Adaptive weighting impact angle optimal guidance law considering seeker's FOV angle constraints

In this paper, a new adaptive optimal guidance law with impact angle and seeker’s field-of-view(FOV) angle constraints is proposed. To this end, the generalized optimal guidance law is derived first. A changeable impact angle weighting(IAW) coefficient is introduced and used to modify the guidance law to make it adaptive for all guidance constraints. After integrating the closed-form solution of the guidance command with linearized engagement kinematics, the analytic predictive models of impact angle and FOV angle are built, and the available range of IAW corresponding to constraints is certain. Next, a calculation scheme is presented to acquire the real-time value of IAW during the entire guidance process. When applying the proposed guidance law, the IAW will keep small to avoid a trajectory climbing up to limit FOV angle at an initial time but will increase with the closing target to improve impact position and angle accuracy, thereby ensuring that the guidance law can juggle orders of guidance accuracy and constraints control.

Optimal Guidance Law to Maximize Terminal Velocity for Missiles with Impact Angle Constraint

In this paper,an optimal guidance law for missiles with impact angle and miss distance constraints is proposed to achieve the maximal terminal velocity. The normal acceleration command that includes the timevarying coefficients is introduced to satisfy the desired impact angle as well as zero miss distance according to the geometric relation and relative motion parameters between missile and target. The problem is formulated as an optimal control problem by defining the angle of velocity error and flight-path angle as state variables and maximizing a performance index of the terminal velocity. The analytical form of the proposed guidance law is obtained as the solution of the optimal control problem combining optimal control theory and numerical value computation method. Nonlinear simulations of various situations demonstrate the performance and feasibility of the proposed optimal guidance law.

Extended optimal guidance law with impact angle and acceleration constriants

The extended optima straints of miss distance and Schwartz inequality. To reduce guidance law with terminal conmpact angle is derived by the terminal acceleration and eliminate gravity disturbance absolutely, the object function, which designs the weight of control command to be the power function of time-to-go＇s reciprocal, is given. And the gravity is considered when building the state equation. Based on the parsing express of the guidance command change with varying time and adjoint system analysis method, the command characteristics and the non-dimensional miss distance of the guidance law are analyzed, a design principle of guidance order coefficients is discussed. Finally, based on the requirement of engineering, the method to calculate the guidance condition and maximal required acceleration of the guidance law is given. The simulation demonstrates that not only the guidance law can satisfy the terminal position and impact angle constraints, but also the terminal acceleration can be converged toward zero, which will support a good situation for the terminal angle of attacking control.

Trajectory shaping guidance law based on virtual angle with terminal constraints

A trajectory shaping guidance law based on virtua angle （TSGLBVA） is proposed for a re-entry vehicle with the constraints of terminal impact angles and their time derivatives. In the view of differential properties of the maneuvering trajectory, a virtual angle and a virtual radius are defined. Also, the shaping trajectory of the vehicle is established by the polynomials of the virtual angle. Then, four optimized parameters are selected according to the theorem of parameters transformation presented in this paper. Finally, a convergent variant of the Nelder-Mead algorithm is adopted to obtain the reference trajectory, and a trajectory feedback tracking guidance law is designed. The simulation results demonstrate that the TSGLBVA ensures the re-entry vehicle to impact a target precisely from a specified direction with smal terminal load factor command, as well as to obtain a maximum or constrained terminal velocity according to various requirements.

Kinetic Optimal Midcourse Guidance Law for Air-to-Air Missiles

A new kinetic optimal midcourse guidance law is derived based on optimal control formulation. A new simplified Runge-Kutta grade numerical method is proposed to find the optimal trajectory. Real data of an Mr-to-air missile is referred to for comparing results using the kinetic optimal midcourse guidance law with those under both the kinematic optimal guidance law and singular perturbation sub-optimal guidance law, wherein the latter two laws are modified in this paper by adding a vertical g-bias command to each law for the sake of trajectory shaping. Simulation results show that using the new kinetic optimal mideourse guidance law can help save energy and maximize terminal velocity effectively.

