of the practical control problems that are based on pattern recognition falls under one of these three categories. Furthermore, by restricting the pattern spaces and control decisions involved in each case, it allows us to formulate problems that can be analyzed using concepts and techniques familiar to control theorists. In view of the complex nature of the problems under consideration, most of the analysis in this thesis is carried out in the context of linear systems.; For patterns in state space, we determine the appropriate state classification such that the state trajectory of an unstable system can be kept bounded when the control input is chosen from a finite set based on the state class. Conditions under which this is possible and bounds of the control accuracy are derived. The dual problem of state estimation based on imprecise output measurements is formulated and solved. The formulation requires a new concept of imprecise output measurement, and corresponds to an observation process in which the point of focus of the measurement device has to change in some fashion as the system evolves. For patterns in parameter space, the main theoretical contributions are the determination of conditions under which misclassification can occur, and their use in class verification. The result has implications to model generation from input-output data as well. For patterns in command space, the patterns dictate which reference trajectory the system output should follow. A stability problem is formulated that arises due to changes in reference trajectory, when the control input is subject to saturation. A control strategy is proposed that gaurantees the stability of the system for any sequence of command patterns. |
