  We propose a dual mode extremum seeking control design technique that
achieves real-time optimization of an unknown measured cost function in a
prescribed time. The controller is shown to achieve semi-global practical
stability of the optimal equilibrium for the state variables and the input
variable for a class of nonlinear dynamical control systems with unknown
dynamics. The design technique proposes a timescale transformation that enables
the use of dither signals with increasing frequencies. The proposed timescale
transformation is designed to avoid the singularity occurring at the prescribed
time. A simulation study is performed to demonstrate the effectiveness of the
proposed technique.
