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

Abstract

This work 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. 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 time-invariant systems and then extended to time-varying systems. As illustrative examples of application of the proposed methodology, we consider several end-point optimization problems in batch chemical and biochemical reactors.