EXTREMUM SEEKING CONTROL FOR A CLASS OF NONHOLONOMIC SYSTEMS

摘要

We propose an extremum seeking control law for a driftless control-affine system with a state-dependent real-valued output function. The purpose of the control law is to asymptotically stabilize the closed-loop system around states at which the output function attains a local minimum. An implementation of the control law only requires measurements of the output values. The approach employs highly oscillatory inputs with suitably chosen frequencies. A detailed averaging analysis reveals that the closed-loop system is driven approximately into descent directions of the output function along Lie brackets of the control vector fields. Those descent directions also originate from an approximation of suitably chosen Lie brackets. The approximation properties are ensured if the amplitudes and frequencies of the oscillatory inputs are sufficiently large. The proposed method can lead to practical asymptotic stability even if the control vector fields do not span the entire tangent. It suffices instead that the tangent space is spanned by the elements in the Lie algebra generated by the control vector fields. This novel feature extends extremum seeking by Lie bracket approximations from the class of fully actuated systems to a larger class of nonholonomic systems.