From Pure State and Input Constraints to Mixed Constraints in Nonlinear Systems

  • Willem Esterhuizen
  • Jean Lévine
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 473)


We survey the results on the problem of pure/mixed state and input constrained control, with multidimensional constraints, for finite dimensional nonlinear differential systems with focus on the so-called admissible set and its boundary. The admissible set is the set of initial conditions for which there exist a control and an integral curve satisfying the constraints for all time. Its boundary is made of two disjoint parts: the subset of the state constraint boundary on which there are trajectories pointing towards the interior of the admissible set or tangentially to it; and a barrier, namely a semipermeable surface which is constructed via a generalized minimum-like principle with nonsmooth terminal conditions. Comparisons between pure state constraints and mixed ones are presented on a series of simple academic examples.


Input and state constraints Mixed constraints Nonlinear systems Barriers Admissible sets 


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.CAS, Mathématiques et Systèmes, MINES-ParisTech, PSL Research UniversityFontainebleauFrance

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