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

03 17 Category: Constraints | All

Authors: Willem Esterhuizen, Jean Lévine, in Feedback Stabilization of Controlled Dynamical Systems, pp. 125-141, Nicolas Petit Ed., Vol. 473 in Lecture Notes in Control and Information Sciences, Springer-Verlag, March 24 2017. DOI: 10.1007/978-3-319-51298-3_5

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.

BibTeX

@Incollection{2017-05-27,

author = {Willem Esterhuizen, Jean Lévine},

title = {From Pure State and Input Constraints to Mixed Constraints in Nonlinear Systems},

booktitle = {Feedback Stabilization of Controlled Dynamical Systems},

editor = {Petit, Nicolas},

publisher = {Springer},

address = {},

pages = {125-141},

year = {2017},

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}}

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.

BibTeX

@Incollection{2017-05-27,

author = {Willem Esterhuizen, Jean Lévine},

title = {From Pure State and Input Constraints to Mixed Constraints in Nonlinear Systems},

booktitle = {Feedback Stabilization of Controlled Dynamical Systems},

editor = {Petit, Nicolas},

publisher = {Springer},

address = {},

pages = {125-141},

year = {2017},

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}}