Three-dimensional guidance law with precise control of attack time and constraints on attack angle.

Real time trajectory planning is vital in rocket precision powered landing guidance. Due to the nonconvex angle of attack (AOA) constraint and other constraints, including nonlinear dynamics and thrust constraint, the powered landing trajectory planning problem is highly nonconvex, which makes it difficult to be solved in real time via existing nonconvex optimization algorithms. As the main contribution of this paper, the AOA constraint is taken into account in the problem. A convex feasible set method is presented to handle it, in which a quadratic concave function is introduced to find a convex feasible subset in the original AOA constraint and the second order term of this function is estimated by Gersgorin disc theorem. For the remaining nonconvexities, the lossless convexification is employed to address the thrust constraint, and the successive linearization is performed to handle the nonlinear dynamics. Thus, a convex optimization problem with AOA constraint for landing trajectory planning is built. The optimal solution to the original problem is obtained by iteratively solving convex problems. Numerical simulations show that the proposed method can find a feasible landing trajectory where the AOA constraint is satisfied and has a better convergence performance compared with the traditional linearization method.

goes here. For targets in different scenarios, in order to solve the problem of poor attack time accuracy due to large time-to-go estimation error faced by the impact time control guidance law, this paper designs an attack time constrained sliding mode guidance law based on time-to go estimation, constructs a sliding mode surface with normalised missile and target distances and weighted summation of impact time error; For the scenarios of striking uniform speed and manoeuvring targets, different time-to-go estimation methods are adopted, and the possible singular terms in the guidance law are transformed to further improve the convergence accuracy of the impact time. Finally, the effectiveness of the proposed guidance law under different time constraints is verified by mathematical simulation. The designed guidance law is more applicable in the process of intercepting a manoeuvring target.

Selection of guidance law is an important factor that affects the tactical performance of surface to air missiles. In order to select a suitable guidance law, a method of comparing the normal available acceleration with demanded or required acceleration is formulated. Two guidance laws i.e., proportional navigation guidance law (PNC) and augmented proportional navigation guidance law (APNC) are tested by this method. These guidance laws are studied by the comparison of normal available acceleration and demanded acceleration. In order to simulate the missile-target engagements for maneuvering and non maneuvering targets, a mathematical model is formed and then it is simulated in SIMULINK/MATLAB to carry out extensive simulations to analyze the PNG and APNG against maneuvering and non maneuvering targets. By observing the simulation results, it can be seen that PNG is suitable for non-maneuvering targets and it is incapable for maneuvering targets. However, the APNG is an optimal guidance law for maneuvering and non-maneuvering targets both.

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.

Phase plane design based fast altitude tracking control for hypersonic flight vehicle with angle of attack constraint

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

For an air-breathing hypersonic vehicle (AHV), the high angle of attack (AOA) caused by longitudinal maneuver may lead to the inlet unstart of a scramjet. Therefore, it is necessary to consider the AOA constraint in the controller design of the AHV. In this article, a finite-time neural optimal controller is proposed to satisfy the tracking performance and the AOA constraint simultaneously. First, a basic tracking controller is built to ensure the finite-time convergence of tracking error. Then, a control-oriented safety quantization is investigated. A specific barrier function based on the safety margin is constructed to quantify the safety risk of the AOA. To enforce the AOA constraint in a minimally invasive fashion, a safe adaptive dynamic programming (ADP) is proposed to optimize the basic controller automatically. The specific barrier function is treated as an extended state and, thus, incorporated into the value function of ADP as a risk penalty term for the tradeoff between the tracking performance and the AOA safety constraint. Finally, a safety-considered policy iteration and a single-critic neural network are developed to build an adaptive AOA safety modified policy online. The comparison simulation results show the effectiveness of the proposed controller.

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.

