Computing the viability kernel using maximal reachable sets

Authors:
Shahab Kaynama;John Maidens;Meeko Oishi;Ian M. Mitchell;Guy A. Dumont
Affiliations:
University of British Columbia, Vancouver, BC, Canada;University of British Columbia, Vancouver, BC, Canada;University of New Mexico, Albuquerque, NM, USA;University of British Columbia, Vancouver, BC, Canada;University of British Columbia, Vancouver, BC, Canada
Venue:
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
Year:
2012

Citing 11
Cited 0

Viability theory

Viability theory
On Reachability Under Uncertainty

SIAM Journal on Control and Optimization
Ellipsoidal Techniques for Reachability Analysis

HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Overapproximating Reachable Sets by Hamilton-Jacobi Projections

Journal of Scientific Computing
Convex Optimization

Convex Optimization
Set-Theoretic Methods in Control

Set-Theoretic Methods in Control
Comparing forward and backward reachability as tools for safety analysis

HSCC'07 Proceedings of the 10th international conference on Hybrid systems: computation and control
Scalable calculation of reach sets and tubes for nonlinear systems with terminal integrators: a mixed implicit explicit formulation

Proceedings of the 14th international conference on Hybrid systems: computation and control
The reachability problem for uncertain hybrid systems revisited: a viability theory perspective

HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Efficient computation of reachable sets of linear time-invariant systems with inputs

HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
On reachability and minimum cost optimal control

Automatica (Journal of IFAC)

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a connection between the viability kernel and maximal reachable sets. Current numerical schemes that compute the viability kernel suffer from a complexity that is exponential in the dimension of the state space. In contrast, extremely efficient and scalable techniques are available that compute maximal reachable sets. We show that under certain conditions these techniques can be used to conservatively approximate the viability kernel for possibly high-dimensional systems. We demonstrate the results on two practical examples, one of which is a seven-dimensional problem of safety in anesthesia.