“Computational Performance Analysis of Nonlinear Dynamic Systems using Semi-infinite Programming”

Authors: Tor A. Johansen,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2001, Vol 22, No 1, pp. 15-27.

Keywords: Hamilton-Jacobi inequality, stability, Lyapunov functions, convex optimization, performance

Abstract: For nonlinear systems that satisfy certain regularity conditions it is shown that upper and lower bounds on the performance (cost function) can be computed using linear or quadratic programming. The performance conditions derived from Hamilton-Jacobi inequalities are formulated as linear inequalities defined pointwise by discretizing the state-space when assuming a linearly parameterized class of functions representing the candidate performance bounds. Uncertainty with respect to some system parameters can be incorporated by also gridding the parameter set. In addition to performance analysis, the method can also be used to compute Lyapunov functions that guarantees uniform exponential stability.

PDF PDF (1590 Kb)        DOI: 10.4173/mic.2001.1.2

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  title={{Computational Performance Analysis of Nonlinear Dynamic Systems using Semi-infinite Programming}},
  author={Johansen, Tor A.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}