Optimal three-dimensional impact time guidance with seeker’s field-of-view constraint

This paper proposes a new three-dimensional optimal guidance law for impact time control with seeker’s Field-of-View (FOV) constraint to intercept a stationary target. The proposed guidance law is devised in conjunction with the concept of biased Proportional Navigation Guidance (PNG). The guidance law developed leverages a nonlinear function to ensure the boundedness of velocity lead angle to cater to the seeker’s FOV limit. It is proven that the impact time error is nullified in a finite-time under the proposed method. Additionally, the optimality of the biased command is theoretically analyzed. Numerical simulations confirm the superiority of the proposed method and validate the analytic findings.     

Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.     

Optimal predictive sliding-mode guidance law for intercepting near-space hypersonic maneuvering target

The design of optimal guidance law for intercepting a near-space hypersonic maneuvering target with bounded inputs is considered. Firstly, a maneuvering model for near-space hypersonic aircraft is given. Then, the aircraft acceleration prediction can be obtained using this model with two neural networks. By using the target acceleration prediction, which is taken into account when calculating the Zero Effort Miss(ZEM), an optimal sliding-mode guidance law is proposed to fulfill the guidance task...     

A Lyapunov-like approach to performance analysis of 3-dimensionalpure PNG laws

The 3-dimensional PPNG (pure proportional navigation guidance) law was proposed about forty years ago, but its performance has been analyzed only on the basis of the linearized trajectory equations, which are valid locally around the collision course. We take into full account the nonlinear dynamic characteristics of pursuit situation in the 3-dimensional space to analyze the performance of the 3-dimensional PPNG law more rigorously. We prove that a missile guided by the 3-dimensional PPNG law can always intercept a target maneuvering randomly in the 3-dimensional space if 1) the target acceleration varies with a known bound, 2) the navigation constant is selected large, and either 3a) the initial heading error is small or 3b) the missile keeps the head toward the target during flight. We also propose a modified PNG law, which seems to exhibit better performance at the final phase of pursuit than the conventional PPNG law. We introduce a Lyapunov-like method that proves to be a very powerful tool in obtaining our results     

基于非线性模型的大气层内拦截弹微分对策制导律

针对新型战术弹道导弹(TBM)和智能巡航导弹等具有高机动性的拦截目标,应用控制受限的非线性对策模型,提出非线性微分对策制导律,并分析了零脱靶量拦截所容许的初始航向误差.目标和拦截弹间的相对运动是非线性的,采用传统线性化模型建立的拦截制导律会因为线性化而带来误差.提出的制导律是在保持拦截弹和目标的非线性运动学关系的基础上...     

一种非线性末制导系统模型的精确线性化

针对未来高机动目标的拦截 ,运用非线性系统几何理论中的精确线性化方法 ,设计了一种空空导弹非线性末制导系统加速度指令。假设目标做逃逸机动 ,弹体 -自动驾驶仪响应用一个二阶环节描述 ,建立了导弹目标三维相对运动方程。根据终端约束直接选取系统输出阵 ,经动态反馈线性化 ,将非线性系统模型转化为线性方程 ,求得了目标任意机动时的非线性末制导系统的加速度指令。以纵向平面为例进行了仿真计算 ,结果表明该方法是行之有效的 ,得到的解可以用来改进导弹大离轴发射角时的进攻能力。     

基于EKF的天线罩误差斜率多模型估计方法

 提出一种新的滤波器结构,利用基于扩展卡尔曼滤波(EKF)的多模型(MM)算法,对天线罩误差斜率进行估计,降低天线罩误差对雷达自寻的导弹的影响,提高系统性能。在三维坐标下,创建包含导弹运动方程、目标运动方程、弹目相对运动方程的滤波模型。采用EKF算法,对包含天线罩误差的非线性观测方程进行线性化处理;依照多模滤波的思想,对天线罩误差进行离散建模,构建伪观测方程,更新模型概率,得到天线罩误差斜率的估计值;将斜率估计结果代入EKF,得到滤除天线罩误差影响的系统状态量估计结果并形成制导指令。仿真结果表明,所提方法可以有效地估计天线罩斜率,提高系统制导精度。     

Design of optimal midcourse guidance sliding-mode control for missiles with TVC

This work discusses a nonlinear midcourse missile controller with thrust vector control (TVC) inputs for the interception of a theater ballistic missile, including autopilot system and guidance system. First, a three degree-of-freedom (DOF) optimal midcourse guidance law is designed to minimize the control effort and the distance between the missile and the target. Then, converting the acceleration command from guidance law into attitude command, a quaternion-based sliding-mode attitude controller is proposed to track the attitude command and to cope with the effects from variations of missile's inertia, aerodynamic force, and wind gusts. The exponential stability of the overall system is thoroughly analyzed via Lyapunov stability theory. Extensive simulations are conducted to validate the effectiveness of the proposed guidance law and the associated TVC.     

