Applications of optimal control theory to distributed parameter systems

The subject of this dissertation is the application of optimal control theory to distributed parameter systems. The dissertation is divided into three parts. In part I, the general techniques of optimal control theory are discussed and highlighted with a help a of a simple but instructive example. In Part II, a two dimensional parabolic system with competitive interac-tions is modeled as a two person zero sum game. The saddle point of the game is established and characterized. The controls are the kernels of the interaction terms. Part III is devoted to the application of optimal control theory to a prob-lem motivated from in situ bioremediation. In this remediation technology the indigenous sub-surface bacteria are stimulated by injecting compounds. The bacteria uses the injected compounds to break down chemical contaminants into less harmful substances. The way the compounds are injected is a crucial component of the technology. Optimal control theory is used to characterize an optimal injection function. The state system is a hybrid system consisting of both partial and oridinary differential equations.