Design And Application Of Fast Extremum Seeking Algorithm

The analysis of the classical extremum seeking algorithm?CESA?are all based on three-time scale separation,that is to say,the dynamic systems are faster than the gradient estimation and the optimizer is slowest,which makes the plant could be approximated as a static nonlinearity to guarantee the stability properties.However,the slower time-scale could be a big drawback of transient performance.This performance makes the practical systems could not get the extremum values rapid enough and it limits the application of CESA in practical systems.The analysis of the existed fast extremum seeking relays on that all the phase shift should be known with an accuracy better than±₂^?for all frequen-cies.In addition,the accuracy and speed of existing gradient estimation are also important aspects of fast extremum algorithm.At present,it has become one of the hot topic about how to improve the convergence speed of the algorithm in international extremum seeking research.First of all,by introducing the mechanism of the CESA,and then analysis the con-vergence and stability of the CESA at different time scales.In addition,the causes of slow convergence and phase shift are illustrated.The analysis shows the convergence process of classical extremum seeking and the existing phase shift problem.The slow conver-gence speed is the essential problem of CESA,which needs to be solved by breaking the basic principle of time scale separation.The phase shift problem is caused by increasing the frequency of the system dither signal,which can be solved by designing a adaptive phase shift compensator.The analysis of the CESA and its limiting factors points out the research direction for the next step of improved design and analysis,and makes it a basis for the research foundation.What's more,the barriers of convergence speed of the extremum seeking algorithm and the problem of solving the phase shift at high dither frequency are studied.According to the three time-scale separation of the CESA analyzed above,where the CESA requires a small frequency of the dither signal,the fast extremum seeking algorithm is proposed.However,the phase shift manifested as the fast extremum seeking algorithm increase the amplitude of the dither signal and an adaptive phase shift compensator is designed to improve the phase lag.Then,the existed fast extremum seeking algorithm requires the input gain to be small,which leads to a slower convergence.A high gain optimizer is designed to improve the speed of convergence to the extreme values.Lastly,the numeri-cal simulation is put forth,and the system simulation results of proper and strictly proper are compared with the existed fast extremum seeking algorithms.The comparison results show that the adaptive phase compensator and high-gain optimizer can improve the sys-tem convergence speed and also ensures the stability of the system,and the effectiveness of the proposed adaptive phase compensator and high-gain optimizer is demonstrated.In addition,the accuracy and speed of the gradient estimation also limit the conver-gence speed of the fast extremum seeking algorithm.A high-gain observer is designed to improve the accuracy and speed of the gradient estimation,and the strict stability of the high-gain gradient estimation algorithm is given.High-gain observer is a nonlinear observer,and it enables the estimation state to recover the true state trajectory when the observer gain is high enough.This characteristic of the high-gain observer plays an im-portant role in the gradient estimation of the extremum seeking algorithm.At the same time,the high-gain observer based extremum seeking algorithm is simulated and verified.Finally,in order to solve the robot's slow response where the CESA based structure is applied to the existed mobile robot source seeking.The proposed fast extremum search algorithm is designed to study the mobile robot with slower sensor and drifting sensor.The experimental results are compared with the existed source seeking methods to verify the effectiveness of the proposed fast extremum seeking algorithm in robot source location search applications.