# Predictive Control for Small Unmanned Ground Vehicles via a Multi-Dimensional Taylor Network
## 1 Introduction  
With the rapid development of artificial intelligence, big data, and data fusion technology, car driving tends to be intelligent and unmanned. Recently, research on Unmanned Ground Vehicles (UGVs) has become a hot topic at home and abroad [1; 2; 3]. Its core technologies include environmental awareness, vehicle positioning, path planning, and path tracking control [4; 5; 6; 7]. Path tracking control, as a key core issue of unmanned driving technology, has attracted much attention from scholars and it ensures that the car drives on the specified path [8; 9]. So, research on path tracking control has both theoretical and practical significance. However, UGV path tracking control is a strongly nonlinear process, which contains time-varying characteristics, uncertainty, etc., and a precise mathematical model is difficult to obtain [10]. As artificial intelligence develops, neural networks can solve the above problem well due to their nonlinear approximation capabilities [11]. For example, a new end-to-end autonomous control method was proposed to simplify the separate modules in the traditional control pipeline into a single neural network [12]. A novel application of the biologically inspired computing paradigm was presented for solving the initial value problem (IVP) of electric circuits based on a nonlinear RL model by exploiting thecompetency of accurate modeling with a feed forward artificial neural network, the global search efficacy of genetic algorithms, and a rapid local search with sequential quadratic programming [13]. Moreover, predictive control, rooted in industrial engineering, is widely used. Usually, the schemes that combine a neural network model and predictive control are more popular and useful to solve the nonlinear control problem. For example, physics-based recurrent neural network modeling approaches were proposed for a general class of nonlinear dynamic process systems to improve the prediction accuracy by incorporating a priori process knowledge, and the proposed physics-based RNN models were utilized in model predictive controllers [14]. A neural-network-based technique for developing nonlinear dynamic models from empirical data for a model predictive control (MPC) algorithm was presented [15]. However, for the neural networks, they easily reach the local minimum [16]. To solve the issues with nonlinearity, time-varying characteristics, uncertainty, real time, etc. and overcome the problem of neural networks, we adopt a multi-dimensional Taylor network (MTN) and collective solutions. The collective solutions are the most effective as they take advantage of each method. The MTN is an inclusive platform that was first proposed by [PERSON] and [PERSON] and can be used to describe the nonlinear dynamic characteristics of a system without prior knowledge of the structural information on the system [17; 18]. It has been successfully applied to system modeling [19; 20] and nonlinear control [21; 22; 23; 24]. In this paper, an improved predictive control scheme based on a MTN is proposed to realize real-time output tracking control of Small Unmanned Ground Vehicles (SUGVs) relative to a given reference path without state feedback. First, the MTN is used as a predictive model to construct the SUGV model and back propagation (BP) is taken as its learning algorithm. Second, a predictive control law is designed to control the SUGV and the traditional objective function is improved to obtain a predictive objective function with a differential term. The optimal control quantity is given in real time through iterative optimization. Meanwhile, the stability of the closed-loop system is proved according to the Lyapunov stability theorem. Based on that, an adjustment method for MTN control law parameters is obtained using the predictive accuracy of the MTN model and the control coefficient. Finally, a tracking control experiment on the SUGV is used to verify the effectiveness of the proposed scheme. For comparison, traditional MTN and RBF predictive control schemes are introduced.