Three-Dimensional Discrete Observability Analysis for Air-to-Air Missile Target Tracking

The interception information of infrared( IR)-guided air-to-air missiles( AAM) is mainly estimated only using the basic bearing measurements. In order to intercept highly maneuverable targets,it is essential to study the system observability to improve the target tracking system performance.The uniqueness of this paper is that the observability analysis is derived based on a discrete three-dimensional (3D) system model. During the maneuvering scenario,the system is approximated by a segment-by-segment system. The relationship between missile-target motion and observability is given by direct and dual approaches. Meanwhile sufficient observability conditions are derived. Moreover,a numerical simulation is conducted and an alternate method is provided to reinforce the proposed observability analysis results.

Relaxed Stable Stability Technology for an Air-to-air Missile

Relaxed Stable Stability(RSS) in an important part of the active control technology.It is a new way to raise the flying speed,distance and maneuverability of missile.Depth study of RSS technology plays an important role for the new concept missile design.This paper describes the detailed definition of RSS and its advantages,presents the research status and prospects for its application in the design of new missiles.

Recorded recurrent deep reinforcement learning guidance laws for intercepting endoatmospheric maneuvering missiles

This work proposes a recorded recurrent twin delayed deep deterministic(RRTD3)policy gradient algorithm to solve the challenge of constructing guidance laws for intercepting endoatmospheric maneuvering missiles with uncertainties and observation noise.The attack-defense engagement scenario is modeled as a partially observable Markov decision process(POMDP).Given the benefits of recurrent neural networks(RNNs)in processing sequence information,an RNN layer is incorporated into the agent’s policy network to alleviate the bottleneck of traditional deep reinforcement learning methods while dealing with POMDPs.The measurements from the interceptor’s seeker during each guidance cycle are combined into one sequence as the input to the policy network since the detection frequency of an interceptor is usually higher than its guidance frequency.During training,the hidden states of the RNN layer in the policy network are recorded to overcome the partially observable problem that this RNN layer causes inside the agent.The training curves show that the proposed RRTD3 successfully enhances data efficiency,training speed,and training stability.The test results confirm the advantages of the RRTD3-based guidance laws over some conventional guidance laws.

Time-varying parameters estimation with adaptive neural network EKF for missile-dual control system

In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LSTM) neural network is nested into the extended Kalman filter(EKF) to modify the Kalman gain such that the filtering performance is improved in the presence of large model uncertainties. To avoid the unstable network output caused by the abrupt changes of system states,an adaptive correction factor is introduced to correct the network output online. In the process of training the network, a multi-gradient descent learning mode is proposed to better fit the internal state of the system, and a rolling training is used to implement an online prediction logic. Based on the Lyapunov second method, we discuss the stability of the system, the result shows that when the training error of neural network is sufficiently small, the system is asymptotically stable. With its application to the estimation of time-varying parameters of a missile dual control system, the LSTM-EKF shows better filtering performance than the EKF and adaptive EKF(AEKF) when there exist large uncertainties in the system model.

Impact point prediction guidance of ballistic missile in high maneuver penetration condition

An impact point prediction(IPP) guidance based on supervised learning is proposed to address the problem of precise guidance for the ballistic missile in high maneuver penetration condition.An accurate ballistic trajectory model is applied to generate training samples,and ablation experiments are conducted to determine the mapping relationship between the flight state and the impact point.At the same time,the impact point coordinates are decoupled to improve the prediction accuracy,and the sigmoid activation function is improved to ameliorate the prediction efficiency.Therefore,an IPP neural network model,which solves the contradiction between the accuracy and the speed of the IPP,is established.In view of the performance deviation of the divert control system,the mapping relationship between the guidance parameters and the impact deviation is analysed based on the variational principle.In addition,a fast iterative model of guidance parameters is designed for reference to the Newton iteration method,which solves the nonlinear strong coupling problem of the guidance parameter solution.Monte Carlo simulation results show that the prediction accuracy of the impact point is high,with a 3 σ prediction error of 4.5 m,and the guidance method is robust,with a 3 σ error of 7.5 m.On the STM32F407 singlechip microcomputer,a single IPP takes about 2.374 ms,and a single guidance solution takes about9.936 ms,which has a good real-time performance and a certain engineering application value.

