Reachability of Uncertain Linear Systems Using Zonotopes

By Antoine Girard. International Conference on Hybrid Systems: Computation and Control, 2005

691 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/e76a36257cd743a04b4454c2c50670e47b3ca448

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In Computational Theory and Mathematics

Citations in the corpus

Approximation Metrics for Discrete and Continuous Systems (2006, methodology): “The reachable sets were computed using the very recent zono-tope techniques [25].”
Set Propagation Techniques for Reachability Analysis (2021, neutral): “1: ellipsoids [57, 58], polytopes [59, 60], zonotopes [61, 62] or support functions [63, 64].”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, methodology): “This problem is complex [79], such that a rougher over-approximation is used which is proposed in [69] for two zonotopes of equal order and equal dimension:”
Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization (2008, background): “[18]), such that Z = Z ∗ + (0, g), Z1 = Z ∗ + (− 1 2g , 12g ) and Z2 = Z ∗ + (12g , 1 2g ), resulting in Z = Z1 ∪ Z2.”
Funnel libraries for real-time robust feedback motion planning (2016, neutral): “(approximations of) backwards and forwards reachable sets (Girard, 2005; Kurzhanski and Varaiya, 2000; Yazarel and Pappas, 2004).”
The Zonotope Abstract Domain Taylor1+ (2009, methodology): “We are working on some techniques, namely those used in [8] and [10], to control the potential increase of the number of noise symbols during analysis.”
Formal verification of hybrid systems (2011, background): “aimed at battling this complexity and/or replacing polyhedra with alternative representations [11, 21, 36, 42].”
A Logical Product Approach to Zonotope Intersection (2010, background): “Zonotopic abstractions are known to give fast and accurate over-approximations in invariant synthesis for static analysis of programs, as introduced by the authors [10, 11, 7], as well as in reachability analysis of hybrid systems [8].”
Approximately bisimilar symbolic models for nonlinear control systems (2007, neutral): “[Var98], [Gir05]) with compact input space.”
A sampling approach to finding Lyapunov functions for nonlinear discrete-time systems (2016, neutral): “, [12], [13], [14], [15] or infinite–time reachability, i.”