  This paper proposes a multivariable extremum seeking scheme using Fast
Fourier Transform (FFT) for a network of subsystems working towards optimizing
the sum of their local objectives, where the overall objective is the only
available measurement. Here, the different inputs are perturbed with different
dither frequencies, and the power spectrum of the overall output signal
obtained using FFT is used to estimate the steady-state cost gradient w.r.t.
each input. The inputs for the subsystems are then updated using integral
control in order to drive the respective gradients to zero. This paper provides
analytical rules for designing the FFT-based gradient estimation algorithm and
analyzes the stability properties of the resulting extremum seeking scheme for
the static map setting. The effectiveness of the proposed FFT-based
multivariable extremum seeking scheme is demonstrated using two examples,
namely, wind farm power optimization problem, and a heat exchanger network for
industrial waste-to-heat recovery.
