# Neural Robust Control for a Mobile Agent Leader-Follower System
## 1 Introduction  
The study and development of autonomous mobile robots have increased in recent years due to their wide range of potential applications and new integration of technologies to improve them. Additionally, multirobot systems have made significant progress in terms of coordination and cooperation, becoming increasingly important in everyday life cooperative implementations [1, 2]. Multiple agents can solve tasks faster and at lower cost if they work cooperatively, in contrast to a single robot trying to perform the same task. On this subject, the leader-follower strategy is the most commonly used methodology in the formation control of multirobot systems [3, 4, 5]. One of the major challenges in dealing with control and automation of any dynamical system, and in particular with control of differential robots, when the tracking control problem is addressed is the management of the model uncertainties and parameter variations. Differential mobile robots are widely used because of their minimal resource requirements in design and construction, as well as their ability to maneuver to any positionusing straight lines, curves, or by rotating on their own axis. However, these are systems that have a large number of parameters that are generally uncertain and exhibit model discrepancies, external disturbances, and parameter uncertainties. These previously mentioned issues must be tackled through a well-suited control system design. Significant results have been obtained in this particular subject, for instance, in [6], a controller was suggested for a differential mobile robot, which utilizes recursive integral back-stepping to track and stabilize the trajectory of robots. Such a controller requires complete knowledge of all parameters and states. In [7], a hybrid controller was proposed that combines a kinematic controller based on a neural network and an adaptive control reference model. The controller parameters are adapted online using the neural network, and by tuning the adaptive kinematic controller, rapid convergence to the desired trajectory is achieved. Moreover, the adaptive reference control model maintains the desired tracking performance when parameters and state uncertainties occur. In [8], a PID controller was used for controlling the angular velocity of the wheels, and in [9], the dynamics of the parameters of the robot were controlled using two PID control blocks. Nevertheless, both cases are limited by the precision of the robot model. In [6], recursive back-stepping control was implemented with good results in semiglobal regions. In [10], a discrete-time case was stated and a recurrent high-order neural network was trained with an extended Kalman filter algorithm to identify the whole state, not just parameters, as we propose. Unlike the works mentioned so far, our approach to this problem combines an adaptable and robust parameter estimation with output feedback linearization control. It is not uncommon for linearization methodologies to be applied in designing nonlinear control systems; the main idea is to partially or fully transform the nonlinear dynamics of the system to be controlled into linearized dynamics, thus being able to apply the known linear control techniques at an operating point [11]. This method has a significant number of limitations: it cannot be used for all kind of systems; the complete state must be measured; and it does not guarantee robustness in the presence of unstructured uncertainties or unmodeled dynamics. In this sense, there are results in which the number of states to be known can be reduced, and, furthermore, the nonlinear dynamics can be estimated so that the controller may counteract them. This is considered robust control, as reported in [12; 13]. Robustness and adaptation against system uncertainties are essential in control system design. Recurrent neural networks have been widely used as an adaptive model for classification, pattern recognition, identification, optimization, and processing [14; 15; 16]. They are mainly based on the Hopfield model [17].