Uncertainty entropy-based exploratory evaluation method and its applications on missile effectiveness evaluation

Some attributes are uncertain for evaluation work because of incomplete or limited information and knowledge.It leads to uncertainty in evaluation results.To that end,an evaluation method,uncertainty entropy-based exploratory evaluation(UEEE),is proposed to guide the evaluation activities,which can iteratively and gradually reduce uncertainty in evaluation results.Uncertainty entropy(UE)is proposed to measure the extent of uncertainty.First,the belief degree distributions are assumed to characterize the uncertainty in attributes.Then the belief degree distribution of the evaluation result can be calculated by using uncertainty theory.The obtained result is then checked based on UE to see if it could meet the requirements of decision-making.If its uncertainty level is high,more information needs to be introduced to reduce uncertainty.An algorithm based on the UE is proposed to find which attribute can mostly affect the uncertainty in results.Thus,efforts can be invested in key attribute(s),and the evaluation results can be updated accordingly.This update should be repeated until the evaluation result meets the requirements.Finally,as a case study,the effectiveness of ballistic missiles with uncertain attributes is evaluated by UEEE.The evaluation results show that the target is believed to be destroyed.

Robust missile autopilot design based on dynamic surface control

Since the dynamical system and control system of the missile are typically nonlinear, an effective acceleration tracking autopilot is designed using the dynamic surface control(DSC)technique in order to make the missile control system more robust despite the uncertainty of the dynamical parameters and the presence of disturbances. Firstly, the nonlinear mathematical model of the tail-controlled missile is decomposed into slow acceleration dynamics and fast pitch rate dynamics based on the naturally existing time scale separation. Secondly, the controller based on DSC is designed after obtaining the linear dynamics characteristics of the slow and fast subsystems. An extended state observer is used to detect the uncertainty of the system state variables and aerodynamic parameters to achieve the compensation of the control law. The closed-loop stability of the controller is derived and rigorously analyzed. Finally, the effectiveness and robustness of the design is verified by Monte Carlo simulation considering different initial conditions and parameter uptake. Simulation results illustrate that the missile autopilot based DSC controller achieves better performance and robustness than the other two well-known autopilots.The method proposed in this paper is applied to the design of a missile autopilot, and the results show that the acceleration tracking autopilot based on the DSC controller can ensure accurate tracking of the required commands and has better performance.

Dynamic attack zone of air-to-air missile after being launched in random wind field

A new concept is presented for air-to-air missile which is dynamic attack zone after being launched in random wind field. This new concept can be used to obtain the 4-dimensional(4-D)information regarding the dynamic envelope of an air-to-air missile at any flight time aimed at different flight targets considering influences of random wind, in the situation of flight fighters cooperated with missiles fighting against each other. Based on an air-to-air missile model, some typical cases of dynamic attack zone after being launched in random wind field were numerically simulated.Compared with the simulation results of traditional dynamic envelope, the properties of dynamic attack zone after being launched are as follows. The 4-D dynamic attack zone after being launched is inside traditional maximum dynamic envelope, but its forane boundary is usually not inside traditional no-escape dynamic envelope; Traditional dynamic attack zone can just be reliably used at launch time, while dynamic envelope after being launched can be reliably and accurately used during any flight antagonism time. Traditional envelope is a special case of dynamic envelope after being launched when the dynamic envelope is calculated at the launch time; the dynamic envelope after being launched can be influenced by the random wind field.

Storage reliability assessment model based on competition failure of multi-components in missile

The degradation data of multi-components in missile is derived by periodical testing. How to use these data to assess the storage reliability(SR) of the whole missile is a difficult problem in current research. An SR assessment model based on competition failure of multi-components in missile is proposed. By analyzing the missile life profile and its storage failure feature, the key components in missile are obtained and the characteristics voltage is assumed to be its key performance parameter. When the voltage testing data of key components in missile are available, a state space model(SSM) is applied to obtain the whole missile degradation state, which is defined as the missile degradation degree(DD). A Wiener process with the time-scale model(TSM) is applied to build the degradation failure model with individual variability and nonlinearity. The Weibull distribution and proportional risk model are applied to build an outburst failure model with performance degradation effect. Furthermore, a competition failure model with the correlation between degradation failure and outburst failure is proposed. A numerical example with a set of missiles in storage is analyzed to demonstrate the accuracy and superiority of the proposed model.

