  In this paper, we consider the optimisation of a time varying scalar field by
a network of agents with no gradient information. We propose a composite
control law, blending extremum seeking with formation control in order to
converge to the extrema faster by minimising the gradient estimation error. By
formalising the relationship between the formation and the gradient estimation
error, we provide a novel analysis to prove the convergence of the network to a
bounded neighbourhood of the field's time varying extrema. We assume the
time-varying field satisfies the Polyak Lojasiewicz inequality and the gradient
is Lipschitz continuous at each iteration. Numerical studies and comparisons
are provided to support the theoretical results.
