The application of the traditional extremum seeking algorithm (ESA) to an extremum seeking system (ESS) with multivalued output function can result in that the output of the controlled plant can’t precisely and smoothly converge to its global extremum.Therefore

a novel ESA based on chaotic annealing recurrent neural network with parameter disturbances (CARNNPD) is proposed for ESS to solve this problem.Utilizing the ergodicity property of chaos and the strategy of parameter disturbances

the coarse search based on chaotic annealing and parameter disturbances will make the output of ESS move to the neighborhood of its global extremum.Then the elaborate search based on recurrent neural network can guarantee the output of ESS precisely and smoothly converge to the global extremum.Moreover

the conditions for asymptotic convergence

solution optimality and global convergence capability of the proposed ESA are derived.Simulation results validate that this design helps to improve the global searching capability of ESA.