On-line Estimation of Stability and Passivity Metrics

We consider the problem of on-line evaluation of critical characteristic parameters such as the ℒ
2
-gain, input feedforward passivity index and output feedback passivity index of non-linear systems using their input-output data. Typically, having an accurate measure of such system indices enables the application of systematic control design techniques. Moreover, if such system indices can efficiently be evaluated on-line, they can be exploited to design intelligent control solutions. However, the existing off-line estimation methods of such system indices are computationally inefficient and require a large amount of input-output data. On the other hand, the existing on-line estimation methods take an averaging-based approach, which may be sub-optimal, computationally inefficient and susceptible to estimate saturation. To overcome these challenges in the on-line estimation of system indices, we establish and exploit several interesting theoretical results on a particular class of fractional function optimization problems. Finally, we provide several numerical examples to highlight our contributions.