Trajectory tracking guidance of interceptor via prescribed performance integral sliding mode with neural network disturbance observer

This paper investigates interception missiles’trajectory tracking guidance problem under wind field and external disturbances in the boost phase.Indeed,the velocity control in such trajectory tracking guidance systems of missiles is challenging.As our contribution,the velocity control channel is designed to deal with the intractable velocity problem and improve tracking accuracy.The global prescribed performance function,which guarantees the tracking error within the set range and the global convergence of the tracking guidance system,is first proposed based on the traditional PPF.Then,a tracking guidance strategy is derived using the integral sliding mode control techniques to make the sliding manifold and tracking errors converge to zero and avoid singularities.Meanwhile,an improved switching control law is introduced into the designed tracking guidance algorithm to deal with the chattering problem.A back propagation neural network(BPNN)extended state observer(BPNNESO)is employed in the inner loop to identify disturbances.The obtained results indicate that the proposed tracking guidance approach achieves the trajectory tracking guidance objective without and with disturbances and outperforms the existing tracking guidance schemes with the lowest tracking errors,convergence times,and overshoots.

Integrated guidance and control design for missile with terminal impact angle constraint based on sliding mode control

Aimed at the guidance requirements of some missiles which attack targets with terminal impact angle at the terminal point,a new integrated guidance and control design scheme based on variable structure control approach for missile with terminal impact angle constraint is proposed.First,a mathematical model of an integrated guidance and control model in pitch plane is established,and then nonlinear transformation is employed to transform the mathematical model into a standard form suitable for sliding mode control method design.A sufficient condition for the existence of linear sliding surface is given in terms of linear matrix inequalities（LMIs）,based on which the corresponding reaching motion controller is also developed.To verify the effectiveness of the proposed integrated design scheme,the numerical simulation of missile is made.The simulation results demonstrate that the proposed guidance and control law can guide missile to hit the target with desired impact angle and desired flight attitude angle simultaneously.

Sliding mode control and Lyapunov based guidance law with impact time constraints

This paper analyses the issue of impact time control of super-cavitation weapons impact fixed targets which mainly refer to the ships or submarines who lost power, but still have combat capability. Control over impact time constraints of guidance law(ITCG) is derived by using sliding mode control(SMC) and Lyapunov stability theorem. The expected impact time is realized by using the notion of attack process and estimated time-to-go to design sliding mode surface(SMS). ITCG contains equivalent and discontinuous guidance laws, once state variables arrive at SMS,the equivalent guidance law keeps the state variables on SMS,then the discontinuous guidance law enforces state variables to move and reach SMS. The singularity problem of ITCG is also analyzed. Theoretical analysis and numerical simulation results are given to test the effectiveness of ITCG designed in this paper.

Fuzzy sliding mode control guidance law with terminal impact angle and acceleration constraints

In this paper, a novel fuzzy sliding mode control（FSMC） guidance law with terminal constraints of miss distance, impact angle and acceleration is presented for a constant speed missile against the stationary or slowly moving target. The proposed guidance law combines the sliding mode control algorithm with a fuzzy logic control scheme for the lag-free system and the first-order lag system. Through using Lyapunov stability theory, we prove the sliding surface converges to zero in finite time. Furthermore, considering the uncertain information and system disturbances, the guidance gains are on-line optimized by fuzzy logic technique. Numerical simulations are performed to demonstrate the performance of the FSMC guidance law and the results illustrate the validity and effectiveness of the proposed guidance law.

Backstepping design of missile guidance and control based on adaptive fuzzy sliding mode control

This paper presents an integrated missile guidance and control law based on adaptive fuzzy sliding mode control. The integrated model is formulated as a block-strict-feedback nonlinear system, in which modeling errors, unmodeled nonlinearities, target maneuvers, etc. are viewed as unknown uncertainties. The adaptive nonlinear control law is designed based on backstepping and sliding mode control techniques. An adaptive fuzzy system is adopted to approximate the coupling nonlinear functions of the system, and for the uncertainties, we utilize an online-adaptive control law to estimate the unknown parameters. The stability analysis of the closed-loop system is also conducted. Simulation results show that, with the application of the adaptive fuzzy sliding mode control, small miss distances and smooth missile trajectories are achieved, and the system is robust against system uncertainties and external disturbances.