Integrated guidance and control of guided projectile with multiple constraints based on fuzzy adaptive and dynamic surface

Based on fuzzy adaptive and dynamic surface(FADS),an integrated guidance and control(IGC)approach was proposed for large caliber naval gun guided projectile,which was robust to target maneuver,canard dynamic characteristics,and multiple constraints,such as impact angle,limited measurement of line of sight(LOS)angle rate and nonlinear saturation of canard deflection.Initially,a strict feedback cascade model of IGC in longitudinal plane was established,and extended state observer(ESO)was designed to estimate LOS angle rate and uncertain disturbances with unknown boundary inside and outside of system,including aerodynamic parameters perturbation,target maneuver and model errors.Secondly,aiming at zeroing LOS angle tracking error and LOS angle rate in finite time,a nonsingular terminal sliding mode(NTSM)was designed with adaptive exponential reaching law.Furthermore,combining with dynamic surface,which prevented the complex differential of virtual control laws,the fuzzy adaptive systems were designed to approximate observation errors of uncertain disturbances and to reduce chatter of control law.Finally,the adaptive Nussbaum gain function was introduced to compensate nonlinear saturation of canard deflection.The LOS angle tracking error and LOS angle rate were convergent in finite time and whole system states were uniform ultimately bounded,rigorously proven by Lyapunov stability theory.Hardware-in-the-loop simulation(HILS)and digital simulation experiments both showed FADS provided guided projectile with good guidance performance while striking targets with different maneuvering forms.

A trajectory shaping guidance law with field-of-view angle constraint and terminal limits

In this paper, a trajectory shaping guidance law,which considers constraints of field-of-view(FOV) angle, impact angle, and terminal lateral acceleration, is proposed for a constant speed missile against a stationary target. First, to decouple constraints of the FOV angle and the terminal lateral acceleration, the third-order polynomial with respect to the line-ofsight(LOS) angle is introduced. Based on an analysis of the relationship between the looking angle and the guidance coefficient,the boundary of the coefficient that satisfies the FOV constraint is obtained. The terminal guidance law coefficient is used to guarantee the convergence of the terminal conditions. Furthermore, the proposed law can be implemented under bearingsonly information, as the guidance command does not involve the relative range and the LOS angle rate. Finally, numerical simulations are performed based on a kinematic vehicle model to verify the effectiveness of the guidance law. Overall, the work offers an easily implementable guidance law with closed-form guidance gains, which is suitable for engineering applications.

Three-dimensional impact angle constrained distributed cooperative guidance law for anti-ship missiles

This paper investigates the problem of distributed cooperative guidance law design for multiple anti-ship missiles in the three-dimensional(3-D)space hitting simultaneously the same target with considering the desired terminal impact angle constraint.To address this issue,the problem formulation including 3-D nonlinear mathematical model description,and communication topology are built firstly.Then the consensus variable is constructed using the available information and can reach consensus under the proposed acceleration command along the line-of-sight(LOS)which satisfies the impact time constraint.However,the normal accelerations are designed to guarantee the convergence of the LOS angular rate.Furthermore,consider the terminal impact angle constraints,a nonsingular terminal sliding mode(NTSM)control is introduced,and a finite time convergent control law of normal acceleration is proposed.The convergence of the proposed guidance law is proved by using the second Lyapunov stability method,and numerical simulations are also conducted to verify its effectiveness.The results indicate that the proposed cooperative guidance law can regulate the impact time error and impact angle error in finite time if the connecting time of the communication topology is longer than the required convergent time.

