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We consider the problem of on-line evaluation of critical characteristicparameters such as the L_2-gain (L2G), input feedforward passivity index (IFP)and output feedback passivity index (OFP) of non-linear systems using theirinput-output data. Typically, having an accurate measure of such "systemindices" enables the application of systematic control design techniques.Moreover, if such system indices can efficiently be evaluated on-line, they canbe exploited to device intelligent controller reconfiguration andfault-tolerant control techniques. However, the existing estimation methods ofsuch system indices (i.e., L2G, IFP and OFP) are predominantly off-line,computationally inefficient, and require a large amount of actual orsynthetically generated input-output trajectory data under some specificinitial/terminal conditions. On the other hand, the existing on-line estimationmethods take an averaging-based approach, which may be sub-optimal,computationally inefficient and susceptible to estimate saturation. In thispaper, to overcome these challenges (in the on-line estimation of systemindices), we establish and exploit several interesting theoretical results on aparticular class of fractional function optimization problems. For comparisonpurposes, the details of an existing averaging-based approach are provided forthe same on-line estimation problem. Finally, several numerical examples arediscussed to demonstrate the proposed on-line estimation approach and tohighlight our contributions.

On-line Estimation of Stability and Passivity Metrics