A feedback-based implementation scheme for batch process optimization

The terminal-cost optimization of a control±ane nonlinear system leads to a discontinuous solution that can be characterized in a piecewise manner. To implement such an optimal trajectory despite disturbances and parametric uncertainty, a cascade optimi- zation scheme is proposed in this paper, where optimal reference signals are tracked. Optimality is achieved by the appropriate de®nition of reference signals (input bounds, state constraints, or switching functions) to track in various sub-intervals. Further- more, conservatism is introduced into the optimization problem to ensure satisfaction of path constraints in the presence of uncertainty. Finally, the proposed cascade optimization scheme is illustrated on a simulation of a fed-batch penicillin fermentation plant.