Computational techniques for hybrid system verification

By Alongkrit Chutinan, Bruce H. Krogh. IEEE Transactions on Automatic Control, 2003

365 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/0aa8337a5447c4b3eed9d2fb49d766b318fc9356

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Citations in the corpus

Differential Dynamic Logic for Hybrid Systems (2008, methodology): “Chutinan and Krogh [13] presented polyhedral approximations of hybrid automata with polyhedral discrete dynamics, invariants, and initial state sets.”
Online Verification of Automated Road Vehicles Using Reachability Analysis (2014, methodology): “Approaches which do not use abstraction are mostly based on computationally demanding optimization techniques [15] o r on a reformulation of the reachability problem as HamiltonJacobi equations, whose solution procedure has exponentia l complexity in the number of continuous state variables [15] – [”
Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization (2008, methodology): “The explicit computation of over-approximated reachable sets has been performed for polynomial nonlinear systems using Bézier control nets in [10] and for general nonlinear systems using global optimization techniques and face lifting in [11], [12] respectively.”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, methodology): “Several geometric representations for linear continuous systems have been investigated: Polytopes [39], griddy polyhedra [10], ellipsoids [102, 103], oriented rectangular hulls [158], zonotopes [69], or support functions [70] which unify the other mentioned representations.”
Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs (2006, methodology): “a non-trivial continuous dynamics, an approximation of the reachable states is generally computed by a combination of numerical integration and geometrical algorithms [GM99], [ CK03 ], [ABDM00], [D00], [BT00], [KV00] [G05].”
Reachability of Uncertain Linear Systems Using Zonotopes (2005, methodology): “It is compatible with high level algorithms used by the toolboxes d/dt [3] and CheckMate [8].”
Safety Verification of Hybrid Systems Using Barrier Certificates (2004, methodology): “Such techniques rely on numerical methods for solving the Hamilton Jacobi equations [23], ellipsoidal calculus [13, 6], flow-pipe approximations [9], and polygonal approximations [5, 4, 2].”
Cyber–Physical Systems: A Perspective at the Centennial (2012, methodology): “Another useful technique is to overapproximate the evolution of continuous variables using polyhedral representation [111], [112].”
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates (2007, methodology): “Other techniques have been proposed for nonlinear systems, for example, based on the Hamilton Jacobi equations [50], polygonal approximations [14], and approximating the system as a piecewise linear system [5].”
A tutorial on sum of squares techniques for systems analysis (2005, neutral): “[3], [2], [8], [54]).”
A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games (2005, neutral): “These include the tools CheckMate [25], [26], HyTech [27] and”