Stability Metrics for Simulation and Flight-Software Assessment and Monitoring of Adaptive Control Assist Compensators

Due to a need for improved reliability and performance in aerospace systems, there is increased interest in the use of adaptive control or other nonlinear, time-varying control designs in aerospace vehicles. While such techniques are built on Lyapunov stability theory, they lack an accompanying set of metrics for the assessment of stability margins such as the classical gain and phase margins used in linear time-invariant systems. Such metrics must both be physically meaningful and permit the user to draw conclusions in a straightforward fashion. We present in this paper a roadmap to the development of metrics appropriate to nonlinear, time-varying systems. We also present two case studies in which frozen-time gain and phase margins incorrectly predict stability or instability. We then present a multi-resolution analysis approach that permits on-line real-time stability assessment of nonlinear systems. I. Introduction We present in this paper the results of our preliminary investigation into the development and use of stability metrics for stability analysis of adaptive control in aerospace vehicles. The primary outcome of this effort is the development of a road map toward the development and implementation of practical stability metrics. Included in this paper are: an overview of the long-term goals, objectives, and expected outcomes related to the development of practical stability metrics; §II; and a description of a potential technical approach for the development of stability metrics, §III. This description begins with a literature review of existing metrics, followed by a description of technology gaps and approaches to fill those gaps. We then present preliminary results in our investigation that indicate the failure of current stability metrics (gain, phase margins). These same results also indicate the potential for a multi-resolution analysis (wavelet decomposition). We conclude this discussion with a formal road map toward the development of stability metrics and associated software implementation.