Composite Finite‐time Convergent Guidance Law for Maneuvering Targets with Second‐order Autopilot Lag

This paper aims to develop a new finite‐time convergent guidance law for intercepting maneuvering targets accounting for second‐order autopilot lag. The guidance law is applied to guarantee that the line of sight (LOS) angular rate converges to zero in finite time and results in a direct interception. The effect of autopilot dynamics can be compensated based on the finite‐time backstepping control method. The time derivative of the virtual input is avoided, taking advantage of integral‐type Lyapunov functions. A finite‐time disturbance observer (FTDOB) is used to estimate the lumped uncertainties and high‐order derivatives to improve the robustness and accuracy of the guidance system. Finite‐time stability for the closed‐loop guidance system is analyzed using the Lyapunov function. Simulation results and comparisons are presented to illustrate the effectiveness of the guidance strategy.     

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.     

考虑自动驾驶仪动态特性的三维双环制导律

针对导弹自动驾驶仪动态特性条件下的机动目标拦截问题,基于非线性干扰观测器和命令滤波器设计一种新的三维双环制导律.将制导系统解耦为外环系统和内环系统.其中:外环控制器产生虚拟制导指令,以零化球坐标系下的弹目法向相对速率;内环控制器产生真实制导指令,以实现导弹自动驾驶仪对外环虚拟指令的快速跟踪.由于外环命令滤波器同时计算出虚拟制导指令的一阶导数和二阶导数,三阶系统的制导律设计问题仅用两步即可完成.拦截高速高机动目标的仿真结果表明,所设计的制导律能够有效补偿导弹自动驾驶仪动态特性影响,抗目标机动鲁棒性强,制导精度优良.     

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...     

Terminal angle constrained time-varying sliding mode guidance law with autopilot dynamics and input saturation

To intercept the maneuvering target at a desired terminal angle, this paper presents a time-varying sliding mode guidance law with consideration of the second-order autopilot dynamics and input saturation. To achieve the finite-time interception and satisfactory overload characteristics, a time-varying sliding mode guidance law is developed, which enables the line-of-sight (LOS) angle error to converge into a small neighborhood of the origin at the interception time. An auxiliary system is constructed to reduce the adverse effect generated from the input saturation. Moreover, with the aid of extended state observers, the proposed guidance law requires no information on the target acceleration and the acceleration derivative of the interceptor. The performance of this guidance law is verified via the numerical simulations.     

Integrated Game Based Guidance with Nonlinear Autopilot Design for Maneuvering Target Interception

The integrated game theory based guidance law with nonlinear autopilot (GGNA) system is presented in this paper. The guidance law is designed based on linear differential game theory while considering the motion of the target in 3‐D space such that the distance between the missile and the target is minimized faster than before. The autopilot system based on quaternion representation is developed using sliding mode control method to generate the attitude command. The stability of the integrated guidance and nonlinear autopilot system is analyzed with Lyapunov stability theory. In addition, this research assumes wingless missiles in our context in order to reduce the nonlinear effect from the aerodynamics. Furthermore, in order to extend the operation range of missiles from endo‐atmosphere to exo‐atmosphere, the missiles are equipped with Thrust Vector Control (TVC) mechanisms and Divert Control System (DCS). Finally, extensive simulations incorporating aerodynamic models are demonstrated to verify the validity of the proposed integrated guidance/autopilot systems. Moreover, the simulation results reveal that the mission of intercepting a maneuvering target is successfully accomplished.     

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.     

Robust Missile Autopilots With Finite‐Time Convergence

This paper presents a new longitudinal autopilot to address the finite‐time tracking problem for uncertain agile missiles. The proposed autopilot is essentially a composite control scheme, which is obtained through the finite‐time control methodology and the nonlinear disturbance observer (NDOB) approach. The key idea in this scheme is that the NDOB is adopted to estimate the aerodynamic uncertainties and external disturbances in an integrated manner. With the aid of the finite‐time bounded function and the Lyapunov function method, the finite‐time stability of the closed‐loop system is established, which shows that the angle‐of‐attack response will converge to the external command signal in finite time. Numerical simulation results are presented to demonstrate the superiority of the proposed scheme.     

