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

Inga J. Wolf, Diego A. Muñoz, Wolfgang Marquardt

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    16 Scopus citations


    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.

    Original languageEnglish
    Pages (from-to)389-398
    Number of pages10
    JournalJournal of Process Control
    Issue number2
    StatePublished - Feb 2014

    Bibliographical note

    Funding Information:
    This research has been partially supported by the German Research Foundation DFG ( MA 1188/33-1 ), the German Academic Exchange Service DAAD (ALECOL) and the European Commission ( CP-IP 228867-2 F3-Factory ). The authors would also like to thank Ralf Hannemann-Tamás, Lynn Würth and Karen Pontes for fruitful discussions.


    • Dynamic real-time optimization
    • Economic nonlinear model-predicitive control
    • Hierarchical control
    • Hybrid systems
    • Integrated scheduling
    • Neighboring-extremal control


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