Adaptive backstepping impact angle control with autopilot dynamics and acceleration saturation consideration

This paper presents a robust impact angle constraint guidance law for maneuvering target interception in the presence of autopilot dynamics and input saturation. The presented guidance law is designed on the basis of a combination of adaptive backstepping control technique and higher‐order sliding mode differentiator. Different from existing impact angle constraint guidance law using sliding mode control, the line‐of‐sight angular rate and impact angle tracking error are regulated by two different virtual control laws. Because the future course of action of the target, an independent entity, cannot be predicted beforehand, adaptive laws are introduced in guidance law derivation for disturbance rejection. Unlike dynamic surface control approach, higher‐order sliding mode differentiator is adopted here as an alternative way to obtain the derivatives of the virtual control laws, thus leading to the exact tracking performance of backstepping control. Detailed stability analysis shows that both the line‐of‐sight angular rate and impact angle error can be stabilized in a small region around zero asymptotically. Simulation results explicitly show that accurate interception is achieved with a wide range of impact angles. Copyright © 2017 John Wiley & Sons, Ltd.     

考虑导弹自动驾驶仪动态特性的带攻击角度约束制导律

针对打击机动目标时带攻击角度约束的制导问题,采用扩张状态观测器和动态面控制方法设计一种考虑自动驾驶仪动态特性的制导律.考虑期望视线角的变化率正比于未知的目标加速度,采用扩张状态观测器对未知目标加速度进行估计.为了避免奇异问题,并克服非匹配不确定项对系统性能的影响,采用非奇异终端滑模和动态面控制方法进行制导律设计.与传统的将目标加速度设为零的制导律相比较,仿真结果表明所提出的制导律具有良好的制导性能.     

考虑攻击角度和视场角约束的自适应终端滑模制导律

针对导弹拦截机动目标的末制导问题,基于有限时间滑模控制理论设计一种带有攻击角度和导弹视场角约束的制导律.首先,将导弹末制导问题转化为带有状态约束的制导系统稳定问题,设计一种新型的非奇异终端滑模面和时变的障碍Lyapunov函数,给出一种终端滑模制导律的设计方法,并针对目标机动的不确定性设计一种对目标机动上界的自适应估计;然后,通过稳定性理论证明制导系统的状态变量最终是有限时间收敛的,并且结合时变的障碍Lyapunov函数和滑模面的设计特性证明在末制导过程中视场角约束条件始终不会被违背,相比于现有的考虑视场角约束的制导律,该制导律不存在指令转换,能够加快制导系统收敛速率,增强制导系统的抗干扰能力;最后,通过仿真实验验证所提出制导方法的有效性.     

考虑终端角度约束的自适应积分滑模制导律

针对机动目标拦截末制导问题,提出一种考虑终端角度约束的自适应积分滑模制导律.首先给出一种有限时间收敛的非线性积分滑模面,采用快速终端滑模设计趋近律;然后设计一种对目标机动加速度上界平方进行估计的自适应律,给出具有光滑特性的自适应积分滑模制导律;最后基于有限时间理论证明闭环系统的有限时间收敛特性,并给出滑模变量、视线角以及视线角速率的收敛域.数值仿真结果验证了所提出设计方案的有效性.     

考虑加速度约束的终端角度约束滑模制导律设计

针对含终端角度约束的滑模制导律在制导初期加速度指令过大的问题,采用趋近律方法和引入阻尼项设计一种考虑加速度约束的角度约束滑模制导律.首先,分析制导指令大小与滑模变量趋近速度的关系;然后,在滑模面函数中引入阻尼项,动态调节制导指令中不同部分的占比,从而降低制导初期整体指令值;最后,设计多幂次自适应趋近律来调节不同阶段的滑模变量趋近速度,达到降低制导指令极值、满足加速度约束的目的,同时保证滑模面函数的快速收敛.与常见的终端角度约束滑模制导律相比,仿真结果验证了所提出方法在降低加速度极值方面的有效性.     

