Observer-Based Guidance Law With Impact Angle Constraint

An optimal pulsed guidance law with a time-varying weighted quadratic cost function that enables imposing a predetermined intercept angle is presented. Due to the characteristic of impulse force, admissible variance of control is redefined. The optimal pulsed guidance law is deduced via extended maximum principle. The optimal pulsed guidance law is eventually transformed to solve the two-point boundary value problem. To decide a shooting point, an efficient algorithm is proposed by combining particle swarm optimization and Kriging surrogate model method. The optimal pulsed guidance law is implemented in several representative engagements. From simulation results, it can be seen that the proposed guidance law can achieve small miss distance with terminal impact angle constraint under different conditions. Moreover, the performance of the proposed guidance law is satisfactory with the comparison of sliding-mode pulsed guidance law.

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

In this paper, distributed three‐dimensional (3D) cooperative guidance laws are designed for leader–follower multiple missiles to achieve simultaneous attack at a specified time. The guidance laws are derived from the biased proportional navigation guidance (PNG) law. Two fixed‐time distributed algorithms with time‐varying coefficients are proposed to track the state of the leader under undirected and directed topologies, respectively. The upper bounds of convergence times for the tracking algorithms are obtained. The biased guidance terms of followers are designed to track the leader with the proposed algorithms and the biased guidance term of the leader is designed to achieve specified impact time. Then, an auxiliary function is included into the biased guidance terms to meet the field‐of‐view (FOV) constraints. The leading angles' properties and convergence times under the proposed guidance laws are further analyzed. Numerical simulations are given to verify the effectiveness of the proposed cooperative guidance laws.

In this paper realistic Six Degrees of Freedom simulation of a pursuer evader engagement during terminal guidance has been carried out using a class of nonlinear guidance law based on Feedback Linearization. This guidance law has been developed as a regulator problem based on nonlinear control theory where line of sight rate derivative along both yaw and pitch plane are made zero by taking line of sight angle and line of sight rate as output feedback. The line of sight angles and rates have been computed from noisy seeker measurements through a nonlinear state observer. The available seeker measurements are pursuer-evader relative range, relative rage rate, gimbal angles and line of sight rates along yaw and pitch plane in seeker inner gimbal frame. The present guidance law has been validated in presence of realistic non Gaussian and correlated seeker measurement noise, estimator, autopilot lag and highly time varying pursuer velocity during engagement. It is demonstrated through realistic Six Degrees of Freedom pursuer-evader engagement simulation in the presence of above constraints in a practical environment that the proposed guidance law is a viable option for intercepting maneuvering target with high heading error over the well known proportional navigation guidance law. This specific type of guidance law being not available in published literature, is claimed as quiet novel.

In this work, design of three-dimensional (3D) proportional navigation guidance law based on input-output linearization (IOL) for tactical missiles is proposed. For the three-dimensional nonlinear missile-target engagement dynamics, the line-of-sight (LOS) rates in pitch and yaw planes are taken as outputs and the IOL theory is used to derive the guidance laws without ignoring the cross-coupling terms. Simulations are carried out by considering maneuvering target, and the results are presented to showcase the efficacy of the proposed design. Further, comparison of the performance of the proposed guidance law with augmented proportional navigation guidance(APNG) laws is carried out and the related results are presented. Lastly, implementation issues of the proposed guidance law are discussed.

A novel biased proportional navigation guidance law for close approach phase

A guidance law with finite time convergence is designed using the sliding mode control method and finite time convergence control theory, accounting for the missile autopilot as second-order dynamics. The high-order derivatives of the line of sight (LOS) angle are avoided in the expression of guidance law such that it can be implemented in practical applications. The designed guidance law is effective in compensating the bad influence of the autopilot dynamics on guidance accuracy. In simulations of intercepting a non maneuvering target or a maneuvering target, respectively, the designed guidance law is compared with the adaptive sliding mode guidance (ASMG) law in the presence of missile autopilot lag. Simulation results show that the designed guidance law is able to guide a missile to accurately intercept a nonmaneuvering target or a maneuvering target with finite time, even if it escapes in a great and fast maneuver and the autopilot has a relatively large lag.

