Nonlinear robust performance analysis using complex-step gradient approximation

Authors:
Jongrae Kim;Declan G. Bates;Ian Postlethwaite
Affiliations:
Control & Instrumentation Research Group, Department of Engineering, University of Leicester, Leicester LE1 7RH, UK;Control & Instrumentation Research Group, Department of Engineering, University of Leicester, Leicester LE1 7RH, UK;Control & Instrumentation Research Group, Department of Engineering, University of Leicester, Leicester LE1 7RH, UK
Venue:
Automatica (Journal of IFAC)
Year:
2006

Citing 4
Cited 1

Using Complex Variables to Estimate Derivatives of Real Functions

SIAM Review
Introduction to Stochastic Search and Optimization

Introduction to Stochastic Search and Optimization
Numerical algorithms based on the theory of complex variable

ACM '67 Proceedings of the 1967 22nd national conference
On the extension of the complex-step derivative technique to pseudospectral algorithms

Journal of Computational Physics

On the generalization of the Complex Step Method

Journal of Computational and Applied Mathematics

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Abstract

In this paper, the complex-step method is applied in the setting of numerical optimisation problems involving dynamical systems modelled as nonlinear differential equations. The main advantage of the complex-step method for gradient approximation is that it entails no subtractive cancellation error, and therefore the truncation error can be made arbitrarily (to machine precision) small. The method is applied to two robust performance analysis problems. The accuracy and convergence rate of the solutions computed using the proposed approach are seen to be significantly better than those achieved using standard gradient approximation methods.