Ellipsoidal Techniques for Reachability Analysis

By A. Kurzhanski, Pravin Pratap Varaiya. International Conference on Hybrid Systems: Computation and Control, 2000

543 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/bccd175afdc8f553607c3d38331ec0113dd14534

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Citations in the corpus

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].”
Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs (2006, methodology): “, ΩN computed by Algorithm 2 are tight in the sense of [KV00].”
Formal verification of hybrid systems (2011, background): “aimed at battling this complexity and/or replacing polyhedra with alternative representations [11, 21, 36, 42].”
Computational techniques for the verification of hybrid systems (2003, methodology): “VeriSHIFT [36] uses ellipsoidal overapproximations of reach sets for linear systems with linear input; it implements techniques developed in [37].”
Convex Computation of the Region of Attraction of Polynomial Control Systems (2012, background): “[25], [30], [32] or transfer operator approaches [44], even”
Set Propagation Techniques for Reachability Analysis (2021, unknown): “1: ellipsoids [57, 58], polytopes [59, 60], zonotopes [61, 62] or support functions [63, 64].”
Approximation of reachable sets using optimal control algorithms (2013, methodology): “Various methods for the approximation of reachable sets for linear control problems have been suggested, among them are set-valued integration schemes [4], optimal control techniques [64, 59, 6], external and inner ellipsoidal techniques [46, 47, 48], estimation methods [30, 42, 43, 28], see also re”
On reachability and minimum cost optimal control (2004, unknown): “Email address: lygeros@ee.upatras.gr (John Lygeros). proximations of these sets [15] [16] [17] [18] [19] [20] [21].”
Stabilization of nonlinear systems with limited information feedback (2005, unknown): “, [14] for ellipsoidal approximation techniques and [1] for related results involving Lyapunov functions).”
Impulse differential inclusions: a viability approach to hybrid systems (2002, methodology): “Theoretical methods have been developed for performing these computations [5], [6], [17], [7], [8], [18], [9], some of them supported by automated or semi-automated tools [20], [22], [23], [26], [24], [25], [29], [21].”
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].”
Guaranteed estimation of the parameters of nonlinear continuous‐time models: Contributions of interval analysis (2011, background): “Linear models with time-varying coefficients could also be considered, as in [21].”
Reachability Analysis and its Application to the Safety Assessment of Autonomous Cars (2010, background): “If PR(r) would be exact, one could give the following statement: The over-approximations due to the box()-operator are tight in the sense of [102], i.”
Computational techniques for hybrid system verification (2003, unknown): “Alternatives to the approach proposed in this paper include: grid-based discretizationsof thecontinuousstatespace,whichcanbeautomated quite easily and robustly, but can lead to enormous finite-state approximations[9], [30];ellipsoidalapproximationsofreachable sets (at a given time), for which exact ”
A Framework for Worst-Case and Stochastic Safety Verification Using Barrier Certificates (2007, background): “For linear systems, there are results based on quantifier elimination [47], ellipsoidal calculus [26], [10], polygonal approximation [8], [6], geometric programming [53], and real algebraic geometry [54].”