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.

Sliding mode control based guidance law with impact angle constraint

The terminal guidance problem for an unpowered lifting reentry vehicle against a sta- tionary target is considered. In addition to attacking the target with high accuracy, the vehicle is also expected to achieve a desired impact angle. In this paper, a sliding mode control （SMC）-based guidance law is developed to satisfy the terminal angle constraint. Firstly, a specific sliding mode function is designed, and the terminal requirements can be achieved by enforcing both the sliding mode function and its derivative to zero at the end of the flight. Then, a backstepping approach is used to ensure the finite-time reaching phase of the sliding mode and the analytic expression of the control effort can be obtained. The trajectories generated by this method only depend on the initial and terminal conditions of the terminal phase and the instantaneous states of the vehicle. In order to test the performance of the proposed guidance law in practical application, numerical simulations are carried out by taking all the aerodynamic parameters into consideration. The effec- tiveness of the proposed guidance law is verified by the simulation results in various scenarios.

Finite Time Convergent Wavelet Neural Network Sliding Mode Control Guidance Law with Impact Angle Constraint

This paper presents a novel guidance law to intercept non-maneuvering targets with impact angle and lateral acceleration command constraints. Firstly, we formulate the impact angle control to track the desired line-of-sight(LOS) angle, which is achieved by selecting the missile s lateral acceleration to enforce the sliding mode on a sliding surface at impact time. Secondly, we use the Lyapunov stability theory to prove the stability and finite time convergence of the proposed nonlinear sliding surface. Thirdly, we introduce the wavelet neural network(WNN) to adaptively update the additional control command and reduce the high-frequency chattering of sliding mode control(SMC). The proposed guidance law, denoted WNNSMC guidance law with impact angle constraint,combines the SMC methodology with WNN to improve the robustness and reduce the chattering of the system. Finally, numerical simulations are performed to demonstrate the validity and effectiveness of the WNNSMC guidance law.

Adaptive sliding mode control of multi-agent relay tracking systems with disturbances

This paper studies the switching topologies and tracking agent replacements for a class of nonlinear multi-agent systems with external disturbances.In particular,it is assumed that a number of monitoring agents are randomly deployed in a two-dimensional space.The agents are committed to tracking any intrusion targets in this area.When one of the following agents exits tracking for some reasons,the agent closer to the target joins the tracking team to ensure the number of tracking agents does not change.In order to achieve the successful tracking of the target,this paper designs a sliding mode controller for the relay multi-agent system with tracking agent replacements.Furthermore,an adaptive law is proposed to estimate the upper bound of disturbance in the relay tracking process.Next,the stability of the overall system will be analysed by applying the multiple Lyapunov function method based on the average dwell time.Finally,the effectiveness of the tracking strategy is verified by numerical simulations.

Saturated super-twisting sliding mode missile guidance

This paper concentrates on developing a missile terminal guidance law against a highly maneuvering target whose maneuvering acceleration is very close to that of the missile or even exceeds the missile normal acceleration in a finite period of time.A new saturated super-twisting algorithm is proposed and applied to the design of missile guidance law.The proposed algorithm has the advantages of simple structure,easy parameter tuning rules and a full utilization of the limit control input.The designed saturated super-twisting sliding mode guidance law is then employed in a missile guidance system.Simulation and its superior performance against strong maneuvering targets is demonstrated.

