Evasion and pursuit guidance law against defended target

This paper investigates a new approach for a scenario in which an Attacker attempts to intercept a defended aerial Target. The problem is formulated as a game among three players, an Attacker, a Defender, and a Target, with bounded controls. In the considered pursuit–evasion problem, the Target uses an optimal evasion strategy and the Defender uses an optimal pursuit strategy.The proposed approach focuses on the miss distance as the outcome of the conflict. The infeasible region for the initial Zero-Effort-Miss(ZEM) distance between the Attacker and the Defender, for a scenario in which the Attacker evades the Defender, is analyzed, assuming that the Attacker uses a control effort chosen from the permitted control region. The sufficient conditions are investigated under which, for ideal players, the Attacker can pursue the Target while evading the Defender launched by the Target. The guidance provided on how the Attacker can accomplish the task is divided into two parts. During the final time between the Attacker and the Defender, the Attacker chooses the control effort that guarantees the miss distance, and then uses the optimal pursuit strategy to accomplish the task. The derived guidance law is verified by nonlinear simulation.     

一种攻击地面固定目标的变系数比例导引律

为了提高命中精度 ,减小控制能量的消耗 ,对攻击地面固定目标且速度随时间变化的追踪器 ,推导出一种以控制能量消耗最小为性能指标的最优导引律 ,其中剩余时间的估算不仅考虑到追踪器速度大小的变化 ,而且考虑了方向的变化。同时 ,为了满足某些追踪器在碰撞点垂直入射的要求 ,给出在铅垂面内攻击时具有修正项的变系数比例导引律。仿真结果表明 ,该导引律与常系数比例导引律相比 ,控制能量少 ,脱靶量小 ,命中精度高。     

考虑目标安全性的最优协同拦截制导律研究

针对目标和其发射的拦截弹对来袭攻击弹进行协同拦截问题,设计了一种最优协同拦截制导律。建立描述目标、攻击弹和拦截弹三者相对运动关系的模型,引入零控脱靶量对模型进行降阶处理。考虑拦截弹对攻击弹的拦截精度、拦截末端时目标的安全性以及目标、拦截弹的控制能量问题,基于攻击弹-拦截弹零控脱靶量、攻击弹-拦截弹终端横向相对运动速度零控脱靶量、目标-攻击弹零控脱靶量以及目标和拦截弹的加速度,建立了性能指标函数,同时考虑目标和拦截弹加速度的有限性,基于极小值原理设计了最优协同拦截制导律。仿真结果表明,相比目标和拦截弹独立飞行的情况,采用协同拦截制导律,在考虑了目标安全性的前提下,机动性较弱的拦截弹能够以较平直的弹道成功拦截攻击弹。     

Empirical virtual sliding target guidance law design: an aerodynamic approach

We present a novel empirical virtual sliding target (VST) guidance law for the midcourse phase of a long range surface-to-air missile that uses the simplicity of the conventional proportional navigation (PN) guidance law while exploiting the aerodynamic characteristics of a missile's flight through the atmosphere to enable the missile to achieve superior performance than that achieved by conventional PN guidance laws. The missile trajectory emulates the trajectory of an optimal control based guidance law formulated on a realistic aerodynamic model of the missile-target engagement. The trajectory of the missile is controlled by controlling the speed of a virtual target that slides towards a predicted intercept point during the midcourse phase. Several sliding schemes, both linear and nonlinear, are proposed and the effect of the variation of the sliding parameters, which control the sliding speed of the virtual target, on the missile performance, are examined through extensive simulations that take into account the atmospheric characteristics as well as limitations on the missile in terms of the energy available and lateral acceleration limits. Launch envelopes for these sliding schemes for approaching and receding targets are also obtained. These results amply demonstrate the superiority of the proposed guidance law over the conventional PN law.     

3D guidance law modeling

Proportional navigation (PN) guidance laws (GLs) have been widely used and studied in the guidance literature. But most of the guidance literature on PN has concentrated on the evaluation of empirical PNGLs or GLs obtained from very specific optimality considerations. The authors present a novel approach (called guidance laws modeling) to derive new GLs. They consider the basic requirements of capture and define a complete class of GLs that meet these requirements. It is shown that PN is a natural candidate in this class. The main consequence of this modeling process is the definition of two new GLs: one in 2D space and the other in 3D space. These new GLs can be interpreted as new generalizations of the true proportional navigation (TPN) GL. Moreover, it is shown that these generalizations allow the TPNGL to match the capturability performance of the pure proportional navigation (PPN) GL in terms of initial conditions which allow the guided object to reach its target     

基于虚拟目标的超视距舰空导弹导引律设计

针对超视距舰空导弹拦截低空飞行的目标时,会导致在制导初段就出现导弹"掉海"的现象,提出一种虚拟目标的设计方法,并利用伪控制量的概念,应用线性二次型最优控制理论,设计了一种最优导引律。仿真结果表明,虚拟目标设计方法具有良好效果,所研制的最优导引律是可行的。     

