A new method for partial image recognition and tracking in the infrared imaging terminal guidance is proposed for the problem of that the field-of-view of infrared seeker filled with target affects target recognition and tracking. The principle of infrared imaging guidance is analyzed. Five characteristic quantities, such as highlight region proportion, standard deviation of gray value, length-width ratio, compactness and complexity, are used as the criteria of feature extraction and target recognition. A fast target recognition algorithm suitable for missile is proposed. The change of target image projection area on seeker’s focal plane in the infrared imaging terminal guidance is calculated. The effects of missile-target distance and relative velocity on aircraft imaging are analyzed. The switching from centroid tracking to partial image tracking is studied. Considering reliability and real-time, the nose cone of aircraft is selected as the tracking point for partial image tracking. The simulation scene of infrared imaging guidance is built. The simulation results are analyzed. Experimental results show that the proposed method can effectively recognize the targets in the infrared images, decrease the blind area, and realize the steadily tracking in the infrared imaging terminal guidance.

To eliminate the phugoid trajectory oscillation and enforce the thermal protection, a predictor-corrector guidance method based on the feedback bank angle control is proposed for the lifting hypersonic vehicles. The design of the guidance method is independent of the traditional quasi equilibrium glide condition (QEGC) that might be out of work in some specific cases. The longitudinal guidance is first developed by predicting the longitudinal range error and correcting the magnitude of the guidance command. The altitude rate is modified in real time by using the feedback bank angle law. The reversal logic of bank angle is designed for the lateral guidance based on the crossrange error and the heading angle error. The numerical simulations show that the phugoid trajectory oscillations of the hypersonic vehicle can be eliminated without QEGC. The Monte Carlo results of the reentry guidance with random initial dispersion also demonstrate the robustness of the proposed algorithm.

Considering the problem of acceleration tracking of gliding guided projectiles in the case of the uncertaint internal and external disturbances and the time delay of canard deflection command, a nonlinear active disturbance rejection acceleration tracking controller is designed based on the active disturbance rejection control technique. The controller is simple and easy to implement, and requires small amount of calculation and less parameters to be adjusted. The numerically simulated results show that the proposed active disturbance rejection controller can accurately control the output acceleration to track the acceleration command under the conditions of strong disturbance and delayed response of canard, and has better disturbance-resistant capability. Moreover, the canard deflection control command changes slowly from zero, which effectively reduces the control burden of canard system. In addition, the proposed controller has strong adaptability and robustness to the large-scale perturbation of the aerodynamic coefficients and the lag coefficient of canard. Key

A miniature embedded and holistic and anti-high-overload structure of micro inertial measurement unit in which micro-electromechanical systems(MEMS) based inertial sensor is used is proposed for the environment features of small installing volume and high-g launching overload of the guided ammunition. Based on the analysis of design principle and requirements MEMS inertial measurement unit(MEMS-IMU) structure, the structure of MEMS-IMU is designed and manufactured, and its actual MEMS-IMU is built. The volume and weight of MEMS-IMU are reduced by making reasonably use of its installing space, and its anti-high overload performance is evidently improved by using one-off embedded design and process technique, and the special filling material and techniques. The results of the finite element model analysis show that this structure has the good dynamic performance, and the results of the land and gunshot experiments also show that it can meet the requirements of the guided ammunition in volume and anti-high overload.

Laser beam riding guidance is an important guidance mode. The accuracy of guidance is affected directly by the quality of laser information field. A testing method based on the spot images of information field is proposed to evaluate the quality of laser information field fastly and intuitively. The proposed method allows the fast setup of a test system in inside and outside fields, and calibrates the system. Based on the principle of transient diffuse reflectance imaging under low illumination, the stripe-shaped spot images are quickly obtained by using low-light-high-speed imaging of laser beam. The rapid image processing technology is used to calculate the spot size, center location, stripe brightness for evaluating the parameters, including optical axis stability and energy uniformity of information field. Experimental results show that the test method can be used to obtain the stripe-shaped spot images of laser information field, and detect the performance of the guidance device rapidly with test accuracy of 1.8 mm and processing time of 0.35 s. Key