带落角约束的末端机动Terminal滑模导引律设计

为了提高反舰导弹的突防概率，有效规避敌方舰空导弹的拦截，并且实现反舰导弹按预定方向精确打击目标的战术要求，首先，基于弹目之间的三维相对运动模型，应用Terminal滑模控制理论，设计了一种带有落角约束的变结构导引律；然后，通过叠加虚拟干扰的方法，在原来导引律基础上叠加了一虚拟干扰，此虚拟干扰不影响导引律的渐进稳定性，不影响反舰导弹的打击精度，并且使得反舰导弹能够产生足够大的过载，但是又不超过其可用过载，使反舰导弹产生一定的机动变轨来实现规避舰空导弹。仿真结果表明了文章设计方法的有效性。

考虑自动驾驶仪延迟的非线性最优末制导方法

针对过载受限和自动驾驶仪延迟等条件下的非线性最优末制导指令在线生成方法进行研究。首先,基于庞特里亚金极大值原理,建立了目标静止的非线性最优末制导问题的最优性条件,并利用饱和函数将过载约束嵌入最优性条件。其次,应用参数化方法使得通过数值积分即可快速生成满足最优性条件的飞行轨迹数据集。然后,利用该数据集训练神经网络,使其拟合弹-目相对运动状态到最优制导指令的映射关系,实现过载约束下制导指令的毫秒量级在线生成。针对自动驾驶仪的延迟响应,通过微分补偿法估计神经网络下一时刻输出的制导指令以实现快速跟踪。最后,仿真结果表明,本文所提出方法针对静止目标与小机动目标都能够在线生成最优制导指令。

考虑终端多约束条件的多项式最优制导律

针对考虑终端脱靶量、碰撞角和加速度多约束的精确制导问题,提出了一种可解析求解的多项式最优制导律。将视场角正切值设定为弹目距离的多项式函数形式,将终端多约束条件转化为多项式系数的代数关系式,并引入优化思想,得到弹目距离加权的能量最优指标下的多项式系数最优解,依据弹目运动关系将视场角正切值变化改写为相应满足终端碰撞角约束与加速度约束的制导指令解析式。针对不同加权系数、不同终端打击角度等条件对制导律制导效果进行了仿真验证,并与弹道成型制导律进行了对比。仿真结果表明,所提出的制导律可以使导弹以任意期望碰撞角准确命中目标,终端过载指令平稳收敛至0,避免了末端指令饱和现象。相较此前多项式制导相关研究,文中制导方法避免了在制导模型中引入小角度线性近似条件,提高了对轨迹与制导指令的设计精度,并能约束视场角大小从而规避系统可能出现的奇异性问题和自变量单调性问题,在终端可实现全向攻击。

Three-dimensional time-varying sliding mode guidance law against maneuvering targets with terminal angle constraint

This paper deals with the problem of intercepting maneuvering targets with terminal angle constraints for missiles subjected to three-dimensional non-decoupling engagement geometry.To achieve the finite-time interception and satisfactory overload characteristics, a time varying sliding mode control methodology is developed based on a time base generator function. The main feature of the proposed guidance law guarantees the Line-of-Sight(LOS) angles to converge to small neighborhoods of the desired values at the interception time. First, a fractional power extended state observer is used to estimate the unknown target acceleration, which can significantly reduce the adaptive switching gain. The fractional power extended state observer enjoys the advantage of better noise tolerance. Then, a newly designed sliding mode surface is constructed by introducing a time base generator function and the time-varying sliding mode guidance law is developed based on this time-varying sliding surface. The proposed guidance law significantly reduces the overload magnitudes. Numerical simulations are carried out to verify the performance of the proposed guidance law.

具有终端角度约束的导引律综述

随着武器作战样式的变革,近年来具有终端角度约束的制导方法受到越来越广泛的关注。根据理论基础的不同,将具有终端角度约束的导引律划分为最优导引律、变结构导引律以及其它类型的导引律。综述了几类典型的具有终端角度约束的导引律的研究进展,对各类导引律的优缺点进行了系统的总结与分析,并通过仿真比较了四种典型导引律的制导性能。

电视制导侵彻炸弹落角约束变结构制导律

针对电视制导侵彻炸弹需要控制弹着角的要求,研究了具有末端落角约束的变结构制导律.该制导律包含了重力对弹道法向加速度的影响,将制导指令经过一阶低通滤波器滤波,实现对弹体攻角的估计.通过数学仿真,讨论了制导律参数对制导效果的影响,检验了制导律在不同投弹条件和不同期望落角下的制导效果.仿真结果表明,所采用的攻角估计方法是可行的,该制导律能够满足侵彻炸弹在攻击固定目标时对脱靶量和弹着角的双重要求.

