Minimum-Seeking for CLFs: Universal Semiglobally Stabilizing Feedback Under Unknown Control Directions

Employing extremum seeking (ES) for seeking minima of control Lyapunov function (CLF) candidates, we develop 1) the first systematic design of ES controllers for unstable plants, 2) a simple non-model based universal feedback law that emulates, in an average sense, the “ $L_{g}V$ controllers” for stabilization with inverse optimality, and 3) a new strategy for stabilization of systems with unknown control directions, as an alternative to Nussbaum gain controllers that lack exponential stability, lack transient performance guarantees, and lack robustness to changes in the control direction. The stability analysis that underlies our designs is inspired by an analysis approach synthesized in a recent work by Dürr, Stankovic, and Johansson, which combines a Lie bracket averaging result of Gurvits and Li with a semiglobal practical stability result under small parametric perturbations by Moreau and Aeyels.