In a single radar guidance mode, air-to-ground missiles often fail to attack the ground targets since the radar seeker can't lock onto a target in the terminal guidance phase. To solve this problem, a radar/infrared compound guidance antenna radar seeker model and a six radiometer infrared seeker model are established, and a radar/infrared compound guidance scheme is designed, including radar guidance, radar/infrared compound guidance and infrared guidance. The attack effects in single radar guidance mode and composite guidance mode are analyzed by comparing the seeker angle error, missile overload and miss distance parameters. It is found that, under the condition of a large number of targets, the missile in compound guidance mode is more stable in overload and has higher hit accuracy compared with the single radar guided mode.Key

Cooperative biased proportional guidance law with impact angle and impact time constraints is presented for cooperative attack of networked missiles. The biased proportional guidance law with impact angle constraints is proposed, and the expression of time-to-go in this guidance law is deduced. The proportional coefficient is adjusted by the difference of the time-to-go of each missile in the network. And the cooperative biased proportional guidance law with impact angle and impact time constraints is presented. It is proved theoretically that the multiple missiles trend to have the same time-to-go by the guidance law. Finally, the mathematical simulation of guidance system of networked missiles illustrates the validity of the proposed guidance law and the expression of time-to-go.

The extended weighted and object functions are proposed based on the time-to-go exponential function. The optimal control theory is used to deduce a family of extended optimal trajectory shaping guidance laws for the constant maneuvering target. According to Schwartz inequality, the analytical solution of the guidance law acceleration command is derived by introducing the initial displacement, initial heading error, target maneuver and final impact angle into the lag-free guidance system. The analysis shows that the final acceleration command approaches to zero when the exponent of the time-to-go exponential function is greater than zero. The non-dimensional position and angle miss distance of guidance system with first order lag are studied using the non-dimensional method and the adjoint method. The results show that the position and angle miss distance induced by the heading error and final impact angle approach to zero when the missile terminal guidance time is about 15 times of the system lag time constant. And also, the position and angle miss-distance are smaller when the signs of initial heading error angle and final impact angle are opposite.

A differential game guidance law based on game theory is developed for the underwater interceptor in order to improve the ability to intercept an unknown target in collaborative defense. A tripartite maneuvering game model is established, in which the homing constraint information can be obtained using the line-of-sight command. The method of solving the terminal problem by the adjoint mathematics is used to get the zero effort miss distance of the differential strategy by taking terminal miss distance and control energy as the performance indexes, which can be applied to arbitrary order control situation for tripartite strategies. The receding horizon control is used to predict the guidance law parameters in real time. The differential game strategy is simple to implement in practical applications under the conditions of homing. The performance of the guidance law is analyzed, and the effects of intercepting the targets by using different guidance laws are compared. The simulated results show that the differential game guidance law is robust adaptability and stability, which is not restricted by the maneuvering forms of targets under the condition of same constraints, and is of better trajectory characteristics.

The problem of optimizing the maximum range of a glide guided bomb is studied based on the principle of solving optimal control problems using the Radau pseudo-spectral method. The dynamic model of the guided bomb is nondimensionalized. Combining with the Pontryagin minimum principle, the analytic solution of the optimal control and the first-order necessary condition are derived. The trajectory optimization problem is translated to a nonlinear programming via the Radau pseudo-spectral method. Based on covector mapping principle, an optimality verification method is presented for the numerical solution. Simulation results show that the Radau pseudo-spectral method can provide a highly valuable optimal solution for engineering application. Compared with the conventional maximum lift-to-drag ratio gliding trajectory, the trajectory after optimization can be extended by more than 10%.

