In this paper, we address the problem of steering the input of a convex function to a value that minimizes the function under a convex constraint. We consider the case where the constraint cannot be violated of more than a user-defined value during the whole transient phase. The mathematical expression of both the cost function and the constraint are assumed to be unknown. The only information available are the on-line values of the cost and the constraint. To tackle this problem, an optimization law, based on a modified-barrier function, and involving the gradient of both the cost function and the constraint, is firstly designed. The Lie bracket formalism is then exploited to approximate this law, by combining time-periodic signals with the on-line measurements of both the cost and the constraint. The stability property of the resulting constrained extremum seeking system is proved, and its effectiveness is shown in simulation.
展开▼
