Constrained extremum seeking in 1 dimension

In this paper we present a novel approach for applying extremum seeking optimization to systems with input constraints. We use an unknown quadratic objective function and provide that the 1-dimensional sinusoidal extremum seeking scheme is domain-limited semi-globally practically asymptotically stable about the constrained minimum. The incorporation of an orthogonal projection operator prohibits the estimate system from leaving the constraint set and the perturbed system from leaving the constraint set dilated by the perturbation amplitude.