Three-dimensional guidance law based on adaptive integral sliding mode control

For the terminal guidance problem of missiles intercepting maneuvering targets in the three-dimensional space, the design of guidance laws for non-decoupling three-dimensional engage-ment geometry is studied. Firstly, by introducing a finite time integral sliding mode manifold, a novel guidance law based on the integral sliding mode control is presented with the target acceler-ation as a known bounded external disturbance. Then, an improved adaptive guidance law based on the integral sliding mode control without the information of the upper bound on the target accel-eration is developed, where the upper bound of the target acceleration is estimated online by a designed adaptive law. The both presented guidance laws can make sure that the elevation angular rate of the line-of-sight and the azimuth angular rate of the line-of-sight converge to zero in finite time. In the end, the results of the guidance performance for the proposed guidance laws are pre-sented by numerical simulations. Although the designed guidance laws are developed for the con-stant speed missiles, the simulation results for the time-varying speed missiles are also shown to further confirm the designed guidance laws.     

An adaptive fast fixed-time guidance law with an impact angle constraint for intercepting maneuvering targets

Sliding mode guidance laws based on a conventional terminal sliding mode guarantees only finite-time convergence, which verifies that the settling time is required to be estimated by selecting appropriate initial launched conditions. However, rapid convergence to a desired impact angle within a uniform bounded finite time is important in most practical guidance applications. A uniformly finite-time/fixed-time convergent guidance law means that the convergence (settling) time is predefined independently on initial conditions, that is, a closed-loop convergence time can be estimated a priori by guidance parameters. In this paper, a novel adaptive fast fixed-time sliding mode guidance law to intercept maneuver targets at a desired impact angle from any initial heading angle, with no problems of singularity and chattering, is designed. The proposed guidance law achieves system stabilization within bounded settling time independent on initial conditions and achieves more rapid convergence than those of fixed-time stable control methods by accelerating the convergence rate when the system is close to the origin. The achieved acceleration-magnitude constraints are rigorously enforced, and the chattering-free property is guaranteed by adaptive switching gains. Extensive numerical simulations are presented to validate the efficiency and superiority of the proposed guidance law for different initial engagement geometries and impact angles.     

自适应严格收敛非奇异终端滑模制导律

针对机动目标的末制导拦截问题，设计了一种带终端角度约束的有限时间收敛终端滑模制导律。首先，分析了现有非奇异终端滑模制导律存在的滑模面不能严格有限时间收敛的问题，进而构造了一种新型的非奇异终端滑模面。其次，设计了一种对目标机动上界的自适应估计，提出了一种自适应严格收敛非奇异终端滑模制导律的设计方法。最后，基于Lyapunov稳定性理论，证明了设计的制导律能够使得制导系统在有限时间内收敛到零，并且保证了滑模面在收敛过程中不存在非收敛因子，是严格有限时间收敛的。仿真实验验证了该制导律能够有效地拦截机动目标，同时和与现有的非奇异终端滑模制导律以及基于转换滑模面的非奇异制导律相比，拦截时间更短，终端攻击角度精度更高，导弹机动消耗的能量更少。     

考虑驾驶仪动态特性的固定时间收敛制导律

针对打击机动目标的制导问题，设计了一种同时考虑攻击角度约束、自动驾驶仪动态特性和固定时间收敛的新型制导律。首先，基于非奇异终端滑模控制和固定时间稳定性理论，采用反步递推方法设计制导律。在制导律设计过程中，设计了一种固定时间收敛的非奇异终端滑模面，基于固定时间控制和滑模控制，设计虚拟控制律，构造一种非线性一阶滤波器解决传统反步设计中的"微分膨胀"问题。基于超螺旋算法和固定时间稳定性理论，设计了一种固定时间收敛的滑模干扰观测器，用于估计目标机动等干扰。然后，基于Lyapunov稳定性理论，对制导律的固定时间稳定性进行了证明，并给出了收敛时间的表达式。最后，通过仿真分析，验证了所提制导律的有效性，和现有制导律相比，所提制导律具有较高的制导精度和角度约束精度、较快的系统收敛速度以及较少的能量消耗。     

