# Neural Robust Control for a Mobile Agent Leader-Follower System
## 1 Introduction
These kind of networks are considered good candidates for nonlinear system applications that face uncertainties, and they are attractive due to their easy implementation, relatively simple structure, robustness, and ability to adjust their parameters online [18; 19; 20; 21]. These networks may estimate uncertain nonlinear functions solely based on velocity measurements. The main idea for this work is to implement a linearizing controller which has access to these aforementioned uncertain estimates to compensate them in the system. In other words, the controller will compensate or attenuate the effect of parametric variations, model errors, and disturbances; this derives high-order recurrent neural network properties. Frequently, in control system design, full-state measurement is difficult to obtain, and reliable velocity measurements are needed in order to eliminate tachometers and numerical differentiation but maintain high control accuracy. One option is to use joint velocity observers. The concept of the model-based observer was tailored to estimate manipulator joint velocities in [22], ensuring local asymptotic stability. In [23], neural networks were used for closed-loop output feedback control without joint velocity measurements. Only the inertia matrix was assumed to be known; a neural network observer was designed to estimate the unknown velocity. In [24], a multilayer perceptron model control was presented that was based on full-state identification. However, it lacked recurrence adaptability properties, and nonlinear structures were not included in the identification process. In the mentioned research papers, observers have been proposed, which assume an exact knowledge of the dynamics of manipulator parameters. For the adaptive control approach, linearity in the unknown parameters is required; therefore, the exact knowledge of the robot dynamics is necessary to be successful. Generally, this cannot be achieved in practice. In this work, the goal consists of designing a nonlinear robust adaptive controller called neuro-robust control to track the angular velocities of both wheels of a differential mobile robot in a leader-follower configuration. We assume that there is no more information of the systems other than the velocity outputs and a nominal value of some parameters. Thus, the desired trajectory is parameterized in the Cartesian plane with the angular velocities of right and left wheels. A system composed of two parts is proposed: the design of a linearizing controller and an estimator with a high-order neural network. The robustness of the RHONN approach is analyzed in [14]. This aspect of our approach offers both online adaptability and nonlinear combined features, contributing to the novelty of this paper. The paper is organized as follows. The next section presents the materials and methods. Section 3 contains the main contribution, consisting of the neuro-robust controller design. In Section 4, the results of the neuro-robust control applied to the differential robots are discussed. Finally, in Section 5, the discussion and conclusions are provided.