Time-varying fault-tolerant formation tracking based cooperative control and guidance for multiple cruise missile systems under actuator failures and directed topologies

This paper studies time-varying fault-tolerant formation tracking problems for the multiple cruise missile system under directed topologies subjected to actuator failures. Firstly, the timevarying fault-tolerant formation tracking process for the multiple cruise missile system is divided into the guidance loop and the control loop. Then protocols are constructed to accomplish distributed fault-tolerant formation tracking in the guidance loop with the adaptive updating mechanism, in the condition where neither the knowledge about actuator malfunctions nor any global information of the communication topology remains available. Moreover, sufficient conditions to accomplish formation tracking are presented, and it is shown that the multiple cruise missile system can carry on the predefined time-varying fault-tolerant control (FTC) formation tracking through the active disturbances rejection controller (ADRC) and the proportion integration (PI) controller by the way of the fault-tolerant protocol utilizing the designed strategies, in the event of actuator failures. At last, numerical analysis and simulation are designed to verify the theoretical results.

Design of a Kind of Model Reference Adaptive Missile Control System

目的设计能够适应环境变化和目标机动的导弹控制系统．方法将模型参考自适应控制理论应用于导弹控制系统的设计，针对反坦克导弹的具体特点做了相应的改进．结果大量仿真得出所设计的控制系统能够满足击顶反坦克导弹的战技要求．结论将模型参考自适应控制应用于导弹控制系统设计是成功的，与常规控制系统相比具有明显的优点。

Observer-based Guidance Law Accounting for Second-order Dynamics of Missile Autopilots

Accounting for the missile autopilot as second-order dynamics, an observer-based guidance law is designed based on the dynamic surface control method. Some first-order low-pass filters are introduced into the design process to avoid the occurrence of high-order derivatives of the line of sight angle in the expression of guidance law such that it can be implemented in practical applications. The proposed guidance law is effective in compensating the bad influence of the autopilot lag on guidance accuracy. In the simulations of intercepting non maneuvering targets, targets with step acceleration, and targets with sinusoidal acceleration respectively, the guidance law is compared with the adaptive sliding mode guidance law in the presence of missile autopilot lag. The simulation results show that the proposed guidance law is able to guide a missile to accurately intercept a maneuvering target, even if it escapes in a great and fast maneuver and the autopilot has a relatively large lag.

Iterative Learning Control for homing guidance design of missiles

This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.

Multi-agent decision support system for missile defense based on improved PSO algorithm

Ballistic missile defense system(BMDS) is important for its special role in ensuring national security and maintaining strategic balance. Research on modeling and simulation of the BMDS beforehand is essential as developing a real one requires lots of manpower and resources. BMDS is a typical complex system for its nonlinear, adaptive and uncertainty characteristics.The agent-based modeling method is well suited for the complex system whose overall behaviors are determined by interactions among individual elements. A multi-agent decision support system(DSS), which includes missile agent, radar agent and command center agent, is established based on the studies of structure and function of BMDS. Considering the constraints brought by radar,intercept missile, offensive missile and commander, the objective function of DSS is established. In order to dynamically generate the optimal interception plan, the variable neighborhood negative selection particle swarm optimization(VNNSPSO) algorithm is proposed to support the decision making of DSS. The proposed algorithm is compared with the standard PSO, constriction factor PSO(CFPSO), inertia weight linear decrease PSO(LDPSO),variable neighborhood PSO(VNPSO) algorithm from the aspects of convergence rate, iteration number, average fitness value and standard deviation. The simulation results verify the efficiency of the proposed algorithm. The multi-agent DSS is developed through the Repast simulation platform and the constructed DSS can generate intercept plans automatically and support three-dimensional dynamic display of missile defense process.