含攻击角约束的网络化弹药分布式模糊协同制导律

在舰炮网络化弹药打击近岸机动目标的末制导段,提出了一种考虑攻击角约束的有限时间分布式模糊协同制导律.构建网络化弹药–目标相对运动模型,设计扩张状态观测器估计目标的切向、法向加速度.在视线切向,为保证命中时刻在有限时间内趋于一致,采用积分滑模设计分布式有限时间协同制导律;在视线法向,为在有限时间内零化视线角误差、视线角速率并改善控制指令终端发散现象,采用非奇异终端滑模设计两阶段制导律.为削弱控制指令抖振、补偿干扰,设计模糊自适应系统,并通过Lyapunov理论证明了全系统状态的一致最终有界性与有限时间收敛性.仿真实验表明:该制导律使网络化弹药在打击机动形式不同的目标时,均具备较好的协同制导性能.     

Adaptive nonsingular fast terminal sliding mode guidance law with impact angle constraints

This paper considers the terminal guidance problem of missiles intercepting maneuvering targets with impact angle constraints. Based on an advanced nonsingular fast terminal sliding mode control scheme and adaptive control, an adaptive nonsingular fast terminal sliding mode guidance law is proposed in the presence of the target acceleration as an unknown bounded external disturbance. In the design procedure, an adaptive law is presented to estimate the unknown upper bound of the external disturbance. Theoretical analysis shows that the proposed guidance law can guarantee the finite-time convergence in both the reaching phase and the sliding phase by applying a Lyapunov-based approach. Numerical simulations are presented to demonstrate the effectiveness of the proposed guidance law. Although the proposed guidance law is developed for the constant speed missiles, by the extensive numerical simulations with a realistic missile model, the performance is shown to be equally good for the varying speed missiles.     

Guidance Laws With Input Constraints and Actuator Failures

A novel three‐dimensional fault‐tolerant control guidance law is proposed for interception of maneuvering targets in the presence of external disturbances, actuator failures, and control input constraints. The input‐to‐state stability (ISS) method is introduced to design the fault‐tolerant control guidance law to guarantee robust tracking of a maneuvering target. Then, a saturated fault‐tolerant control guidance law is constructed using a modified saturation function to ensure the resulting control signal will never incur input constraints, and the convergence to a small neighborhood of origin is ensured in theory. Simulation results show that the presented approach is effective in achieving a successful interception against target maneuvers, external disturbances, actuator failures, and control input constraints.     

On an Optimized Fuzzy Supervized Multiphase Guidance Law

Proportional navigation (PN) is an effective guidance law in chasing a constant speed target. However, intercepting a maneuvering target requires extra provisions to contain target acceleration. This is observed in the next generation of guidance laws, namely augmented proportional navigation (APN) and the optimal guidance law (OGL). The other advanced guidance method is integral sliding mode (ISM), which exhibits superb low miss distance (MD), but unfortunately at the cost of disappointing effective lateral acceleration (C_eff), higher than the modest level that APN and OGL demand. Reducing both MD and C_eff can be achieved using a multiphase algorithm. A setup of APN, OGL and ISM is proposed to integrate the strength of each and overcome their weaknesses. Hybrid algorithm smooth management is conducted by an optimally tuned fuzzy supervisory controller. The results indicate that in facing a constant acceleration target, an APN‐ISM twin yields the best results, while in case of a constant jerk target an APN‐OGL‐ISM triplet renders excellent interception. Miss distance as low as 0.012m can be achieved with significantly lower control effort than required by ISM alone. The simulations results confirm the conclusions and illustrate the capacity of the algorithm in combating maneuvering targets.     

带攻击角度约束的非奇异终端滑模固定时间收敛制导律

针对拦截机动目标的末制导问题,设计一种带攻击角度约束的末制导律.该制导律构造一种新型的固定时间收敛非奇异终端滑模面,能够在解决终端滑模面奇异性问题的同时使得滑模面、弹目视线角和弹目视线角速率在固定时间内收敛,保证收敛时间的上界是独立于弹目初始条件,可以被预先设定的.与传统的固定时间收敛控制相比,该制导律通过调节滑膜面和弹目视线角误差的趋近律指数使得制导系统收敛速率更快.同时,针对目标机动引起的未知扰动,引入一种扩张状态观测器进行估计,能够增强制导系统的鲁棒性,避免震颤现象的发生.最后,通过仿真实验验证所提出制导律能够以不同的攻击角度对机动目标进行有效拦截,且与其他制导律相比,所提出的制导律使得制导系统收敛更快,导弹拦截时间更短,拦截精度更高.     

