# Deep Neural Network-Based Guidance Law Using Supervised Learning
## 1 Introduction  
Proportional navigation guidance (PNG) is one of the most widely known missile guidance laws in existence [1]. This guidance law generates an acceleration command proportional to the line-of-sight (LOS) rate from the perspective of a missile looking at a target. This is easy to implement based on simple principles.  
[PERSON] [2] demonstrated the performance of PNG by showing that PNG is effective in intercepting a low-maneuvering target in a two-dimensional missile target engagement scenario. [PERSON] and [PERSON] [3] showed that PNG is the optimal solution for engagement scenarios for a missile with constant speed and a stationary target by solving linearized engagement equations. This guidance law enables various designs according to the navigation constants with arbitrary real number values. Based on the fact that the form or size of the guidance command varies depending on the navigation constants, [PERSON] [4] proposed a recursive optimal pure proportional navigation (PPN) scheme that predicts recursively optimal navigation gain and time-to-go. It also showed that the proposed algorithm applies to maneuvering targets. [PERSON] [5] proposed a robust PNG law, a form of combination of the conventional PNG and the switching part made by using the Lyapunov approach. This was robust when used against a highly maneuvering target.  
Recently, deep learning [6]-based artificial intelligence technology has received attention in academia and industry. Various studies using artificial neural networks (ANNs) are also being studied in the defense technology sector, and among them, guidance laws have become the focus of various research as they are essential in homing missiles [7; 8; 9; 10; 11; 12; 13]. [PERSON] and [PERSON] [7] presented a new neural structure providing feedback guidance solutions for any initial conditions and time-to-go for two-dimensional scenarios. [PERSON] et al. [8; 9] proposed a neural network guidance algorithm for bank-to-turn (BTT) missiles. This guidance performance was verified by comparing it with PNG. [PERSON] and [PERSON] [10] presented a method of designing a feedback controller of homing missileusing feed-forward multi-layer perceptron (MLP). They demonstrated the efficiency of the proposed method by performing simulations on various initial input values. [PERSON] et al. [14] presented an ANN-based approach using MLP to replace PNG. It showed that MLP-based guidance can effectively replace the PNG in a wide range of engagement scenarios.  
In this paper, we propose a deep neural network-based guidance (DNNG) law imitating PNG. This approach learns the DNN model with training data acquired from PNG. The DNN model applies to the missile system instead of PNG, and its performance is comparable with PNG. Then, we design the controller model and discuss how the proposed DNNG law changes according to time constants.  
This paper is organized as follows: In Section 2, the two-dimensional missile-target engagement scenario and equations of motion of the missile will be explained. Section 3 briefly describes the conventional PNG law. In Section 4, the DNNG law that applied supervised learning, such as training data collection, DNNG structure, training methods and evaluation, is described in detail. Additionally, the simulation results of the DNNG law are shown through numerical simulation. Section 5 introduces a new DNN-based guidance law with the input variables of only the LOS rates. We run simulations at the initial position outside the range of training data. In addition, we design the first-order system and examine the energy performance of the missile according to the time constant. Finally, conclusions are given in Section 6.