Mixed-integer extremum seeking control for unknown static maps

This study proposes a new design for the solution of mixed integer extremum seeking controllers for unknown static maps subject to a combination of saturated and quantized actuators with unknown characteristics but with measurable final control elements. The proposed design techniques incorporates a filter for each uncertain actuator that enables the design of a constrained extremum seeking control that operates at a slow time-scale. The stability analysis demonstrates that the closed-loop system has a practically asymptotically stable equilibrium at the unknown constrained optimum of the optimization problem. A simulation is presented that demonstrates the effectiveness of the proposed technique.