Semi-global stability analysis of source seeking with dynamic sensor reading and a class of nonlinear maps

This paper considers an extremum-seeking-based source seeking with dynamic sensor reading and a class of nonlinear maps to localise a stationary source emitting from an unknown signal field. Unlike the majority of existing extremum-seeking-based source seeking strategies that only deal with the quadratic map, the more universal case is considered that the map is quasi-concave nonlinear. In addition, the dynamic sensor reading is also considered which arises in many applications. However, this dynamic sensor could cause poor performance and could be a potential cause of instability. To resolve it, combined filters and a phase-lead compensator are utilised to improve the performance. Furthermore, a critical semi-global stability analysis is theoretically proven which shows that the proposed scheme can seek an arbitrarily small neighbourhood of the signal's source from an arbitrarily large set of initial location. Finally, the effectiveness of the proposed scheme is illustrated by numerical simulations.