Integrated cooperative guidance framework and cooperative guidance law for multi-missile

An integrated cooperative guidance framework for multi-missile cooperatively attacking a single stationary target is proposed in this paper by combining both the centralized and decentralized communication topologies. Once missiles are distributed into several groups, missiles within a single group communicate with the centralized leader-follower framework, while the leaders from different groups communicate using the nearest-neighbor topology. To implement the integrated cooperative guidance framework, a group of Finite-Time Cooperative Guidance (FTCG) laws considering the saturation constraint on FOV (FTCG-FOV) are firstly derived within the centralized leader-follower framework to satisfy the communication topology of missiles in a single group. Then, an improved sequential approach is developed to adapt the FTCG-FOV to satisfy the communication topology between groups. The numerical simulations demonstrate the effectiveness and high efficiency of the integrated cooperative guidance framework and the cooperative guidance laws, as well as the superiority of the developed sequential approach.     

Generalized guidance law for homing missiles

The concept of a generalized guidance law is presented, and the closed-form solution for a homing missile pursuing a maneuvering target according to generalized guidance laws is given. It is shown that the guidance laws appearing in the literature are merely special cases of the one proposed by the authors. The derived generalized forms of capture area, missile acceleration, and homing time duration that are derived provide insight into the performance of the guidance laws being considered and lead to the discovery of new ones. The problem of finding a nonlinear optimal guidance law for a homing missile with controlled acceleration, applied so as to capture a maneuvering target with a predetermined trajectory while minimizing a weighted linear combination of time of capture and energy expenditures, is solved in closed form. The derived optimal control law is equal to the LOS (line of sight) rate multiplied by a trigonometric function of the aspect angle. Numerical simulation shows that the resulting guidance law appears to yield a significant advantage over true proportional navigation     

一种瞬时圆周加速度制导律设计

为了保证导弹攻击目标的精确性,根据平面弹道的几何特性,设计了一种输出指令为过载的瞬时圆周制导律.描述了瞬时圆周加速度制导律原理,详细推导了制导方程.利用导弹质心和目标质心的位置及速度信息,得出导弹攻击目标的过载制导指令,并进行了弹道仿真.仿真结果表明,所设计的瞬时圆周加速度制导律不仅能够保证导弹准确命中目标,而且弹道平...     

Self-organizing fuzzy learning CLOS guidance law design

A new self-organizing fuzzy logic control (SOFLC) design method is proposed. The proposed method is applied to the command line-of-sight (CLOS) guidance law design. The SOFLC contains two sets of fuzzy inference logic. One is the fuzzy logic controller and the other is the rule modifier. The new learning method of the rule modifier is developed based on a fuzzy learning algorithm. The modification value of each rule is based on the fuzzy firing weight, so that learning of the rule bases is reasonable. Finally, two engagement scenarios are examined, and a comparison between a fuzzy logic control (FLC), an optimal learning FLC, and the proposed SOFLC CLOS guidance laws is made. Simulation results show that the proposed SOFLC guidance law can achieve better guidance performance than the other guidance laws.     

一种导弹导引律及参数的非线性MMAE辨识方法

针对现代空战中来袭导弹导引律参数辨识问题,提出了一种非线性的多模型自适应(MMAE)辨识方法。采用无色卡尔曼滤波(UKF)方法对非线性多模型集进行状态估计。利用多模型自适应估计方法,设计了导弹的导引律及参数辨识器,在三维坐标内实现了对导弹IPN,APN,OGL和PP导引律及对应导引参数的辨识,并通过算例仿真验证了该方法的快速性和准确性。     

Stochastic optimal control guidance law with bounded acceleration

A novel stochastic optimal control guidance law is presented for a missile with bounded acceleration. The nonlinear optimal guidance law (NOGL) is obtained by numerically solving the stochastic optimization problem. Since the certainty equivalence principle is not valid in the investigated problem, the resulting NOGL depends on the conditional probability density function of the estimated states. It is shown that the NOGL is also nonlinear in the estimated zero effort miss distance, and that the probability density function of the miss distance is non-Gaussian. The dependence of the new guidance law on the acceleration limit is investigated and it is shown that only for an extremely large acceleration limit does the proposed guidance law degenerate to the classical optimal linear one     