Leap trajectory tracking control based on sliding mode theory for hypersonic gliding vehicle

The aim of this study was to develop robust tracking control schemes for the 3D leap trajectory of hypersonic gliding vehicles using sliding mode theory. A predictor-corrector guidance method was applied to the generation of the reference trajectory, and drag acceleration was selected as the profile of reference tracking. A combined super-twisting sliding mode controller(CST-SMC) is proposed to decrease the tracking error and guarantee the tracking performance in the presence of system nonlinearities compared to three other common controllers: the linear sliding mode controller(L-SMC), global fast terminal sliding mode controller(GFT-SMC), and super-twisting sliding mode controller(ST-SMC). By using the developed controller, the system state of a second-order drag acceleration tracking error system can approach the global fast terminal sliding manifold in finite time. By using the Lyapunov approach, sufficient conditions are deduced to ensure that the tracking performance is obtained for a closed-loop system. Furthermore, we show that the controller is robust to initial uncertain parameters and other perturbations, as validated by simulation results with appropriate gains.

A Novel Sliding-mode Guidance Law Based on Lie-group Method

Although the channel-decoupling assumption is often used in design of three-dimensional guidance laws, it loses its rationality for aircrafts with strong kinematics coupling because body rotation arises. To overcome this trouble, a novel guiding method was proposed based on Lie-group. After a model of 3D guidance is formulated using vectors, the precision guidance with ending angular constraints can be transformed into a problem involving the relation between directional angles and rotational angular velocities of certain vectors. When the guidance model is imposed a SO(3)-based description, a novel 3D sliding mode guidance law with ending angular constraints can be developed via Lie-group control method and variable structure control theory. Finally, the feasibility and performance of the guidance law were shown by simulating the examples.

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.

Output-feedback based partial integrated missile guidance and control law design

An output-feedback based partial integrated guidance and control (IGC) law for missile interceptor is proposed with the smooth finite time convergence property. Firstly, a novel outputfeedback based smooth sliding mode control is proposed for a class of nonlinear systems in the presence of immeasurable state and disturbance. The finite time convergence property of this control scheme is proved based on the Lyapunov stability and homogeneous principle. Then, the proposed control method is applied to the design of partial IGC law. A kind of scaling methods is also developed to reach the rapid convergence of the system. An important dominance of this control scheme is the smooth characteristic, which may result in chattering free convergence. The simulation results indicate the high precision and smooth elevator deflection of the proposed output feedback base partial IGC law. © 2016 Beijing Institute of Aerospace Information.

Remote Control Guidance Law Design Using Variable Structure Control

A method of sliding mode variable structure control for the missile body being a time varying system is presented. A remote control guidance law is designed. The method has strong robustness to target＇ s maneuver. To reduce the chattering phenomena, quasi-sliding mode variable structure control method is used. Simulation results show that the proposed method has small miss distance for any kind of maneuvering targets and requires small control energy.

基于自适应滑模的欠驱动无人艇轨迹跟踪控制算法

针对欠驱动水面无人艇在航行过程中存在的海洋环境干扰、数学模型参数不确定、执行器故障等问题,提出了一种基于扰动观测器与神经网络技术的自适应滑模轨迹跟踪控制算法;在欠驱动无人艇的三自由度模型基础上,结合视线制导律,提出了一种新的轨迹跟踪制导策略;采用自适应滑模控制技术设计了欠驱动无人艇的轨迹跟踪控制器,有效地抑制了执行器衰减故障对无人艇控制系统产生的影响;同时运用了非线性扰动观测器和自适应径向基函数神经网络分别对无人艇受到的外界时变干扰和模型参数不确定性进行补偿和拟合,提高了无人艇控制系统的鲁棒性;基于Lyapunov定理证明了所设计的控制算法的稳定性,并在MATLAB中进行了仿真测试;仿真结果表明,所提出的轨迹跟踪控制算法可以在较为复杂的环境下实现对欠驱动无人艇的精准控制;相较于对比算法,欠驱动无人艇在文章算法下的位置平均跟踪误差减小了80%以上,具备较高的稳定性和容错能力。

