APPROXIMATION OF POINCARE SECTIONS ARISING IN ATTITUDE-CONTROL
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While earlier papers have demonstrated that adaptive control schemes for the emerging class of evolutionary spacecraft can exhibit pathological instability, and even chaotic response, this paper addresses issues of approximating and predicting the nature of the response in these cases. This problem is of utmost importance for two reasons. First, inasmuch as robust adaptive control schemes are required, and have been the topic of much debate over the past few years, it is crucial to obtain a method for approximating how the dynamics of a given system changes qualitatively with the selection of control design parameters. Hence, it is necessary to characterize the parametric dependence of the dynamics; exhaustive studies of control system performance for systems with large numbers of degrees of freedom is not computationally feasible. Secondly, numerous authors have suggested control methodologies that are based upon the fact that the system under consideration is, in fact, exhibiting chaotic response. In these cases, it is necessary to be able to detect the onset of chaos, as well as obtain a reasonable approximation to the dynamics of the system on-line. Thus, this paper present three approximation methods for characterizing Poincare sections arising in adaptive attitude control: (1) wavelet analysis to determine the onset of chaos from Poincare sections, (2) iterated function systems for interpolating Poincare sections as a function of control system parameters, and (3) tensor product approximation of Poincare sections.