导弹协同作战飞行时间裕度

 基于导弹协同作战任务规划系统进行合理任务分配的需求,研究了导弹可以修正控制飞行时间的裕度。根据导弹-目标在视线坐标系和角动量坐标系下的运动关系,得出了导弹相对于目标的加速度,并基于此给出了导弹剩余飞行时间的估算方法;当前时刻导弹剩余飞行时间的估算值与已经飞行的时间以及任务规划系统指定的期望到达时间构成时间反馈作用,用于修正控制导弹到达目标的最终飞行时间。由于真比例导引律在工程实现和解析运算中具有一定的优势,选择在真比例制导加速度的视线方向施加时间反馈控制作用,进而得出了基于真比例导引律的导弹协同作战飞行时间控制导引律;最后重点研究了在该时间控制导引律的作用下,存在导弹的飞行速度限制以及弹目相对运动约束时,导弹飞行过程中任一时刻对应解析形式的可控飞行时间的裕度。仿真结果表明,本文的设计合理可行,对于多弹协同作战的实现具有重要意义。     

Lyapunov-based switched-gain impact angle control guidance

To hit stationary ground targets in specified direction, a nonlinear impact angle control guidance law based on Lyapunov stability theory is proposed. The proposed law ensures the convergence of the heading angle and the miss distance to guarantee a successful engagement. The impact angle can be adjusted by varying a single parameter. And the maximum value of acceleration has been analyzed to get the proper range for control parameter. Considering the achievable impact angle set is limited, an additional phase is added to form a two-phase control strategy. The first phase is to establish a proper initial condition for the second phase, and the second phase is to hit the target with a certain impact angle. An analysis of the proper selection of control parameters to expand the achievable impact angle set is presented. The performance of the proposed guidance law is illustrated with simulations.     

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.     

Two-phase guidance law for impact time control under physical constraints

An impact-time-control guidance law is required for the simultaneous attack of suicide attack unmanned aerial vehicles. Based on the nonlinear model, a two-phase guidance strategy is proposed. The impact time is derived in a simple analytical form of initial states and switching states, and it can be controlled by switching at an appropriate range. Firstly, a two-phase guidance law is designed to make the magnitude of the heading error decrease monotonically from its initial value to zero. And then, the feasible interval of the switching ranges and of the impact times under the acceleration constraint are given analytically in sequence. Furthermore, a general form of two-phase guidance law is proposed, which allows the magnitude of the heading error to increase in the first phase, to improve the applicability of the methodology. Having the same structure as proportional navigation guidance with a time-varying gain, the proposed algorithms are simple and easy to implement. The corresponding feedback form is presented for realistic implementation. When a predefined impact time is taken within its permissible set, the constraints on the acceleration and field-of-view will not be violated during the interception. Finally, simulations validate the effectiveness of the methodology in impact time control and salvo attack.     

LQG Guidance Law with Bounded Acceleration Command

A novel missile guidance law that is dependent on the conditional probability density function of the estimated states is presented. The guidance law is derived by analyzing an interception scenario in the framework of an linear quadratic Gaussian (LQG) terminal control problem with bounded acceleration command. The nonlinear saturation function is represented by the equivalent random input describing function. Since for the investigated problem the certainty equivalence property is not valid, the resulting controller depends on the measurement noise level and on the saturation limit. In comparison to the classical optimal guidance law (OGL), the maximal value of the effective navigation gain is achieved during the engagement instead of near the terminal time. Thus, the saturation limit is reached earlier so as to have enough time to reduce the guidance errors. Using Monte-Carlo simulations, the superiority of the new guidance law over the classical OGL is shown. This validates the new approach of designing an estimation statistics dependent guidance law by using a random input describing function to approximate the missile's acceleration saturation.     

