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

Chapter
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 473)

Abstract

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.

Keywords

Input and state constraints Mixed constraints Nonlinear systems Barriers Admissible sets 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

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

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