Solution Examples on Ellipsoidal Methods: Computation in High Dimensions

Part of the Systems & Control: Foundations & Applications book series (SCFA, volume 85)


In this chapter we describe solution examples for controlled systems that illustrate the contents of Chaps. 1– 3. These include the multiple integrator, planar Newtonian motions and calming down a chain of springs. Special sections are devoted to relevant computational formulas and high-dimensional systems. Also discussed are possible degeneracy effects in computation and the means of their avoidance.


Multiple integrator Newtonian motion Oscillating system Graphic illustration Regularization High dimensions 


  1. 57.
    Daryin, A.N., Kurzhanski, A.B.: Estimation of reachability sets for large-scale uncertain systems: from theory to computation. In: Proceedings of CDC-2012 (2012)Google Scholar
  2. 58.
    Daryin, A.N., Kurzhanski, A.B.: Parallel algorithm for calculating the invariant sets of high-dimensional linear systems under uncertainty. Comput. Math. Math. Phys. 53(1), 34–43 (2013)MathSciNetCrossRefGoogle Scholar
  3. 89.
    Godunov, S.K.: Guaranteed Accuracy in Numerical Linear Algebra. Springer, Dordrecht (1993)CrossRefzbMATHGoogle Scholar
  4. 90.
    Godunov, S.K.: Ordinary Differential Equations with Constant Coefficients, vol. 169. AMS Bookstore, Providence (1997)Google Scholar
  5. 92.
    Golub, G.H., Van Loan, C.F.: Matrix Computations. John Hopkins Un. Press, Baltimore, MI (1996)zbMATHGoogle Scholar
  6. 132.
    Kurzhanskiy, A.A., Varaiya, P.: Ellipsoidal Toolbox. University of California at Berkeley. (2005)
  7. 174.
    Kurzhanski, A.B., Vályi, I.: Ellipsoidal Calculus for Estimation and Control. SCFA. Birkhäuser, Boston (1997)CrossRefzbMATHGoogle Scholar
  8. 182.
    Kurzhanski, A.B., Varaiya, P.: Ellipsoidal techniques for reachability analysis. Part II: internal approximations. Box-valued constraints. Optim. Methods Softw. 17(2), 207–237 (2002)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Faculty of Computational Mathematics and CyberneticsMoscow State (Lomonosov) UniversityMoscowRussia
  2. 2.Electrical Engineering and Computer SciencesUniversity of California, BerkeleyBerkeleyUSA

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