Head-on interception is a common guidance method for interception problem. The adaptive variable structure guidance law guiding the line-of-sight angular rate to converge to zero is available to improve the guidance precision. However, the variable structure guidance law leads to large required acceleration of interceptor before the line-of-sight angular rate converges to zero, especially in a situation where the target has strong maneuverability as well as high velocity. A strategy making the coefficients of the guidance law vary according to a typical rule via fuzzy control is proposed. Smaller guidance coefficients are selected at the beginning of terminal guidance. Therefore, the guidance command is reduced and a smaller acceleration of interceptor is incurred. As the coefficients grow to the fixed and desired values, the line-of-sight angular rate converges to zero rapidly so that the stability of the guidance system is guaranteed. It is concluded that the fuzzy variable coefficients strategy is highly effective for head-on interception as shown in the simulation.

A novel sliding-mode-observer-based variable structure controller is proposed and proved by Lyapunov’s theorem for integrated guidance and control(IGC) synthesis for extended range guided projectiles (ERGP) in order to realize hit-to-kill interception with limited measurement. Accounting for the short-period dynamics of the ERGPs and first-order lag of the canard servo, the two-loop IGC model is formulated in the presence of the discrepancies from aerodynamic parameters and target maneuver. The outer-loop of the IGC generates the commanded pitch rate to regulate the line-of-sight (LOS) rate to zero in finite time; the inner-loop is designed to track the outer-loop command. Simulation results show the effectiveness of the proposed controller and that the acceleration requirement is reduced. Key

Distributed cooperative guidance is proposed for the missiles with heterogeneous constraints of field-of-view. Communication among missiles is periodic, and only the information of range-to-go is exchanged among the neighboring missiles in the network to generate a consensus error. Based on the missile’s field-of-view and the lead angle, a saturation function is used, and a distributed consensus protocol is developed by the consensus error sothat the coordination variables can reach consensus. Multiple missiles are disconnected to the communication network and are guided to a target independently when they approach a target and their coordination variables are consistent. Based on feedback linearization, graph and matrix theories, the sufficient conditions are established to make the multiple missiles realize the cooperative attack under the cooperative guidance law. Compared with the conventional cooperative guidance of multiple missiles, the proposed cooperative guidance law can satisfy each missile’s constraints of heterogeneous field-of-views, and the communication effort is easy. Simulated results show that the salvo attack of multiple missiles is achieved, and the target is locked on during each missile’s flight. Key

The multi-missile cooperative salvo attack problem with communication time-delay and topological structure uncertainty in fixed topology and dynamic switching topology is studied. Based on graph theory, the asymptotic consensus problem of multi-missile cooperative guidance time is converted to the asymptotic stability problem of different system. Then the asymptotic stability problem of different system with network transmission delay and topological structure uncertainty is analyzed based on Lyapunov function method. The method can get the condition of time-delays which satisfy the asymptotic consensus. This method is expanded to the situation of network transmission time-delay and topological structure uncertainty under switching topology for the analysis of guidance time consensus. The simulation results are coincident with the theoretical consensus analysis.

A novel optimal guidance law is proposed for the terminal guidance with impact angle constraints by using the combination of the minimal principle and Gauss pseudospectral method. An impact angle coordinate system is defined with an coordinate axis in the direction of the desired impact angle, and the linear engagement kinematics is established using this coordinate system. The control system of missile is simplified into a first-order inertial system. The canonical equation is obtained via the minimal principle, and then translated into a set of algebraic equations by employing the Gauss pseudospectral method. According to the boundary conditions, an analytical solution is finally derived for the optimal guidance law with impact angle constraints without any integral process or solving the Riccati differential equation. Numerical simulations show that the proposed guidance law ensures the much fast convergence of impact angle to the reference line, and has smaller required terminal acceleration compared with other guidance laws. In addition, the proposed guidance law can easily tackle with the guidance problem with complex weighting matrices.

A new maneuvering-deceleration guidance algorithm based on atmosphere estimation is presented for the precise guidance and velocity control of hypersonic reentry vehicle. The maneuvering-deceleration guidance command is composed of optimal guidance command and deceleration command. The optimal guidance command is obtained by guidance law with position and impact angle constraints. Sinusoid aneuvering-deceleration command is used to minimize the position disturbance caused by deceleration. And the parameters of maneuvering command are produced from mismatch between terminal predicted velocity and nominal-velocity by numerical integration method. The atmosphere parameter identification technology is also used to improve the prediction precision. The simulation results show that the maneuvering-deceleration guidance algorithm has strong robustness against uncertain conditions; it can accomplish the integrated design of precise guidance and deceleration control efficiently.

