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 37 articles )

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  1. Chirikjian, Gregory S.; Shiffman, Bernard: Applications of convex geometry to Minkowski sums of (m) ellipsoids in (\mathbbR^N): Closed-form parametric equations and volume bounds (2021)
  2. Rauh, Andreas; Jaulin, Luc: A computationally inexpensive algorithm for determining outer and inner enclosures of nonlinear mappings of ellipsoidal domains (2021)
  3. Khatibi, Mahmood; Haeri, Mohammad: A unified framework for passive-active fault-tolerant control systems considering actuator saturation and (\mathrmL_\infty) disturbances (2019)
  4. Meyer, Pierre-Jean; Devonport, Alex; Arcak, Murat: TIRA: toolbox for interval reachability analysis (2019)
  5. Qin, Xiaolong; An, Nguyen Thai: Smoothing algorithms for computing the projection onto a Minkowski sum of convex sets (2019)
  6. Yousefi, Mahdi; van Heusden, Klaske; Mitchell, Ian M.; Dumont, Guy A.: Model-invariant viability kernel approximation (2019)
  7. Bogomolov, Sergiy; Forets, Marcelo; Frehse, Goran; Viry, Frédéric; Podelski, Andreas; Schilling, Christian: Reach set approximation through decomposition with low-dimensional sets and high-dimensional matrices (2018)
  8. Doyen, Laurent; Frehse, Goran; Pappas, George J.; Platzer, André: Verification of hybrid systems (2018)
  9. Silvestre, Daniel; Rosa, Paulo; Hespanha, João P.; Silvestre, Carlos: Self-triggered and event-triggered set-valued observers (2018)
  10. Dreossi, Tommaso; Dang, Thao; Piazza, Carla: Reachability computation for polynomial dynamical systems (2017)
  11. Goubault, Eric; Putot, Sylvie: Forward inner-approximated reachability of non-linear continuous systems (2017)
  12. Vinod, Abraham P.; HomChaudhuri, Baisravan; Oishi, Meeko M. K.: Forward stochastic reachability analysis for uncontrolled linear systems using Fourier transforms (2017)
  13. Zhai, Shouchao; Wan, Yiming; Ye, Hao: A set-membership approach to integrated trade-off design of robust fault detection system (2017)
  14. Hamri, H.; Kara, R.; Amari, S.: Model predictive control of P-time event graphs (2016)
  15. Adzkiya, Dieky; De Schutter, Bart; Abate, Alessandro: Computational techniques for reachability analysis of Max-Plus-Linear systems (2015)
  16. Franzè, G.; Lucia, W.: An obstacle avoidance model predictive control scheme for mobile robots subject to nonholonomic constraints: a sum-of-squares approach (2015)
  17. Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko: Computing the signed distance between overlapping ellipsoids (2015)
  18. Shmatkov, A. M.: A smoothing filter based on an analogue of a Kalman filter for a guaranteed estimation of the state of dynamical systems (2015)
  19. Yan, Yan; Chirikjian, Gregory S.: Closed-form characterization of the Minkowski sum and difference of two ellipsoids (2015)
  20. Kurzhanski, Alexander B.; Varaiya, Pravin: Dynamics and control of trajectory tubes. Theory and computation (2014)

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