Ellipsoidal Toolbox

Ellipsoidal Toolbox for MATLAB. Ellipsoidal Toolbox (ET) is a standalone set of easy-to-use configurable MATLAB routines to perform operations with ellipsoids and hyperplanes of arbitrary dimensions. It computes the external and internal ellipsoidal approximations of geometric (Minkowski) sums and differences of ellipsoids, intersections of ellipsoids and intersections of ellipsoids with halfspaces and polytopes; distances between ellipsoids, between ellipsoids and hyperplanes, between ellipsoids and polytopes; and projections onto given subspaces. Ellipsoidal methods are used to compute forward and backward reach sets of continuous- and discrete-time piecewise affine systems. Forward and backward reach sets can be also computed for piecewise linear systems with disturbances. It can be verified if computed reach sets intersect with given ellipsoids, hyperplanes, or polytopes.

References in zbMATH (referenced in 17 articles )

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  1. Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Computing the signed distance between overlapping ellipsoids (2015)
  2. Yan, Yan; Chirikjian, Gregory S.: Closed-form characterization of the Minkowski sum and difference of two ellipsoids (2015)
  3. Kurzhanski, Alexander B.; Varaiya, Pravin: Dynamics and control of trajectory tubes. Theory and computation (2014)
  4. Ushakov, V.N.; Matviichuk, A.R.; Parshikov, G.V.: A method for constructing a resolving control in an approach problem based on attraction to the feasibility set (2014)
  5. Kurzhanskii, A.B.; Tochilin, P.A.: Tracking within a time interval on the basis of data supplied by finite observers (2013)
  6. Mitchell, Ian M.; Kaynama, Shahab; Chen, Mo; Oishi, Meeko: Safety preserving control synthesis for sampled data systems (2013)
  7. Johnson, Taylor T.; Green, Jeremy; Mitra, Sayan; Dudley, Rachel; Erwin, Richard Scott: Satellite rendezvous and conjunction avoidance: case studies in verification of nonlinear hybrid systems (2012)
  8. Kuehn, Christian: Deterministic continuation of stochastic metastable equilibria via Lyapunov equations and ellipsoids (2012)
  9. Sijs, Joris; Lazar, Mircea: State fusion with unknown correlation: ellipsoidal intersection (2012)
  10. Amigo, Isabel; Vaton, Sandrine; Chonavel, Thierry; Larroca, Federico: Maximum delay computation under traffic matrix uncertainty and its application to interdomain path selection (2011)
  11. Kurzhanski, A.B.; Varaiya, P.: Optimization of output feedback control under set-membership uncertainty (2011)
  12. Kurzhanskiy, Alex A.; Varaiya, Pravin: Reach set computation and control synthesis for discrete-time dynamical systems with disturbances (2011)
  13. Lughofer, Edwin: Evolving fuzzy systems -- methodologies, advanced concepts and applications. (2011)
  14. Tyatyushkin, A.I.; Morzhin, O.V.: Numerical investigation of attainability sets of nonlinear controlled differential systems (2011)
  15. Weber, Gerhard-Wilhelm; Defterli, Ozlem; Alparslan Gök, Sırma Zeynep; Kropat, Erik: Modeling, inference and optimization of regulatory networks based on time series data (2011)
  16. McInroy, John E.; Qi, Zhen: A novel pose estimation algorithm based on points to regions correspondence (2008)
  17. Vostrikov, I.V.; Dar’in, A.N.; Kurzhanskii, A.B.: On the damping of a ladder-type vibration system subjected to uncertain perturbations (2006)