Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems

By E. Asarin, T. Dang, Oded Maler, O. Bournez. International Conference on Hybrid Systems: Computation and Control, 2000

367 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Software

View Paper: https://www.semanticscholar.org/paper/cfb44d50d6f12622a0c54ed94fc75173c90ff94e

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Citations in the corpus

Impulse differential inclusions: a viability approach to hybrid systems (2002, background): “mation techniques have been proposed to facilitate the analysis [17]–[19].”
Reachability of Uncertain Linear Systems Using Zonotopes (2005, methodology): “Methods have been proposed using several set representations such as general polytopes [7] oriented hyperrectangles [18], orthogonal polyhedra [2], ellipsoids [14] or level sets [16].”
Formal verification of hybrid systems (2011, methodology): “aimed at battling this complexity and/or replacing polyhedra with alternative representations [11, 21, 36, 42].”
Approximation Metrics for Discrete and Continuous Systems (2006, methodology): “It consists in solving a static game where the cost function is the branching distance (see Theorems 16 and 20).”
Cyber–Physical Systems: A Perspective at the Centennial (2012, methodology): “Another useful technique is to over-approximate the evolution of continuous variables using polyhedral representation [111], [112].”
Provably safe and robust learning-based model predictive control (2011, positive): “The main insight of LBMPC is that performance and safety can be de-coupled in an MPC framework by using reachability tools [4,14,56,23,5,69,52].”
Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs (2006, methodology): “The first set of the sequence, Ω0, can be obtained by bloating the convex hull of the sets I and ΦI where Φ = e (see [CK03], [ABDM00], [D00], [G05]).”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, background): “vehicle A s(0) ∈ [40, 52] m v(0) ∈ [10, 12] m/s vehicle B s(0) ∈ [5, 17] m v(0) ∈ [10, 12] m/s vehicle C s(0) ∈ [25, 37] m v(0) ∈ [6, 8] m/s vehicle D s(0) ∈ [5, 17] m v(0) ∈ [8, 10] m/s”
SpaceEx: Scalable Verification of Hybrid Systems (2011, background): “The second wave of hybrid verification tools [6,3,12] indeed abandoned exact computations and focused more on computing approximations of the reachable states for systems admitting less trivial continuous dynamics.”
Computational techniques for the verification of hybrid systems (2003, methodology): “The tools [30], [31] and Checkmate [32], [33] represent sets as convex polyhedra and propagate these polyhedra under linear and affine dynamics, which could represent overapproximations of nonlinear dynamics along each surface of the polyhedra.”