Nonlinear sliding sector design for multi‐input systems with application to helicopter control

The ability of helicopters to hover and land vertically has spurred an interesting field of research on the development of autonomous flight for these rotatory wing aircrafts. Linear control theory with gain scheduling, which is based on linearizing the system at the equilibrium points, dominated the helicopter autopilot design. Unlike the linear cascaded autopilot structure used in the existing literature, this paper uses state‐dependent linear like structure, including rate‐limited actuator dynamics, with cascaded autopilot topology. This approach allows nonlinear control laws to be implemented throughout the entire flight envelope, providing satisfactory robustness and stability over the various parameter uncertainties and time delays. The cascaded autopilot topology with nonlinear dynamical equations contains a new sliding sector control (SSC) mechanism which is derived for multi‐input nonlinear dynamical systems. The proposed SSC structure for multi‐input nonlinear systems is used in the inner loop of the cascaded autopilot system where the fastest dynamics are required to be controlled for rapid changes in the helicopter dynamical characteristics which enables one to stabilize the helicopter over a wide range of flight conditions. The proposed cascaded autopilot topology with the new SSC mechanism is tested in simulations to assess its robustness and stability properties. To establish its feasibility, the proposed control method is replaced with a suboptimal control method, namely state‐dependent differential Riccati equation (SDDRE) method, for the inner loop and the results of the proposed control architecture are compared with those of SDDRE method.     

Robust differential game guidance laws design for uncertain interceptor-target engagement via adaptive dynamic programming

In this paper, the problem of intercepting a maneuvering target is formulated as a two-player zero-sum differential game framework affected by matched uncertainties. By introducing an appropriate cost function that reflects the uncertainties, the robust control is transformed into a two-player zero-sum differential game control problem and therefore ensures the compensation of the matched uncertainties. Additionally, the corresponding Hamilton--Jacobi--Isaacs (HJI) equation is solved by constructing a critic neural network (NN). The closed-loop system and the critic NN weight estimation error are proved to be uniform ultimate boundedness (UUB) by utilising Lyapunov approach. Finally, the effectiveness of the proposed robust guidance law is demonstrated by using a nonlinear two-dimensional kinematics, assuming first-order dynamics for the interceptor and the target.     

Decentralised Standoff Tracking of Moving Targets Using Adaptive Sliding Mode Control for UAVs

This paper proposes a decentralised vector field guidance algorithm for coordinated standoff tracking of a ground moving target by multiple UAVs. In particular, this study introduces additional adaptive terms in an existing sliding mode control concept for standoff tracking guidance, in order to reduce the effect of unmodelled dynamics and disturbances. Decentralised angular separation control between UAVs, in conjunction with decentralised estimation, is also introduced using either velocity or orbit radius change by different information/communication structures. Numerical simulations are performed to verify the feasibility and benefits of the proposed approach under a realistic ground vehicle tracking scenario, using multiple UAVs having unknown parameters in the heading-hold autopilot.     

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.     

Exoatmospheric interception problem solved using output feedback law

Interception problems are often dealt with by separating guidance and autopilot design. Guidance law can be obtained using optimal control theory and autopilot design is performed on a linearized system. In this paper, we introduce a new approach that determines a global guidance and autopilot law, based on direct output feedback design. Application of this method to exoatmospheric interception problem results in good performances. Extension to endoatmospheric case is under investigation.     

Robust fuzzy 3D path following for autonomous underwater vehicle subject to uncertainties

This paper addresses a three-dimensional (3D) path following control problem for underactuated autonomous underwater vehicle (AUV) subject to both internal and external uncertainties. A two-layered framework synthesizing the 3D guidance law and heuristic fuzzy control is proposed to achieve robust adaptive following along a predefined path. In the first layer, a 3D guidance controller for underactuated AUV is presented to guarantee the stability of path following in the kinematics stage. In the second layer, a heuristic adaptive fuzzy algorithm based on the guidance command and feedback linearization Proportional-Integral-Derivative (PID) controller is developed in the dynamics stage to account for the nonlinear dynamics and system uncertainties, including inaccuracy modelling parameters and time-varying environmental disturbances. Furthermore, the sensitivity analysis of the heuristic fuzzy controller is presented. Against most existing methods for 3D path following, the proposed robust fuzzy control scheme reduces the design and implementation costs of complicated dynamics controller, and relaxes the knowledge of the accuracy dynamics modelling and environmental disturbances. Finally, numerical simulation results validate the effectiveness of the proposed control framework and illustrate the outperformance of the proposed controller as well.     