To solve the control problem of missile formation without support of weapon data-link, a new guidance algorithm for systems grouped by the leader-follower structure based on multi-agent consensus theory is proposed, which only requires the motion parameters, such as relative distance and relative speed among missiles, which can be measured by the followers’ active radar seeker. The proposed algorithm needs no data communication among missiles and absolute positions of formation members, but can make all members approach to ideal positions and consistent velocity simultaneously. Algebraic graph theory is employed to prove the asymptotic stability of closed loop control system, and a model of required force for missile formation control is built based on coordinate conversion and missile motion equation. Simulated results are used to verify the validity of the proposed algorithm and its application prospect for general design of missile formation system. Key

The addition of the midcourse guidance in the guided munition attack and the geometrical position between the missile and the target during the missile flight are studied. The key analysis focuses on the angle of the target intercepted from the seeker when the missile attacks the ground fixed target. The fast calculation method and the analytic method are put forward. In the result of the approximate calculation which is from the space distribution ellipsoid and the ground distribution ellipse, the view angle calculation formula is derived. Furthermore, a general mathematical model to get the target acquisition probability from the view of statistical probability is created. According to the 3σ principle, whether to add the midcourse guidance is decided. The zero-effect miss and the maneuvering ability of the guided munition are researched. The results show that the maneuvering ability of the guided munition covers the zero-effort miss. The confidence interval of the view angle first decreases and then increases when the distance between the seeker and the target decreases. Finally, the influences of different disturbance factors on the view angle's confidence interval are calculated. The calculated results show that the wind in x direction has more influence on the view angle than the wind in z direction.

The real-time accurate target recognition and localization are the key factors to implement the guidance integrated fuzing (GIF) technique and enhance the performance of terminal guidance and the accuracy of burst control. A real-time and accurate terminal target contour reconstruction algorithm for RF imaging GIF technique is proposed based on the principle of RF imaging and the target properties. The gray values with target information are extracted by gray mapping transform, thus decreasing the data quantity and the power-law transformation for image enhancement. Based on threshold segmentation and corner detection, the statistical methods are utilized to filter the background noise and suppress the target boundary interference. The target contour reconstruction is achieved by the convex hull technique, which is the optimal convex coveringa target area. Both the simulation and theoretical analysis results show that the time complexity of the proposed algorithm is lower, thus it can be used to achieved the real-time and accurate terminal target recognition and localization for RF imaging GIF.

Background noise and reverberation interference are the main interference sources in the sonar target detection. How to reduce their effects on sonar performance effectively has been a focus of underwater acoustic signal processing. According to Volterra series theory, a nonlinear dynamic model of underwater acoustic signal is established to realize the noise reduction of background noise and the suppression of reverberation interference by predicting the underwater acoustic signal. The direct and iterative methods are used for the one-step and multi-step predictions of the underwater acoustic signal, respectively, by using the two-order Volterra adaptive filter and the singular value decomposition adaptive algorithm. The simulation results show that the iterative method has higher prediction performance and effec- tive multi-step prediction capability.

An optimal midcourse trajectory correction algorithm considering the zeroing effort interception is designed for the defensive combat in near space. The zeroing effort interception condition is derived by analyzing the relative motion of interceptor and target in the terminal guidance phase, which is uniquely determined by the velocity ratio of target and interceptor and the respective angles among their velocity vectors and the line-of-sight. In terms of the cases where the nominal trajectory fails to satisfy the zeroing effort condition due to the updated target information, a scheme of optimal trajectory correction in the midcourse guidance phase is proposed to modify the interceptor states to re-satisfy the zeroing effort interception condition at the handover moment in the midcourse and terminal guidance phases. The compensation commands of control are derived by further differentiating the first order optimal conditions and transversality conditions that are satisfied by the nominal trajectory. The deviations of interceptor initial states and terminal constraints are considered in the resolving of compensation commands. The simulated results testify the effectiveness and the superiority of the proposed method.Key

