Efficient polyhedral enclosures for the reachable set of nonlinear control systems

  • Stuart M. Harwood
  • Paul I. Barton
Original Article


This work presents a general theory for the construction of a polyhedral outer approximation of the reachable set (“polyhedral bounds”) of a dynamic system subject to time-varying inputs and uncertain initial conditions. This theory is inspired by the efficient methods for the construction of interval bounds based on comparison theorems. A numerically implementable instance of this theory leads to an auxiliary system of differential equations which can be solved with standard numerical integration methods. Meanwhile, the use of polyhedra provides greater flexibility in defining tight enclosures on the reachable set. These advantages are demonstrated with a few examples, which show that tight bounds can be efficiently computed for general, nonlinear systems. Further, it is demonstrated that the ability to use polyhedra provides a means to meaningfully distinguish between time-varying and constant, but uncertain, inputs.


Control systems Reachability Linear programming Affine relaxations 



The authors thank Novartis Pharmaceuticals as part of the Novartis-MIT Center for Continuous Manufacturing for funding this research, and Garrett Dowdy for some suggestions on the technical results.


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Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  1. 1.Process Systems Engineering LaboratoryMassachusetts Institute of TechnologyCambridgeUSA

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