A proportional integral extremum-seeking control approach

This paper proposes an alternative extremum seeking control design technique for the solution of real-time optimization control problems. The technique considers a proportionalintegral approach that avoids the need for a time-scale separation in the formulation of the ESC. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The dynamics are assumed to be asymptotically stable and relative order one with respect to the objective function. The extremum-seeking problem is solved using a time-varying parameter estimation technique.