The paper deals with the extremum seeking problem for a class of cost
functions depending only on a part of state variables of a control system. This
problem is related to the concept of partial asymptotic stability and analyzed
by Lyapunov's direct method and averaging schemes. Sufficient conditions for
the practical partial stability of a system with oscillating inputs are derived
with the use of Lie bracket approximation techniques. These conditions are
exploited to describe a broad class of extremum-seeking controllers ensuring
the partial stability of the set of minima of a cost function. The obtained
theoretical results are illustrated by the Brockett integrator and rotating
rigid body.Comment: This is the author's version of the manuscript accepted for
publication in the Proceedings of the Joint 8th IFAC Symposium on Mechatronic
Systems and 11th IFAC Symposium on Nonlinear Control Systems (MECHATRONICS &
NOLCOS 2019