THE GLOBAL DEFORMATION AND LOCAL DAMAGE ANALYSIS OF FILLED METALLIC CYLINDRICAL SHELLS IMPACTED BY MISSILES

A group of theoretical models has been developed for analyzing transient dynamic re-sponse to filled metallic cylindrical shells impacted by flat-nosed missiles at normal obliquity on the ba-sis of the analogy modeling method of beam-on foundation.It can be used for solving the global defor-mation and the local failure of cylindrical shells in the impact process.The ballistic limit speed and im-pact response history have been calculated by this group of theoretical models,and the inner pressureeffect on the ballistic limit speed and some parameters are discussed at length.The quantitative rela-tionship between internal pressure and the ballistic limit speed and some significant conclusions havebeen obtained,which are basically identical with previous experimental results.

Missile formation controller design based on disturbance observer and finite-time control

To keep multiple missiles to fly in a formation,a robust controller for missile formation is designed.Based on the leader-follower formation mode,two formation relative motion models in different coordinate frames are established and compared.The three-dimension model built in a follower reference coordinate frame is chosen due to its control inputs decoupling,then this model is decoupled into three subsystems.For each subsystem a robust formation controller is proposed based on the disturbance observer and finite-time control theory when the external disturbance exits.The stability of the closed-loop system adopting the controller is proved theoretically.Simulation results show that the follower can follow the leader and keep the desired formation despite the external disturbance,which validates the effectiveness of the proposed robust formation controller.

A distributed decision method for missiles autonomous formation based on potential game

The distributed cooperative decision problems of missiles autonomous formation with network packet loss are investigated by using the potential game based on formation principles.In particular,a dynamic target allocation method for missiles formation is provided based on the potential game and formation principles,after the introduction of cooperative guidance and control system of the missiles formation.Then we seek the optimization of a global utility function through autonomous missiles that are capable of making individually rational decisions to optimize their own utility functions.The first important aspect of the problem is to design an individual utility function considering the characteristics of the missiles formation,with which the objective of the missiles are localized to each missile yet aligned with the global utility function.The second is to equip the missiles with an appropriate coordination mechanism with each missile pursuing the optimization of its own utility function.We present the design procedure for the utility,and present a coordination mechanism based on spatial adaptive play and then introduce the idea of“cyclical selected spatial adaptive play”and“negotiation based on time division multiple address(TDMA)protocol formation support network”.Finally,we present simulations for the distributed dynamic target allocation on the comprehensive digital simulation system,and the results illustrate the effectiveness and engineering applicability of the method.

A Variational Method for the Fuse-Warhead Coordination Design of an Air-Faced Missile

This paper presents a variational method for the fuse-warhead coordination design of an air-faced missile, which takes the distribution density of fragments for a variable and the totalprobability of kill of single missile against an air-target for an objective function.

Study on Anti-ship Missile Saturation Attack Model

Based on the analysis for the interception process of ship-to-air missile system to the anti-ship missile stream, the antagonism of ship-to-air missile and anti-ship missile stream was modeled by Monte Carlo method. This model containing the probability of acquiring anti-ship missile, threat estimation, firepower distribution, interception, effectiveness evaluation and firepower turning, can dynamically simulate the antagonism process of anti-ship missile attack stream and anti-air missile weapon system. The anti-ship missile's saturation attack stream for different ship-to-air missile systems can be calculated quantitatively. The simulated results reveal the relations among the anti-ship missile saturation attack and the attack intensity of anti-ship missile, interception mode and the main parameters of anti-air missile weapon system. It provides a theoretical basis for the effective operation of anti-ship missile.

RUPTURE OF THIN METAL TUBES BY NORMAL AND OBLIQUE IMPACT OF BLUNT CONICALNOSED MISSILES:EXPERIMENTS

Impact tests at both normal and oblique angles of incidence were conducted on thin mildtubes using a moderate size of 90° conical-nosed missiles.The minimum impact speed that generated cracksthrough the thickness of the wall,termed the speed for rupture,was measured,and various modes of rupturewere identified.For a thin tube hit by a missile at a normal angle of obliquity at the speed for rupture,thecontact region spreads across the nose of the missile,and the transverse shear deformation is predominant inthe final failure process.If the angle of obliquity is 30~,the missile pierces a hole through the wall of thetube.At the speed for rupture,the kinetic energy of the missile for oblique angle 30°is only about 45 % thatrequired for plugging at a normal angle of obliquity.