基于终端角度约束的二阶滑模制导律设计

针对空地导弹具有终端角度约束条件的制导律设计问题,提出了一种在有限时间内稳定的新型二阶滑模制导律。首先,在弹目相对运动学模型基础上,将终端弹道倾角约束转化为终端视线(LOS)角度约束,作为制导系统的终端控制目标。其次,通过选取一种新型二阶滑模面,结合螺旋控制算法的思想,设计了一种二阶滑模变结构制导律,来抑制系统中的不确定性因素,从而满足零化视线角速率和制导系统的终端角度约束条件的要求。采用一种新的Lyapunov函数,基于Lyapunov稳定性理论,严格证明了制导系统在有限时间内的稳定性。最后,对空地导弹制导系统进行数字仿真,通过和一阶传统滑模制导律以及基于超螺旋算法的二阶滑模制导律进行对比分析,验证了所设计的制导律在保证制导精度的同时,更能在有限时间内提高终端约束角度的精度,并且避免了超螺旋算法中参数选取较多的问题。     

Adaptive nonlinear guidance law considering control loop dynamics

A new adaptive nonlinear guidance law is proposed here. The fourth order state equation for integrated guidance and control loop is formulated taking into consideration the target uncertainties and control loop dynamics. The state equation is further changed into the normal form by nonlinear coordinate transformation. Using the normal form of state equation, an adaptive nonlinear guidance law is proposed to compensate for the uncertainties in both target acceleration and control loop dynamics. The proposed law adopts the sliding mode control approach with adaptation for unknown bound of uncertainties. The present approach can effectively solve the existing guidance problem against target maneuver and the limited performance of control loop. We have provided the stability analyses and performed simulations comparing favorably our approach to the state of the art.     

三维空间内导弹弹着角可控制导律

针对导弹飞行末端弹着角度变化特点,采用最优控制理论,探索控制导弹末端弹着角度的方法。研究了三维空间下的弹着角度可控制导律。对俯冲平面和水平平面,分别运用最优控制理论中的极大值原理及求解Riccati方程的方法给出了两种形式的制导律。通过对两个平面及多枚导弹不同条件下的飞行数据仿真,可以看出这种制导律应用于控制导弹以期望的弹着角度攻击目标时的有效性和可行性。     

基于Lyapunov稳定性的扩展比例制导律设计

基于一般弹目平面运动模型,以视线角、视线角速率为状态变量将弹目运动关系转换为二阶控制系统状态空间表达,把制导律设计转化为系统控制律的设计问题.在此控制模型的基础之上,利用Lyapunov稳定性定理,以视线角速率平方项作为能量函数设计了一种新型的扩展比例导引律,与其他扩展比例导引律相比,该导引律不需要增加任何制导观测信息,可以有效抑制噪声影响,并将基于Lyapunov稳定性的末制导律设计方法推广到有终端角约束的制导律设计中.仿真结果比较表明,该制导律可以提高制导精度、有效减小制导信息中的噪声影响.     

Design of a CLOS guidance law via feedback linearization

An application of the feedback linearization technique to the design of a new command to line-of-sight (CLOS) guidance law for short-range surface-to-air missiles is described. The key idea lies in converting the three-dimensional CLOS guidance problem to the tracking problem of a time-varying nonlinear system. The result may shed new light on the role of the feedforward acceleration terms used in the conventional CLOS guidance laws. Through computer simulation, the effect of the dynamics of the ground tracker and the autopilot on the guidance performance of the new CLOS guidance law is investigated     

Three-dimensional adaptive finite-time guidance law for intercepting maneuvering targets

To intercept maneuvering targets at desired impact angles, a three-dimensional terminal guidance problem is investigated in this study. Because of a short terminal guidance time, a finitetime impact angle control guidance law is developed using the fast nonsingular terminal sliding mode control theory. However, the guidance law requires the upper bound of lumped uncertainty including target acceleration, which may not be accurately obtained. Therefore, by adopting a novel reaching law, an adaptive sliding mode guidance law is provided to release the drawback. At the same time, this method can accelerate the convergence rate and weaken the chattering phenomenon to a certain extent. In addition, another novel adaptive guidance law is also derived; this ensures systems asymptotic and finite-time stability without the knowledge of perturbations bounds.Numerical simulations have demonstrated that all the three guidance laws have effective performances and outperform the traditional terminal guidance laws.     

基于结构不确定性的非线性鲁棒制导律设计

根据多普勒雷达导引头和红外成像导引头多模制导导弹弹道中段制导信息精度的特点,以非线性鲁棒控制理论为依据,设计了一种制导律.仿真结果表明,该制导律对弹目相对距离测量干扰有较好的鲁棒性,对目标大机动也有鲁棒性.因此,这种制导律可以作为多普勒雷达导引头和红外成像导引头多模制导导弹弹道中段的制导律使用.     

双轨控发动机动能多拦截器制导律研究

在多拦截器反导应用背景下,对双轨控发动机动能多拦截器制导律进行了研究,并基于三维最优制导律对三维空间内平面拦截弹道制导方法进行了研究。该方法基于三维最优制导律寻找初始拦截弹道平面,在弹道平面内根据新的目标末端估计值产生指令过载,最后对该方法进行了仿真计算,试验结果表明该方法具有科学性和工程应用价值。