基于终端滑模的航天器自适应预设性能姿态跟踪控制

针对航天器姿态跟踪控制的快速性需求,提出一类自适应终端滑模有限时间控制方法,通过引入饱和函数解决了终端滑模控制器的奇异问题,并结合实际有限时间稳定概念显式地给出了系统状态收敛时间和收敛范围之间的对应关系;为在提高系统鲁棒性的同时避免控制器抖振,设计了一种新型自适应律估计并补偿未知环境干扰。进一步地,针对如遥感卫星对地扫描成像等姿态跟踪任务中存在的状态约束问题,通过在控制器中引入具有对数形式的预设性能项,使系统滑模面响应具有期望的动态过程,约束了航天器姿态跟踪误差及其一阶导数的变化范围。仿真结果表明,设计的控制器具有较高的控制精度和响应速度,满足实际任务对状态约束的需求,且其控制输出不存在奇异和抖振,具备良好的工程应用价值。     

三维自适应终端滑模协同制导律

针对多枚导弹协同作战的问题,且多枚导弹之间保持有向拓扑通信的条件下,基于终端滑模法设计了视线方向及视线法向的双层协同制导律。其中,视线方向的制导指令能够保证导弹同时完成拦截任务;视线法向上的三维制导律能够保证每枚导弹以期望的视线角攻击目标,从而发挥各枚导弹的最大杀伤力,并且视线角的约束相当于规划了末制导段导弹的弹道问题,在一定程度上避免攻击目标前导弹间发生碰撞。同时,针对所设计的滑模制导律设计了新的自适应律,从而加快了滑模面的收敛速度并且削弱了由符号函数引起的系统抖振现象。基于李雅普诺夫稳定性理论,证明了所设计制导律的正确性,并在最后给出了数学仿真实验,验证了所设计制导律的有效性及优越性。     

考虑落角约束的制导炸弹有限时间控制制导律

为了提高制导炸弹对目标的毁伤能力,更加有效地约束终端落角,利用终端滑模变结构控制理论和有限时间收敛性理论,在选取自适应趋近律和建立弹目相对运动模型的基础上,提出了一种考虑落角约束的制导炸弹有限时间控制制导律。然后,利用Lyapunov理论证明了所选取的滑模面和趋近律是有限时间收敛的。通过仿真实验验证了所提算法的有效性。仿真结果表明:与比例制导律相比,所提制导律既能使制导炸弹在有限时间内收敛到所期望的入射约束角附近,又能使炸弹的视线角及其角速度收敛的更快,具有一定的工程应用价值。     

越肩发射反导拦截弹复合制导律研究

研究了优化反导拦截弹的越肩发射制导律,实现了对尾追目标的拦截,采用伪谱法和滑膜变结构理论设计了全弹道复合制导规律。利用Radau伪谱法求解以转弯时间最优为指标泛函的最佳转弯规律,通过曲线拟合给出了初制导转弯段的过载指令。选择零控脱靶量作为滑动模态对末制导律进行设计;利用这两种制导律的加速度指令构造了交接班导引律实现弹道的平滑。最后,对载机越肩发射反导拦截弹拦截来袭导弹的反导场景进行了数字仿真,结果表明所设计的复合制导律能够完成反导拦截任务。     

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 desir...     

Three-dimensional finite-time cooperative guidance for multiple missiles without radial velocity measurements

In order to simultaneously attack a target with impact angle constraint in threedimensional(3-D) space, a novel distributed cooperative guidance law for multiple missiles under directed communication topologies is proposed without radial velocity measurements. First, based on missiles-target 3-D relative motion equations, the multiple missiles cooperative guidance model with impact angle constraint is constructed. Then, in Line-of-Sight(LOS) direction, based on multiagent system cooperative control theory, one guidance law with directed topologies is designed with strict proof, which can guarantee finite time consensus of multiple missiles' impact times. Next, in elevation direction and azimuth direction of LOS, based on homogeneous system stability theory and integral sliding mode control theory, two guidance laws are proposed respectively with strict proof, which can guarantee LOS angles converge to desired values and LOS angular rates converge to zero in finite time. Finally, the effectiveness of the designed cooperative guidance law is demonstrated through simulation results.