In this paper, a suboptimal guidance law with the terminal constraints on impact angle, acceleration, and time-derivative of acceleration (jerk) is presented. The proposed homing guidance problem is an over-determined problem, i.e., the number of constraints is much larger than the order of system. Since it is difficult to solve the problem by using the conventional optimal control theory, we newly introduce the control input which consists of an additional feed-forward command and the optimal feedback command. The additional feed-forward command is defined as a polynomial function of time-to-go with two degree-of-freedoms. Here, the coefficients of the function in the feed-forward command are determined to satisfy the constraints on terminal acceleration and jerk. The optimal feedback command in consideration of a feed-forward command is determined by Schwartz inequality. The guidance command obtained from the proposed scheme shows a similar form of the biased proportional navigation (BPN) guidance obtained by the optimal control theory. However, the proposed guidance law is less sensitive to the time-to-go estimation error than the BPN law, and it can be easily implemented in the real system. Furthermore, since the coefficients of time-to-go in the feed-forward command remain as design parameters, the proposed guidance law provides more flexibility in application aspect such as trajectory shaping. The characteristics of the proposed guidance law is studied and its performance is also evaluated through numerical simulation.

In this paper, a finite-time convergent sliding-mode guidance law with terminal impact angle constraint is presented. The guidance law insures that the line-of-sight angular rate will converge to zero before the final time of the guidance process. Meanwhile the flight-path angle will meet the terminal impact angle requirement. Based on the finite-time convergence stability theory and the variable structure control theory, the finite convergence time is determined. Finally, the simulation results show that the guidance law is effective.

The extra-atmospheric aircraft model is established, and then the control system is designed. The control system consist of attitude control system and orbit control system, the attitude control system used PID controller and the orbit control system used augmented proportional navigation method. The traditional Proportional Navigation (PN) guidance law has higher accuracy. But for highly maneuvering targets, the accuracy of traditional PN guidance law is still not enough. An Augmented Proportional Navigation (APN) guidance law is designed, an acceleration compensation of the target is introduced on the basis of PN guidance law to overcome the effect of the acceleration on the guidance accuracy. And the engine control method is designed based on the fixed engine thrust. Simulation results indicated that, for homing against maneuverable targets, the APN guidance law is better than the PN guidance law in the following aspects: guidance accuracy is higher, miss distance is lower, interception time is shorter. And the new guidance law provides significant performance improvements over the commonly used classical proportional navigation law.

In this paper, the three-dimensional terminal guidance problem of a missile intercepting a maneuvering target is studied. Augmented proportional navigation (PN) guidance laws based on Lyapunov stability theory are presented. Augmented terms are target accelerations such that proposed guidance laws have the ability to track the target maneuver. But, target accelerations cannot be accurately obtained in practice. To solve this problem, the nonlinear disturbance observer (NDOB) technology is introduced to estimate target accelerations. Estimated target accelerations will be employed as compensation terms in the proposed augmented PN guidance laws. Composite guidance laws combining augmented PN guidance laws with NDOB are proposed. Finally, simulation comparison results are provided to demonstrate the effectiveness of the presented guidance laws.

Optimal guidance of extended trajectory shaping

Three-dimensional terminal angle constraint finite-time dual-layer guidance law with autopilot dynamics

A Backstepping guidance (BSG) law with saturating actuator is proposed for nonlinear kinematics of missile-target motion in the three-dimensional (3D) spherical coordinates system. The most important characteristic of Backstepping control (BSC) is high robustness. The proposed guidance law can reduce interception time and increase robustness in comparison with other guidance laws. In the proposed guidance outline, a Backstepping guidance law is designed to eliminate the effect of external perturbation. Then, it is illustrated that derived guidance law stabilize system. Some scenarios are considered for the engagement and simulated. Simulation results confirm above pretensions.

Deep reinforcement learning-based impact time control guidance law with constraints on the field-of-view