International Journal of Aerospace Engineering

Volume 2018, Article ID 6081801, 10 pages

https://doi.org/10.1155/2018/6081801

## Adaptive Fuzzy Sliding Mode Guidance Law considering Available Acceleration and Autopilot Dynamics

^{1}School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China^{2}System Design Institute of Hubei Aerospace Technology Academy, Hubei, 430040, China

Correspondence should be addressed to Jie Guo; nc.ude.tib@1891eijoug

Received 21 November 2017; Accepted 8 April 2018; Published 29 April 2018

Academic Editor: Vaios Lappas

Copyright © 2018 Yulin Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Terminal guidance law for missiles intercepting high maneuvering targets considering the limited available acceleration and autopilot dynamics of interceptor is investigated. Conventional guidance laws based on adaptive sliding mode control theory were designed to intercept a maneuvering target. However, they demand a large acceleration for interceptor at the end of the terminal guidance, which may have acceleration saturation especially when the target acceleration is close to the available acceleration of interceptor. In this paper, a terminal guidance law considering the available acceleration and autopilot dynamics of interceptor is proposed. Then, a fuzzy system is utilized to approximate and replace the variable structure term, which can handle the unknown target acceleration. And an adaptive neural network system is adopted to compensate the effects caused by the designed overlarge acceleration of interceptor such that the interceptor with small available acceleration can intercept the high maneuvering target. Simulation results show that the guidance law with available acceleration and autopilot dynamics (AAADG) is highly effective for reducing the acceleration command and achieving a small final miss distance.

#### 1. Introduction

In recent years, the hypersonic flight vehicles with high maneuverabilities have been widely developed [1]. It is necessary to design an appropriate guidance law to intercept the hypersonic flight vehicles for its high strike ability. However, the widely used PNG law [2, 3] and its variants [4–8] would fail to satisfy the requirement of high accuracy for the task of intercepting the hypersonic flight vehicles with high maneuverabilities [9]. An effective approach to intercept maneuverable targets is applying robust control methods, such as sliding mode control (SMC) [10], adaptive control [11], nonlinear control [12], and optimal control [13].

The guidance law based on SMC has become an active research area because of its strong robustness and easy implementation [10, 14, 15]. In the guidance law design, the zero-effort miss distance is usually used to define sliding mode surface. For example, Shima et al. [16] proposed a sliding mode guidance law for integrated missile autopilot with the zero-effort miss distance as sliding mode surface. The sliding mode guidance laws are also designed by guiding the line-of-sight (LOS) angular rate converge to zero. Then, Zhang et al. [17] developed a novel guidance law based on integral sliding mode control and employed a nonlinear disturbance observer to estimate the target acceleration. By estimating the target acceleration via an extended state observer, Zhu et al.[18] designed a guidance law without requiring the information on the target acceleration. However, a compromise should be made between the tracking accuracy and control input since the high tracking accuracy will lead to a very large control input. Thus, the proper values for the control parameters, such as the amplitude of variable structure term, are hard to choose. Considering finite-time convergence, Zhou et al. [19] proposed a variable structure finite-time-convergent guidance law and proved that the LOS angular rate would converge to zero before the ending of the terminal guidance. To attack the target with a predefined impact angle, the guidance laws with impact angle constraints were proposed in [20–23]. Lee et al. [24] developed a guidance law using the high-performance sliding mode control theory to intercept a stationary or slowly moving target. Kumar et al. [20] presented a guidance law to intercept the targets from any initial heading angle without exhibiting any singularity. Furthermore, some guidance laws take autopilot dynamics into consideration [25, 26]. Sun et al. [27] studied a second order sliding mode guidance law with autopilot dynamics. Li et al. [28] took both the autopilot dynamics and uncertainties into consideration and proposed a finite-time-convergent guidance law to intercept a maneuvering target.

To the best of our knowledge, the existing sliding mode guidance laws may require a greater guidance command than the available acceleration of interceptor when the maximum acceleration of target is equal to or larger than the available acceleration of interceptor. To solve this problem, an acceleration limiter is adopted to reduce the saturated acceleration demand [29, 30]. Xiong et al. [31] proposed a strategy making the coefficients of the sliding mode guidance law vary according to the fuzzy rule to reduce the acceleration demand at the beginning of the terminal guidance. However, it cannot guarantee the stability of the guidance system when the designed acceleration is significantly reduced at the end of the homing guidance. In this paper, a neural network system is employed to compensate the effects of the designed overlarge acceleration and the stability of the guidance system is proved. However, to guarantee a good performance of the guidance system when the missile intercepts the hypersonic flight vehicle with a high maneuverability, the gain of switching term needs to be chosen larger than the upper bound of target acceleration, which is hard to choose in advance and will cause the chattering problem. Then, with the universal approximation property of fuzzy systems, a continuous adaptive fuzzy system is used to approximate and replace the variable structure term, which can handle the unknown target maneuver and avoid the chattering phenomenon. The input information of the adaptive fuzzy system is the relative distance and the LOS angular rate which can be measured by the interceptor seeker easily. Besides, before designing a guidance law, it is necessary to consider the autopilot dynamics because the autopilot lag of a homing missile will decrease the precision of guidance. Then, a sliding mode guidance law considering the available acceleration and autopilot dynamics of missile for intercepting a high maneuvering target is proposed.

The main contribution of this paper is that, by adopting neural network system to reduce the acceleration command, so that the interceptor is able to intercept the hypersonic flight vehicles whose maximum acceleration is equal to or larger than the available acceleration of interceptor. In addition, the information needed to estimate the upper bound of target acceleration is limited and easy to obtain, so the proposed guidance law is easy to be implemented in practice. The rest of this paper is organized as follows. Section 2 describes the formulations of the guidance system considering the available acceleration and autopilot dynamics of interceptor. In Section 3, the control methods for the proposed guidance law are introduced. In Section 4, the stability of the guidance law is verified. At last, compared with proportional navigation guidance (PNG) and finite-time convergence guidance (FTCG), simulation results demonstrate the effectiveness of AAADG.

#### 2. The Dynamics of the Relative Motion between the Interceptor and Target

This section presents the mathematic model of the guidance system for intercepting. The planar relative motion of the interceptor and target is shown in Figure 1. The interceptor and the target are denoted by the subscripts M and T, respectively. In order to simplify the guidance law design, the interceptor and target are assumed to have two mass points. The corresponding equations are given by as follows: where is the relative distance and is the relative velocity between the interceptor and the target. is the velocity of the interceptor. is the normal acceleration of the interceptor. is the flight-path angle of the interceptor. is the target velocity. is the normal acceleration of the target. is the flight-path angle of the target. and are the light-of-sight (LOS) angle and LOS angular rate between the interceptor and target, respectively.

*Assumption 1: [31]. *In the terminal guidance, the magnitudes of the speeds of the interceptor and target are assumed as two constants such that and .