具有角度和时间约束的固定时间协同制导律

针对多飞行器协同打击机动目标问题,提出一种具有终端角度约束和时间一致性约束的固定时间收敛协同中制导方法。建立二维场景下飞行器-目标视线(LOS)坐标系,将加速度分解为沿视线方向和与视线垂直方向。首先,基于代数图论和分布式合作协议算法,对飞行器的沿视线方向加速度进行设计,以保证多个飞行器的剩余飞行时间在固定时间内收敛至一致。其次,基于滑模控制理论和固定时间到达算法,构建飞行器视线法线方向加速度计算方法,使得视线角在固定时间内收敛到期望值。此外,针对目标加速度未知的问题,采用固定时间观测器进行估计,并在制导指令中进行补偿。仿真结果表明所提出的协同制导方法能够在固定时间内实现剩余飞行时间和视线角度的收敛。

基于动态规划制导的无人艇自主回收控制方法

[目的]针对欠驱动无人艇(USV)自主回收的需求,提出一种基于动态规划制导的跟踪控制方法。[方法]在运动学层面,将平行接近制导(CB)与动态窗口算法(DWA)相结合,引导USV实现目标跟踪与动态避障;在动力学层面,针对模型参数及回收环境的不确定性,采用径向基函数神经网络(RBFNN)设计动力学滑模控制器,实现对制导输出的跟踪控制。随后,采用Lyapunov理论对系统的稳定性进行分析。[结果]仿真结果表明,所提方法使USV具备了稳定跟踪性能,可有效规避回收过程中的动态障碍,并能自适应估计模型中的不确定因素和未知的环境干扰。[结论]所提方法展现出较强的鲁棒性与灵活性,可为USV在动态环境下的回收进行制导与目标跟踪提供参考。

系统收敛时间和攻击角度控制的滑模导引律

针对打击机动目标带攻击角度约束的导引律设计问题,采用滑模控制理论、任意收敛时间控制方法和干扰观测器,设计了一种攻击角度和收敛时间控制的导引律。根据弹目相对运动关系,将目标机动和建模误差等视为干扰,构建了考虑攻击角度约束的制导系统状态方程。分析了任意收敛时间控制方法在干扰情况下的性能,采用滑模控制和干扰观测器对任意收敛时间控制方法进行改进,提升鲁棒性。将该方法用于滑模面和趋近律设计中,采用干扰观测器对系统扰动进行估计,基于滑模控制理论,结合制导控制系统状态方程,推导出了收敛时间和攻击角度可控的滑模导引律。相比有限时间收敛导引律,该导引律的收敛时间和攻击角度可直接设定,无需根据制导参数计算。设置不同的目标机动方式以及不同的攻击角度和收敛时间,进行了多场景的数值仿真。结果表明,所提导引律能够有效实现攻击角度和收敛时间控制,并精确命中目标,同时相比现有导引律其制导性能更佳。

基于粒子群优化的组合导引律模型

针对导弹打击机动目标的问题,提出了一种基于组合导引律的粒子群优化算法以应对战场环境中的机动目标打击问题。首先对三维弹目运动关系进行分析,设计了一种包含角度和时间偏置项的比例导引律,旨在有效抑制终端角度变化,同时确保打击时间的精确控制。为实现最优导引律参数的求解,研究构建了以打击角、打击时间、法向加速度和脱靶量等约束条件为基础的代价函数。采用标准粒子群算法进行自适应寻优,通过迭代计算确定使代价函数最小化的最优导引律参数,进而得到满足约束条件的最优弹道。为验证算法的有效性,设置了机动目标场景,并设计了与原始比例导引律的对比仿真实验以及多种打击时间测试实验。实验结果表明,相较于传统比例导引律,基于粒子群优化的组合导引律算法在应对机动目标时能够生成满足打击时间要求及其他约束条件的弹道,并在不同打击时间设定下均展现出良好的打击效果,具有广阔的应用前景。