Based on target-missile relative motion equation in plane, a two-dimensional guidance law subject to acceleration command constraint is designed using command filtered backstepping approach, and the second-order dynamics characteristics of missile autopilot is considered. The guidance system is divided into two sub-systems in the light of stability requirement of the main states. Then the command filtered backstepping approach is used to design the guidance laws for two sub-systems based on the principles of zeroing line-of-sight(LOS) angular rate and letting the relative velocity between missile and target be less than a negative constant, respectively. The command filtered backstepping approach can not only address saturation constraint on acceleration command but also overcome the deficiency of “explosion of terms” in the conventional backstepping method. Finally, the simulations are performed for controlling and non-controlling along LOS in the case of acceleration command saturation and missile autopilot with big lag. The results show that the guidance law has excellent performance for intercepting a highly maneuvering target.

A hybrid near-minimax acceleration guidance law for first-order lag systems is proposed to avoidthe control saturation of missiles with control limits and large impact angle constraint. By designing the switch point and the lag compensation term in the latter phase, the proposed guidance law is composed of a circular arc-straight line guidance phase and a polynomial guidance phase with first-order autopilot compensation. It is proved by mathematical deduction that the switch point must exist and the peak acceleration of the whole trajectory appears at the switch point. Combining the optimization ability of the circular arc-straight line guidance law, the near-optimality of the hybrid guidance law is obtained. Simulatedresults show that the acceleration does not increase after the switch point, and the impact angle constraint is satisfied. Comparisons with the numerical optimal solutions further verify the near-optimality of the hybrid guidance law. Key

Multiple missiles in the cooperative guidance may communicate via a random network in virtue of packet loss and communication delay, resulting in an unsustainable connected or even interrupted communication topology. Hence, a distributed cooperative guidance strategy is proposed. Based on sampled data, a distributed linear consensus protocol is designed, and a deviation system is constructed, which can be stabilized such that all the coordination variables of missiles asymptotically achieve a common state. Multiple missiles disconnect to the communication network and are guided to a target independently when they approach the target. Theoretical analysis reveals that the proposed consensus protocol doesn’t make any requirements on the communication topology at any time, in other words, the communication topology may be disconnected or even be interrupted. Finally, two simulation examples with regard to cooperative guidance with unsustainable connected communication topology are given. The presented guidancestrategy can be used to ensure the impact times of all the missiles being the same.

The firepower compatibility judgment is one of the chief components of firepower compatibility technology of naval vessel. The judgment of the final-impacting firepower compatibility of cross-platform non-guided projectile is researched. The firepower compatibility criterion is proposed based on the characteristics of the jamming and the conflicts in the final-impacting area of non-guided projectile, and a solution method for estimating the final-impacting firepower compatibility of non-guided projectiles of ship formation is given based on firing effectiveness. The simulated results show that the proposed method can be used to describe the firepower compatibility of non-guided projectiles during impact terminal, and overcome the weakness of overestimation of weapons by exclusive judgment. Key

The kill probability calculating models of one-missile to one-target for the gimbaled warhead, which is designed to fire the fragments in the target direction, are studied in order to optimize lethality. Two encounter concepts of side-attack and forward-intercept at endgame are formulated in the missile coordinate system. The kill probability is calculated using Monte-Carlo method. Based on the circular spray pattern with uniform pattern density, the optimum lethal radius is established for forward-intercept concept. And then the effects of missile-target relative velocity and miss distance on kill probability are analyzed. According to the study, the preferred conditions for side-attack or forward-intercept are proposed: if v_r≥1 700 m/s and ρ≤2.5 m or v_r≥3 000 m/s and ρ≤4 m，then the encounter concept of forward-intercept is preferable; In other cases, the encounter concept of side-attack is preferable.