Applying a novel extended Kalman filter to missile–target interception with APN guidance law: A benchmark case study

This paper considers the estimation of the target acceleration with unknown dynamics along with other states of a benchmark example of a nonlinear 2D missile–target engagement system in presence of model uncertainties and measurement noises. The objective is to implement the augmented proportional navigation (APN) guidance law for the missile–target interception to minimize the distance between the missile and the target. The estimated target acceleration can be treated as an unknown input to the nonlinear 2D missile–target engagement system. A novel analytical recursive approach referred to as extended Kalman filter with unknown inputs without direct feedthrough (EKF-UI-WDF) is derived with the weighted least squares estimation for an extended state vector including states and unknown inputs which can be any type of signals without prior information. By applying the proposed EKF-UI-WDF approach to a 2D missile–target interception control system, simulation results demonstrate that this approach is capable of (i) estimating the states and unknown input (target acceleration) well, and (ii) achieving more reasonable interception performance comparing with the traditional extended Kalman filter (EKF) approach.     

考虑导弹速度时变的角度约束最优中制导律

以导弹逆轨拦截高速运动目标为背景,本文运用间接高斯伪谱法设计带攻击角度约束的最优中制导律.通过零化弹目相对法向速度,将攻击角度约束转化为视线角约束.考虑导弹速度时变的情况,建立带角度约束的制导方程.根据极小值原理推导最优中制导律的解析表达式,运用高斯伪谱法对最优中制导律进行离散化,把微分方程转化为代数方程,避免了求解Riccati方程.该方法不需要预先知道导弹未来的速度信息,计算量小,具有较好的实时性.仿真结果表明该中制导律可以满足逆轨拦截对弹目交会角的约束,且中制导末端的过载较小.     

Design of sliding mode guidance law with dynamic delay and impact angle constraint

A sliding mode guidance law with dynamic delay and impact angle constraints is designed for the relative motion between the missile and the target in the intercepting plane. First of all, the missile’s first order dynamic delay is involved into the system model to design the guidance law based on sliding mode variable dynamic method. Secondly, the target’s maneuvering is taken as the system disturbance, and a non-homogeneous disturbance observer is applied to estimate such maneuvering in finite time rapidly, which, through dynamic compensation, realizes the missiles precision attack to targets of different maneuvering at a desired line-of-sight (LOS) angle. Finally, numerical simulations are performed to demonstrate the effectiveness of the designed guidance law.

     

考虑自动驾驶仪与角度约束的制导律设计

以末端拦截高机动目标为背景,针对带有攻击角约束和自动驾驶仪动态特性情形下的二维平面制导问题进行了研究分析。在提出固定时间终端滑模面基础上,通过自适应算法在线估计干扰的上界值,针对带有攻击角约束和自动驾驶仪动态特性的制导系统模型设计了自适应终端滑模制导律,使得系统状态在有限时间内趋于零附近任意小的区域。利用李雅普诺夫理论对所设计制导策略给出了严格的稳定性证明,仿真结果验证了所提制导方案的有效性。     

Sliding Mode Guidance Law Considering Missile Dynamic Characteristics and Impact Angle Constraints

In order to improve the precision of guidance for the missile intercepting maneuvering targets, this paper proposes a sliding mode guidance law with impact angle constraints based on the equation of the relative motion of the missile and the target in a 2D plane. Two finite-time convergent guidance laws are proposed based on the nonsingular terminal sliding mode, while, two exponential convergent guidance laws involving dynamic delay are developed through applying the higher-order nonsingular terminal sliding mode. The simulations denote that, in all the four scenarios of the target’s maneuvering, the guidance laws are able to inhibit the chattering phenomenon of the sliding modes effectively; and from an expected aspect angle, the missiles could attack the targets with high precision and fast speed.     

