Robust Performance Analysis of Source-Seeking Dynamics with Integral Quadratic Constraints

We analyze the performance of source-seeking dynamics involving vehicles embedded in an underlying scalar field with gradient based forcing terms. We leverage the recently developed framework of α-integral quadratic constraints (IQCs) to obtain convergence rate estimates. We first present the hard Zames-Falb (ZF) α-IQCs involving general non-causal multipliers and show that a parameterization of the ZF multiplier, suggested in the literature for the standard version of the ZF IQCs, can be adapted to the α-IQCs setting. Owing to the time-domain arguments, we can seamlessly extend these results to linear parameter varying (LPV) vehicles possibly opening the doors to non-linear vehicle models with quasi-LPV representations. We illustrate the theoretical results on a linear time invariant (LTI) model of a quadrotor, a non-minimum phase LTI example and an LPV example of a quadrotor with two modes which show a clear benefit of using general non-causal dynamic multipliers to drastically reduce conservatism.