一种导弹终端侵彻多约束最优制导方法

针对地面目标精确打击及高效毁伤的需求,提出一种满足终端位置、落角及攻角约束的最优制导方法。利用比例导引项、落角约束项及加速度约束项保证终端命中多种约束条件,并且设计制导阶次实现全程加速度指令的优化分配,保证命中目标时的加速度指令收敛为小量。通过仿真计算验证了该制导方法能够满足精度、落角及攻角等终端约束条件,同时具有更好的加速度指令特性,有利于增强导弹的精确毁伤能力。

带落点和落角约束的最优末制导律研究

为了研究带有落角约束的最优末制导律,利用拉格朗日法,构造带有落点和落角约束的导弹运动方程,研究了制导系统中的动力学滞后对脱靶量和落角误差的影响.指出高阶动力学滞后的时间常数是影响误差的主要因素,而系统阶数对误差收敛时间的影响较小.研究结果表明,增加末导时间可以减小导弹的脱靶量和落角误差,并给出满足脱靶量和落角误差要求所需要的最少末导时间与时间常数的关系.

终端角度约束制导及制导控制一体化方法综述

针对制导武器终端角度约束下的制导方法和制导控制一体化方法进行综述。首先,对比分析了几种典型的终端角度约束定义,针对二维、三维交战场景构建了面向终端角度约束的制导及制导控制一体化设计的状态空间模型;其次,针对终端角度约束下的制导方法以及制导控制一体化设计方法进行分类、归纳总结与对比;最后,针对终端角度约束制导和制导控制一体化设计中存在的多约束落角控制、信息估计、落角范围估计、协同制导等问题进行了展望。

侵彻制导武器终端多约束最优制导律

针对侵彻型制导武器终端多约束制导问题,建立包含一阶弹体动力学的多约束制导模型,采用最优控制方法推导终端多约束制导问题的通解。根据终端约束与罚函数的关系,求解了实际工程中关心的3种最优制导律,并结合当前主流制导控制体制,在小角假设下,将其表述为便于工程实现的形式,即包含弹体动力学的最优比例导引制导律、弹道成型最优制导律和终端多约束最优制导律。理论分析和典型末制导条件仿真表明,后2种制导律可为侵彻制导武器终端位置与角度双约束以及位置、角度与加速度多约束制导问题提供理论基础和工程应用参考。

电视制导侵彻炸弹落角约束变结构反演制导律设计

针对电视制导侵彻炸弹需要弹着角控制的要求,提出了带落角约束的变结构反演制导律。通过数学仿真,讨论了制导律参数对制导效果的影响,并检验了制导律在不同投弹条件和不同期望落角下的制导效果。仿真结果表明了该制导律的鲁棒性和有效性。

带攻击角度约束的非奇异快速终端滑模制导律

本文利用先进的终端滑模控制和李雅普诺夫稳定性理论设计了一种非奇异、本质上连续和有限时间收敛的带攻击角度约束的制导律,它可用于打击固定、匀速运动和机动目标.为了在有限时间内高精度地获得给定的攻击角度并不出现奇异问题,非奇异快速终端滑模函数被用于设计滑模面.快速终端滑模函数被用于设计趋近律,在整个到达阶段系统轨迹可以从任意初始状态快速地收敛到滑模面并形成本质上连续的制导律.由于非奇异、本质上连续和全局快速收敛的特性,和传统的终端滑模制导律相比,本文方法可以在更短时间内以更高精度的攻击角度对目标实施打击.大量的仿真算例表明了本文制导律的有效性.