Numerical Optimization-Based Extremum Seeking Control And Its Application In Robot Formation Control

Extremum seeking control is a kind of adaptive control method which can obtain the extremum and keep the system working at the extremum state.In this article,we study extremum seeking based on numerical optimization control strategy.In this article,we study Numerical Optimization based extremum seeking control.Under the premise of ensuring the system's extremum is exist,the extremum seeking controller does not depend on the priori knowledge of the input and output mapping to achieve the extremum of the system.In this article,we study numerical optimization based extremum seeking control.It is different from traditional extremum seeking control,numerical optimization based extremum seeking control is based on mathematical optimization,using mathematical optimization theory and algorithm,transform the original problem to an optimization problem with constraints.By numerical optimization theory of linear search,direct search series algorithm,the gradient method,the conjugate direction method,simplex gradient method,the non-gradient trust region algorithm,Newton's method and quasi-newton method optimization algorithm,combined with the properties of the control system,such as controllability,accessibility,stability and robustness,to design the performance function,according to the performance function,combining with the system control requirements,extremum seeking controller is designed,so as to realize the control goal.On the other hand,with the development of the application of robot system,mobile robot formation control has become a hot topic in research field.In recent years,multi-robot coordination and cooperation has become possible,more and more applications has been put into application.Multiple robot coordination and cooperation can accomplish tasks that a single robot can't accomplish.The problem of formation control is a typical problem,in this article,the goal of multi-robot formation control is to make multi-robot maintain fixed formation and at the same time,to track a changing unpredictable signal,this signal can be actual physical process such like a source of odor,leak source,etc.The main work of this article:1)On the one hand,make a careful analysis of the numerical optimization based extremum seeking control.On the other hand,make a simple overview of the numerical optimization algorithm.Mainly put forward two kinds of extremum seeking control algorithm under the framework of numerical optimization based extremum seeking control algorithm,one is direct search based extremum seeking control and the other is trust region based extremum seeking control.2)Using artificial potential field method to establish performance function containing the formation information and the target trajectory information.Using the performance function as the optimization goal of extremum seeking control.The above two extremum seeking control algorithm is applied to the robot formation control and target tracking.The two algorithms are both no-gradient needed algorithm and the only information is to real-time measure the value of the performance function(the combination of system state variables)the target can be realized.By extremum seeking control to optimize the performance function(artificial potential function),the extremum seeking controller can get the optimal state sequence,through the state regulator,the regulator will regulate the system to reached the new state,until get the optimal state,then we can realize the formation control,target tracking control.3)At last,a simulation experiment is to validate the effectiveness of the two algorithms,at the same time we made a comparison and analysis of the two algorithms and some conclusions are drawn from different angles.In this article,under the framework of numerical optimization based extremum seeking control algorithm,two mathematical optimization algorithms are embedded into the extremum seeking control scheme,one is direct search algorithm and the other is trust region algorithm.This two kinds of mathematical optimization algorithm is to improve the existing numerical optimization based extremum seeking control,to overcome the shortcomings of large amount of calculation and the defects of matrix inversion.Combined with the application of these two algorithms,and artificial potential method,robot formation control and target tracking can be achieved.