In order to intercept the maneuvering targets and overcome the adverse effect of the missile autopilot’s dynamics on the guidance performance, this paper aims to propose a H_∞ robust guidance law with the dynamics of the autopilot considered. The third-order linear time-varying state equation for the integrated guidance and second-order dynamics of autopilot is expressed as a polytopic LPV system. A novel H_∞ robust guidance law, in the form of linear state-feedback with parameter-dependent gain, is designed using LMI method. The coefficients in the parameter-dependent gain are obtained by solving a convex optimization problem with LMI constraints. Simulation results indicate that, even if the target’s acceleration is not known, the H_∞ guidance law can still achieve strong robustness and obtain high guidance precision.

A novel cooperative localization and guidance approach based on the leader-follower framework with two leaders is proposed to allow the seeker-less missile to hit a stationary target accurately. A cooperative localization method for seeker-less missile is designed based on the extended Kalman filter to enhance the localization accuracy. To address the issue that a large terminal acceleration command is required for the proportional navigation guidance (PNG) law combined with the proposed localization method,a novel PNG law with time-varying navigation gain is presented. The impacts of the guidance parameters on miss distance, terminal acceleration and maximum acceleration are demonstrated through si- mulation.Simulated results show that the large miss distance due to the localization error of seeker-lessmissile could be reduced by the proposed cooperative localization method, and the large terminal acceleration command could be avoided by PNG law with time-varying navigation gain. Key

The guiding performance of a self-developed underwater docking device is analyzed based on the docking test of autonomous underwater vehicle (AUV) in Qiandao Lake. An AUV docking collision model is established using the software ADAMS based on the hydrodynamic characteristics of AUV and contact impact parameters. The effectiveness of the proposed model is verified by comparing the attitudes and velocities of AUV in the test and simulated results. The guiding capabilities of convex, conical and concave guiding covers are discussed in terms of the offset distance and included angle of AUV docking. The generatrix curvature of guiding cover was optimized to design an improved S-shaped guiding cover by analyzing the simulated results. It is found that, under the same conditions of AUV docking attitude, the maximum AUV docking offset distance adjusted by the improved S-shaped guiding cover is 100 cm, which is 20 cm longer than that adjusted by convex guiding cover, and the maximum AUV docking angle adjusted by the improved S-shaped guiding cover is 22°, which is 1° lower than that adjusted by convex guiding cover. But the impact force generated by S-shaped guiding cover and the AUV docking time both are decreased, and the effect of adjusting AUV movement trend is obviously improved. The guiding performancesof the improved S-shaped cover and the convex guiding cover were validated through the AUV docking tests. The test results show that the guiding performance of the improved S-shaped guiding cover is dramatically improved. Key

When a homing missile tracks a target, it may fail to lock the target because of complicated background. For example, when a missile attacks a target in look-down mode, the missile’ capability of intercepting or acquiring a target is weakened by complicated surface background and clutter. A new modeling method which regards the ideal line-of-sight as the control objective is put forward. And an optimal guidance law is designed based on restraining the terminal direction of relative motion between missile and target and the trajectory overload. The guidance law is used to control the motion of missile in a direction vertical to ideal line-of-sight. The simulation result shows that this method can meet the requirement of terminal trajectory shaping better, distribute the overload more reasonably and decrease the influence of ground background and clutter on target tracking effectively.

An integrated control law is designed by modifying the existing modeling results and using the intelligent control method for the guidance and control of interceptor during the terminal course. While the modeling error caused by approximate linearization and ignoring couplings is taken into consideration, a model error compensation is used to modify the interceptor dynamics. A nonlinear model for the integrated guidance and control (IGC) is obtained. The adaptive dynamic surface control is proposed for the controller design of this mismatched nonlinear system. The influence of mismatched uncertainties on the system performance is eliminated, and the term explosion in traditional backstepping method is voided. The integrated control law is used to establish a direct relationship between control objective and actuators command. Compared with the controller which ignores the modeling error in interception simulation, the proposed controller shows better interception performance.