CLOS+IRTH composite guidance

A composite guidance scheme based on the command to line-of-sight (CLOS)+infrared terminal homing (IRTH) for a short-range surface-to-air missile system is proposed in an attempt to complement drawbacks of a single guidance law. Launch boundaries for a successful guidance handover are analyzed according to missile maneuverability and seeker gimbal angle limits. This paper also concentrates on developing practical guidance laws for the IRTH phase in the presence of inherent missile heading errors at the time of guidance handover and missile deceleration due to aerodynamic drag.     

三维制导的几何方法与鲁棒控制方法

 在考虑导弹速度和目标速度均为时变的情况下,将微分几何方法与李雅普诺夫稳定理论结合起来,提出了一种导弹三维导引规律设计新方法。对机动目标,PPNG方法的主要问题是在导引末段,它要求导弹在俯仰和偏航通道上具有较大的加速度,为了解决这一问题,本文应用基于李雅普诺夫稳定理论的鲁棒控制方法,提出了一种三维鲁棒制导算法。这种方法在导引末段不需要过大的加速度命令,不需要知道目标精确的加速度和速度方位信息。     

Guidance law with impact time and impact angle constraints

A novel closed-form guidance law with impact time and impact angle constraints is pro- posed for salvo attack of anti-ship missiles, which employs missile’s normal acceleration (not jerk) as the control command directly. Firstly, the impact time control problem is formulated as tracking the designated time-to-go (the difference between the designated impact time and the current flight time) for the actual time-to-go of missile, and the impact angle control problem is formulated as tracking the designated heading angle for the actual heading angle of missile. Secondly, a biased proportional navigation guidance (BPNG) law with designated heading angle constraint is constructed, and the actual time-to-go estimation for this BPNG is derived analytically by solving the system differential equations. Thirdly, by adding a feedback control to this constructed BPNG to eliminate the time-to-go errorthe difference between the standard time-to-go and the actual time-to-go, a guidance law with adjustable coefficients to control the impact time and impact angle simultaneously is developed. Finally, simulation results demonstrate the performance and feasibility of the proposed approach.     

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.     

带有攻击角度和攻击时间控制的三维制导

 在三维空间导引动力学与运动学模型的基础上,假设目标静止,而导弹本身以恒速运动,根据实际的攻击角度与设定的攻击角度误差,分析和设计了期望的视线（LOS）角运动学,基于李雅普诺夫稳定性理论设计了带有攻击角度控制的三维导弹导引律。为了对攻击时间进行预测与控制,假设导弹本身以恒速或者匀加/减速运动,先将导弹导引到预定的攻击角度上,根据待飞直线距离对待飞时间进行估算,再根据预测时间误差,确定导弹按照特定的圆弧轨迹机动飞行的指令和机动飞行的时间,通过机动飞行来对时间误差进行补偿,最后,再利用所设计的导引律攻击目标。给出了仿真结果。     

Three-dimensional cooperative guidance strategy and guidance law for intercepting highly maneuvering target

Cooperative interception of the target with strong maneuverability by multiple missiles with weak maneuverability in the three-dimensional nonlinear model is studied. Firstly, the three-dimensional nonlinear model of cooperative guidance is established. The three-dimensional reachable region is represented composed of lateral acceleration and longitudinal acceleration in the two-dimensional coordinate system. Secondly, the problem of the multiple missile's reachable coverage area is transformed into the problem of cooperative coverage. A cooperative coverage strategy is proposed and an algorithm for quickly calculating the number of required missiles is designed. Then, the guidance law based on the cooperative coverage strategy is proposed, and it is proved that cooperative interception of the target can be achieved under the acceleration limit. Moreover, the relations among the number of missiles, the initial array position of terminal guidance and the coverage area of the target’s large maneuver are analyzed. The dynamic adjustment strategy of guidance parameters is proposed to reduce the guidance error. Finally, simulation results show that multiple missiles with low maneuverability can achieve effective interception of target with strong maneuverability through the proposed cooperative strategy and cooperative guidance method.     

基于普通分离原理的制导/估计综合设计方法

现有的先进制导律研究常常分离设计最优估计器和最优制导律,但是这种分离设计没有被证明是有效和最优的设计方法.本文基于普通分离原理(GST),提出一种制导/估计综合设计方法.首先,将拦截器反导作战模型考虑为一类非线性、非高斯追逃拦截问题,建立了噪声环境中追逐-逃逸对策模型;其次,引入追逃未达集概念,利用几何方法将估计器设计...