This paper addresses the dual challenges of attack angle constraints and obstacle avoidance during the terminal guidance phase of anti-ship missiles. Based on Deep Reinforcement Learning(DRL), an intelligent guidance law is proposed to simultaneously satisfy obstacle avoidance and attack angle constraints. First, the missile motion model and obstacle model are established according to the kinematic equations of the anti-ship missile and the types of obstacles. Second, a reasonable state input is designed for the obstacle avoidance and angle constraint problems, and the rate of change of lateral overload is selected as the action output, avoiding jitter in overload commands. Meanwhile, the reward function is designed in stages according to the different spatial and temporal characteristics of the two objectives, preventing interference between rewards. The multi-step return reward calculation method is employed to enable backward propagation of the terminal angle reward, alleviating the problem of sparse process rewards. Finally, the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm is used to train the guidance law in random scenarios. Simulation results demonstrate that the proposed intelligent guidance law exhibits high stability, strong adaptability, and smooth trajectories, effectively avoiding obstacles and achieving the desired attack angle.

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.

In this paper, a nonsingular, essentially continuous and finite-time convergent impact angle constrained guidance law for intercepting stationary, constant speed, and maneuvering targets is developed using advanced terminal sliding mode control schemes and extended state observer. In order to achieve the specified intercept angle in finite time without singularity, the nonsingular fast terminal sliding mode control algorithm is employed to construct sliding surface. The fast terminal sliding mode control technique is used to establish the reaching law, so the system trajectory converges quickly from initial state to the switching surface in the whole reaching phase and the proposed guidance law is essentially continuous. Noticing the interception of a maneuvering target, the unknown target acceleration is estimated and compensated using extended state observer. Due to its inherent attribute of singularity-free, continuity, and faster convergence rate, no approximation is necessary in the implementation of the proposed guidance law, so better tracking accuracy of the desired intercept angle in a shorter time with a smoother guidance command can be guaranteed compared with conventional terminal sliding mode guidance law. A large number of numerical simulations are implemented to justify the effectiveness of the proposed guidance law.

It has been recognized by several researchers that a guidance algorithm effective against maneuvering targets is the one that drives the heading error rapidly to zero and then maintains a zero heading error for the remainder of the flight. We have referred to this guidance algorithm as nonlinear guidance (NLG) as its implementation generally requires some nonlinear features. There are may ways in which NLG can be put into practice. We examine a new way of applying NLG that does not require knowledge of line-of-sight rate, or target acceleration. However, information on the target aspect angle is required. The new guidance law is derived using the Lyapunov optimizing feedback control method. We make some performance comparisons with augmented proportional navigation. Not only do we maintain the performance advantage previously demonstrated in our earlier applications (2000) of NLG (requiring line-of-sight rate and target acceleration) but we also obtain a dramatic improvement in performance in the presence of measurement noise.

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.

Taking into consideration the autopilot dynamics, a finite-time convergent guidance law with terminal attack angle constraint, is designed for homing missiles to intercept maneuvering targets. The approach taken here is based on the existing finite-time 2-sliding mode control theory. Firstly, the constraint problem of terminal attack angle is transformed to that of terminal line-of-sight(LOS) angle, and an exact observer is employed to estimate the target maneuvers in finite time. Then, it is proved that, the guidance law has the ability to achieve the design requirement of zero miss distance and the anticipant terminal attack angle in finite time. Compared with the previous work, this guidance law is robust to target maneuvers, and can compensate for the effects of missile autopilot dynamics effectively, and the information required in it is easy to obtain in practice. Simulation results show the benefits of the design.

The paper presents a new differential game guidance law for intercepting highly maneuvering targets while having noisy measurements. The proposed law takes into account the interceptor's direct lift associated with canard or tail aerodynamic control surfaces and the target's maneuver dynamics. The capture conditions for both configurations are presented and it is shown that the direct lift generated by a canard configuration reduces the requirements on the missile's maneuverability and dynamic response time. For the implementation in a noise-corrupted environment, a first order Gauss Markov process is used for the target acceleration model and the perfect information guidance law is modified to take into account the inherent delay in estimating the target's acceleration. By modeling the delay as being range dependent instead of constant as was done in a recent study, the need for searching for the best delay is eliminated. The improved performance of the new guidance law is confirmed by a set of Monte Carlo simulations.