At present, one of the development trends of air-to-air missiles is that the missile is used to attack both ground and air targets. On the basis of the three-dimensional proportional guidance law， the genetic algorithm is used to solve the optimal fuzzy control rules, and then the fuzzy control theory is used to control the proportional coefficient component of the three-axis in the proportional guidance law, thus establishing an integrated guidance law that enables the missiles to effectively attack the air and ground targets. The missile air-ground integrated attack guidance law is compared with the traditional three-dimensional proportional guidance law through the simulation experiment. The simulated results show that the proposed navigation law can be used for missile attacking the air-to-ground targets effectively and hasving a greater hit angle in the attack on ground target, so it is suitable forthe air-to-ground integrated attack mode.Key

For the multiple missiles intercepting a maneuvering target cooperatively, a cooperative guidancemethod considering a cooperative detection geometry configuration is designed based on the finite-time control theory. For the first-order dynamics of the missiles, a cooperative interception model with detection geometry configuration is established according to the relative motion equations of particles and the principle of cooperative detection. The sufficient conditions for the finite time boundedness of system state and the finite time stability of system input and output are given based on the differential inequality theory. And on this basis, a finite time cooperative guidance method is designed. The proposed method uses the measurement matrix to characterize the dynamic quality of system state and output, and can ensure that the state and output of guidance system are bounded and stable within a finite time interval. The simulatedresults show that the proposed guidance method can ensure that the LOS separation angle converges to the preset angle, the LOS angular rate converges to zero, and the acceleration does not exceed the maximum physical limit when a target is maneuvering. Compared with proportional navigation and optimal guidance law, the proposed method has the advantages in cooperative detection and guidance.Key

To study the effect of phantom-bit technology for phased array radar seeker (PARS) on missile guidance system, the cause of boresight error slope (BSES) is discussed according to the principle of antenna element shift phase, the transfer function of line-of-sight rate containing BSES is derived under the disturbance of missile body, and the change rules of amplitude and phase angle are analyzed. A model of BSES parasitic loop is established based on the pointing angle of beam space, and the effect of phantom bit number (PBN) on the stability boundary of parasitic loop is studied with Routh criteria. Under the condition of the typical radar noise input, the dimensionless and adjoint methods are used to research the influence of PBN on miss distance. The result shows that phantom-bit technology of PARS leads to BSES；the larger the PBN is, the bigger the BSES is, the easier the parasitic loop loses its satbility, and the larger the miss distance is. The receiver noise has a greater effect on miss distance compared to target glint noise under the same condition. Therefore an error calibration method, which is used to calibrate the error among different beam angle directions according to different PBNs, needs to be studied to reduce BSES and improve the accuracy of missile terminal guidance.

A reinforcement learning-based cooperative guidance law utlitizing a deep deterministic policy gradient descent neural network is proposed to achieve the cooperative attack of multiple missiles against a target and improve the attack effectiveness.The estimation equation of time-to-go based on the linear engagement dynamics is revised to improve the estimation accuracy of time-to-go, which is no longer restricted by the assumption of small angle. The time-to-go error of each missile is regarded as the coordination variable. The time-to-go error and range-to-go of each missile are used as the observables of the reinforcement learning algorithm. The reward function is constructed by using miss distance and time-to-go error, and then a reinforcement learning agent is generated by offline training. In the process of closed-loop guidance, the reinforcement learning agent generates guidance commands in real time, by that simultaneous attack can be achieved. Simulated results verify that the proposed reinforcement learning guidance law can achieve simultaneous attack on the target. Compared with the traditional cooperative guidance law, the reinforcement learning cooperative guidance law can be used to obtain smaller miss distances and smaller attack time errors.