A three-dimensional robust nonlinear terminal guidance law with ISS finite-time convergence

This paper presents a novel three-dimensional nonlinear terminal guidance law with finite-time convergence for intercepting manoeuvring targets. Different from the usual method of decoupling the missile-target relative motion into two-dimensional planes, this law is designed via using the coupled dynamics. The guidance law is derived based on the theory of finite-time input-to-state stability (ISS), which needs no assumption of the linearisation and the estimation of target accelerations. Under this law, the line-of-sight angular rates can be stabilised to a small domain of convergence around zero in finite time. The convergence rate and convergence domain can be adjusted by changing the guidance parameters. First, a sufficient condition on finite-time ISS of the guidance system is given, and is subsequently used to design the guidance law. Finally, simulation results are provided to show that the proposed guidance law possesses fast convergence rate and strong robustness to target manoeuvres.     

A novel sliding mode guidance law without line-of-sight angular rate information accounting for autopilot lag

This paper proposes a new composite guidance law to intercept manoeuvring targets without line-of-sight (LOS) angular rate information in the presence of autopilot lag. The presented formulation is obtained via a combination of homogeneous theory and sliding mode control approach. Different from some existing observers, the proposed homogeneous observer can estimate the lumped uncertainty and the LOS angular rate in an integrated manner. To reject the mismatched lumped uncertainty in the integrated guidance and autopilot system, a sliding surface, which consists of the system states and the estimated states, is proposed and a robust guidance law is then synthesised. Stability analysis shows that the LOS angular rate can be stabilised in a small region around zero asymptotically and the upper bound can be lowered by appropriate parameter choice. Numerical simulations with some comparisons are carried out to demonstrate the superiority of the proposed method.     

无人机三维航路自适应跟踪控制

针对无人机自动驾驶仪参数标称值偏离实际值情况下的航迹跟踪问题,提出一种无人机三维航路自适应跟踪导引律。首先在无人机自动驾驶仪参数无偏离的条件下,推导出能够跟踪三维航路的速度指令、航迹倾斜角指令和航迹方位角指令,并使用Lyapunov稳定性理论证明了跟踪系统全局渐进稳定;之后考虑自动驾驶仪参数标称值偏离实际值的情况,设计自适应算法在线估计自动驾驶仪参数,得到无人机三维航路自适应跟踪导引律。仿真实验表明所提出的自适应跟踪导引律能够使无人机在自动驾驶仪参数偏离条件下有效跟踪三维航迹。     

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.     

一类3阶非线性系统的非奇异终端滑模控制

针对传统非奇异终端滑模控制方法不适用于3阶系统的问题,提出一类具有不确定和外干扰的3阶非线性系统的新型非奇异终端滑模控制方法.该方案首先结合backstepping控制中的动态面方法和传统2阶非奇异终端滑模控制构造非奇异3阶终端滑模面,首次提出采用高阶滑模微分器估计值代替控制器中的负指数项.采用非线性干扰观测器任意精度地估计不确定和干扰,设计控制器中的补偿项.采用终端吸引子函数做趋近律避免抖振的同时能保证有限时间趋近滑模面.基于有限时间稳定李雅普诺夫定理证明了被控状态将在有限时间内收敛到任意小的闭球内.所提出方案快于传统的递阶线性滑模控制和其他非奇异终端滑模控制.仿真中与其他滑模控制方案对比,总误差减小18%以上,超调及收敛时间也显著下降.     

Adaptive sliding‐mode control for Mars entry trajectory tracking with finite‐time convergence

This paper presents a novel adaptive sliding‐mode control (ASMC) method for Mars entry guidance and the finite‐time convergence in the presence of large uncertainties can be guaranteed. With the help of gain adaptive law, the nonoverestimating value of control gains can be achieved, and then, the chattering can be attenuated by the proposed ASMC method. Meanwhile, the extended state observer is introduced to estimate and compensate for uncertainties and the nonoverestimating problem is resolved further. In addition, the proposed method does not require any knowledge on the upper bound of uncertainty, which yields to be used in practical systems. Finally, the numerical simulation results are given to demonstrate the effectiveness of the proposed guidance law.