Consistent hierarchical economic NMPC for a class of hybrid systems using neighboring-extremal updates

• We propose a fully consistent two-layer dynamic real-time architecture for a special class of hybrid systems.
• The arising challenges for solution methods are discussed when (hybrid) eNMPC is applied.
• The fast hybrid neighboring-extremal controller (NEC) on the lower layer ensures consistency by considering the same economic optimal control problem as the hybrid eNMPC.
• The NEC avoids infeasibilities and steers the process to its operational bounds under disturbances.
• An important step towards integrated scheduling and control is taken.

A hierarchical two-layer control algorithm is developed for a class of hybrid (discrete-continuous dynamic) systems to support economically optimal operation of batch or continuous processes with a predefined production schedule. For this class of hybrid systems, the optimal control moves as well as the controlled switching times between two adjacent modes are determined online. In contrast to closely related schemes for integrated scheduling and control, the sequence of modes is not optimized. On the upper layer, the economic optimal control problem is solved rigorously by a slow hybrid economic model predictive controller at a low sampling rate. On the lower layer, a fast hybrid neighboring-extremal controller is based on the same economic optimal control problem as the slow controller to ensure consistency between both layers. The fast neighboring-extremal controller updates rather than tracks the optimal trajectories from the upper layer to account for disturbances. Consequently, the fast controller steers the process to its operational bounds under disturbances and the economic potential of the process is exploited anytime. The suggested two-layer control algorithm provides fully consistent control action on the fast and slow time-scale and thus avoids performance degradation and even infeasibilities which are commonly encountered if inconsistent optimal control problems are formulated and solved.