Localization with autonomous agents in the form of single agent or multi agent is one of the active research fields in control. Localization with autonomous agents has been commonly used by location finder. Since the utilization of these instruments in circumstances such as under water, caves and urban environments, is not feasible and further the navigation system is too costly, the source localization control of autonomous agent in order to arrive at a specific point without GPS has been considered in last decades. In the source localization issue without location finder, it is assumed that the agent is in the domain of a signal field. The distribution of the signal field is unknown, however the intensity of signal decreases as agent gets away from the source. The only available information to control the agent has been received from the sensor located on the agent. The aim of agent is seeking the maximum value, therefore, extremum seeking control is an appropriate method to solve the source localization problem. Extremum seeking control is a real-time non-model based method for optimization of a nonlinear map. Recently, source localization with first order integrator agent, second order integrator agent and non-holonomic agents using extremum seeking control have been studied. Also, compensation of constant and known delay with arbitrary value in the actuator path and/or measurement system of a nonlinear map to be optimized has been considered. In this research, a predictor has been proposed to adjust the forward and angular velocity of a nonholonomic agent in the presence of sensor delay. The design of this predictor has been done using the high pass filter in the extremum seeking loop. To analyze the stability of the system in the presence of predictor, singular perturbation theory is exploited. Using the singular perturbation theory, separately turns the system into fast and slow time scales. The stability analysis of the slow system, i.e. the agent dynamics, is carried out using averaging thoerem. To analyze the stability of the fast system, i.e. the predictor dynamics, the root locus method is used. To reap the benefit of the singular perturbation theory in the stability analysis, a low pass filter is employed in the predictor structure. In the end, the validity of theoretical results has been analyzed through computer simulation. Moreover, the ability of proposed predictor in compensating the uncertain delay and variable time delay has been investigated with the help of computer simulation. Keywords: Extremum seeking Control, Localization, Nonholonomic agent, Delay, Predictor.
