Synthesis of state feedback laws for end-point optimization in batch processes

his thesis studies the class of singular optimal control problems, where a performance index must be optimized at the final time of operation of a batch process. It is shown that geometric tools can be used o obtain a more concrete and transparent representation of the necessary conditions for optimality. Optimal state feedback laws for the singular region of operation are derived for the first time. The existence of a singular region as well as the nature of the feedback law (static or dynamic) are completely characterized in terms of the Lie bracket structure of the system dynamics. Explicit synthesis formulae for the state feedback laws are first obtained for the case where the final time is fixed and there are no state inequality constraints. Utilizing the same methodology, these results are extended to include the case where the final time is free and there is a state inequality constraint. As illustrative examples of application of the proposed methodology, several end-point optimization problems in batch chemical and biochemical reactors are considered. It is observed that under certain conditions the end-point optimization problem is equivalent to a regulation problem in a time-varying system. Feedback laws are derived to solve this regulation problem. A nonlinear transformation is derived which provides a linear time-invariant input-output response. A standard linear controller with integral action is then used for offsetless tracking of the desired trajectory. Internal stability results under the state feedback are provided. Then, a dynamic output feedback controller for the time-varying system is synthesized. Finally, end-point optimization of cephamycin C, an industrially important...