Nested Optimization in DOA Estimation for Nonlinear Dynamical Systems: Spacecraft Large Angle Manoeuvres

Dempster, M.A.H. (1980). Nested Optimization in DOA Estimation for Nonlinear Dynamical Systems: Spacecraft Large Angle Manoeuvres. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-80-179

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Abstract

This paper discusses the formulation and numerical development of an algorithm for the estimation of the domain of attraction of a general nonlinear autonomous dynamical system. The method is based on stability analysis using Lyapunov's direct method with quadratic Lyapunov functions. It requires the nesting of an unconstrained and a constrained optimization problem -- both highly nonlinear. The Powell '64 conjugate direction algorithm and the BFGS quasi-Newton algorithm may be used as alternatives at the outer loop, while the recent Powell-Han projected Lagrangean algorithm is used for the inner loop nonlinear programme. Difficulties intrinsic to the Powell-Han algorithm, in obtaining global constrained minima and in providing sensitivity analysis of the inner loop problem in order to use BFGS at the outer loop are discussed in the context of stable control of large angle manoeuvres for astronomical satellites.

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