The ballistic missiles are easily intercepted by the missile defense systems due to the absence of maneuverability in exo-atomosphere. It is important to design an effective guidance law to improve the success penetration rate of ballistic missile. An active defense nonsingular terminal sliding mode cooperative guidance law is presented. In ballistic missile active defense scenarios, one or more defending missiles, named defenders, accompany the ballistic missile to intercept the incoming interceptor missiles launched from the missile defense systems. The guidance process for the defenders is divided into two phases: Phase 1 and Phase 2. For Phase 1, a line of sight (LOS) based guidance law is designed, by which the defending missile positions itself on LOS betweenthe ballistic missile and the interceptor missile. In this phase, the proposed guidance law can notably reduce the needed maneuverability of defending missile. To simplity the designing, the guidance law uses an approximate relative motion model, of which accuracy is acceptable in Phase 1. For Phase 2, a guidance law based on LOS angular velocity nullifying strategy is proposed. In this phase, the proposed guidance law uses more accurate relative motion models and avoids the increased errors induced by the approximate relative motion model in Phase 2. Simulation results show the high performance of the guidance laws.

The multi-unmanned aerial vehicles (UAVs) cooperative tracking can not only get the information of targets in various directions, but also respond to the interference of obstacles and reduce the probability of losing the targets. A distributed guidance law is presented for multi-UAV cooperative tracking that relies only on information of target and neighboring UAVs. The distributed guidance law is used to avoidthe dependence of UAV formation on the leaders in traditional leader-follower method and improve the robustness of formation. A distributed cooperative guidance law of multi-UAVs based on relative distance and bearing angle was designed for stationary targets, and the stability of the cooperative guidance law was proved. The guidance law is used fortracking the targets with constant and variable speeds. The hardware-in-the-loop simulation of multi-UAVs tracking the targets was made by using the X-Plane software, MATLAB/Simulink software and flight controller (hardware).The simulated results show the effectiveness of proposed guidance law.Key

An extended optimal guidance law with terminal miss distance and impact angle constrains is derived. The guidance law is obtained as the solution of a linear quadratic optimal control problem with the goal function weighted by a power of the time-to-go. Based on the analytical expression for the change of guidance command with time and the adjoint system analysis method, the command characteristics and dimensionless miss distance of guidance law are analyzed. The result shows that the acceleration command of guidance law can be converged into zero in the final time of guidance, which may create a good situation for terminal angle of attack control. A design principle for selection of guidance law gain is discussed. Finally, according to the requirements of engineering application, the methods on calculating the guidance initial condition and maximal required acceleration are given. The effectiveness and practicality of the guidance law are demonstrated through simulation.

To solve the problem of multiple missiles attacking a maneuvering target simultaneously from desired directions in plane, a novel cooperative guidance law with line-of-sight angle constraint is proposed. A multiple missiles cooperative guidance model with line-of-sight angle constraint is constructed based on in-plane missiles-target relative motion equations. A distributed finite time cooperative guidance law in the line-of-sight direction is designed based on multi-agent system cooperative control theory and integral sliding mode control theory, which can guarantee the consensus of all missiles' impact times in finite time. In vertical direction of line-of-sight, a nonlinear disturbance observer is adopted to estimate the target's acceleration in finite time, and a guidance law with line-of-sight angle constraint is designed based on finite time sliding mode control theory. The guidance law can guarantee the missile impact the maneuvering target and the missile's line-of-sight angle converge to its desired value in finite time. The cooperative guidance law is demonstrated through simulation results, which makes multiple missiles impact the maneuvering target simultaneously from desired directions. Key

For the penetration probability of air-to-ship missile adopting traditional flight trajectory is poor when it is intercepted by long-range ship-to-air missile, a scheme of modifying the descending phase trajectory to spiral maneuver dive trajectory is proposed. The design process of variable structure guidance law with terminal angular constraint is analyzed. On this basis, a kind of spiral maneuver variable structure guidance law is proposed. It can be used to guide the air-to-ship missile to realize the spiral maneuver dive trajectory, and ensure that the air-to-ship missile turns into the low altitude cruise phase in the end of the descending phase. The simulation results show that the proposed spiral maneuver variable structure guidance law improves remarkably the penetration probability of air-to-ship missile against the long-range ship-to-air missile.