Adaptive terminal angle constraint interception against maneuvering targets with fast fixed‐time convergence

In this paper, a modified adaptive fast nonsingular terminal sliding mode guidance law is proposed based on the theory of fixed‐time convergence, which is applied for intercepting maneuvering targets considering terminal angle constraint. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and provides no singularity and globally rapid convergence property by accelerating the convergence rate when the system is close to the origin. The upper bound of settling time can be obtained in advance by the controller's parameters. Besides, in order to achieve chattering‐free property, a continuous adaptive switching control is introduced and the achieved acceleration‐magnitude constraints are rigorously enforced. Finally, the fixed‐time convergence of the sliding mode manifold and the system states is demonstrated by Lyapunov stability theory. Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law.     

拦截高速机动目标的非线性自抗扰制导律

为实现导弹对目标的高精度拦截, 本文提出了基于加权齐次函数的非线性自抗扰拦截制导设计方法. 首先, 提出了基于加权齐次函数的非线性扩张状态观测器在线估计视线角速率和由目标加速度等内外不确定性因素构成的总扰动. 其次, 设计了基于非线性扩张状态观测器的非线性自抗扰三维制导律对总扰动进行补偿, 该制导律克服了高阶非线性项与强耦合项等不利因素的影响, 提高了拦截制导精度. 本文通过分析误差系统的动力学行为证明了闭环制导系统的稳定性和收敛性. 本文提出的方法在拦截精度等方面优于已有的基于线性扩张状态观测器和基于fal函数的扩张状态观测器的自抗扰制导方法. 仿真结果验证了本文所提出方法的有效性和优越性.     

基于模糊滑模方法的双舵控制导弹制导控制一体化

针对单舵控制导弹舵角在大攻角下易饱和的问题, 提出一种适用于双舵控制导弹的制导控制一体化模糊滑模方法. 分析具有鸭舵/尾舵结构导弹动力学特性, 建立制导控制一体化模型, 利用双滑模变结构控制方法, 分别选取零控脱靶量和控制相关量作为滑动模态, 前者保证脱靶量趋于零, 后者提供阻尼响应, 将制导律嵌入在控制器的设计之中. 为了克服滑模抖振问题, 利用指数趋近率方法设计控制器, 并将模糊环节加入控制器中. 最后, 对拦截蛇形机动目标的过程进行仿真, 仿真结果验证了所提出方法的有效性.

     

Three‐dimensional impact angle‐constrained adaptive guidance law considering autopilot lag and input saturation

This work investigates three‐dimensional accurate guidance problem in the presence of impact angle constraint, input saturation, autopilot lag, and external disturbance, and presents a robust adaptive guidance method for maneuvering targets. More specifically, based on integral Lyapunov control algorithm, a robust guidance law, which can drive both terminal line‐of‐sight angle error and its rate to a small region around zero, while resisting the terrible influence caused by external disturbance, is proposed in this work. To deal with input saturation, guidance command is separated into two parts: real input and saturation error, and an adaptive control technique is employed to compensate the influence resulting from external disturbance and saturation error. Moreover, regarding autopilot lag as a first‐order dynamics, a backstepping designed controller with an adaptive term is proposed. Numerical simulations are carried out and their results demonstrate the proposed properties.     

Adaptive nonsingular fast terminal sliding mode control for underwater manipulator robotics with asymmetric saturation actuators

In this paper, an adaptive nonsingular fast terminal sliding mode control (ANFTSMC) is proposed for underwater manipulator robotics with asymmetric actuator saturations and unknown time-varying (TV) external disturbances. Firstly, the nonsingular fast terminal sliding mode (NFTSM) control scheme is conducted for the underwater manipulator robotics, which guarantees the boundedness of all the signals in the control system. Secondly, the adaptive method and the smooth hyperbolic tangent (tanh) function are introduced to address the unknown TV external disturbances and the input saturation errors. Thus the prior knowledge about the upper bounds of the system uncertainties is not needed in this paper. To deal with the nonlinear asymmetric input saturation issue, a Gaussian error function is employed in the asymmetric saturation module so that the discontinuous input signals can be transformed into smooth forms. Thirdly, the rigorous mathematical verification is conducted to demonstrate the stability and finite-time convergence of the closed-loop control system via the Lyapunov theory. Finally, numerical simulations are performed on a two-link underwater manipulator robotic system to illustrate the effectiveness of the proposed controller.