Guidance Law For Homing Missiles Research Articles

Time and FOV constraint guidance applicable to maneuvering target via sliding mode control

This paper focuses on designing a novel homing missile guidance law applicable to intercepting maneuvering target while considering time and field-of-view (FOV) constraints. To realize accurate zero miss-distance and time control, a sliding mode manifold consisting of the range-to-go, expected impact time and two newly-defined weighting functions is constructed based on a nonlinear model, which can guarantee the interception at a prescribed impact time once the sliding mode has reached. Then, an overall guidance command is derived by taking both finite time convergence of sliding mode manifold and non-singularity into consideration. A new guidance strategy with boundary conditions is proposed to satisfy FOV requirement. Furthermore, the feasibility for intercepting maneuvering target is demonstrated via a Lyapunov-like approach. Numerical simulations validate the performance of the proposed guidance law, and a comparative study indicates that the proposed method is superior to relative guidance laws in terms of maneuvering target interception.

Generalized Guidance Formulation for Impact Angle Interception with Physical Constraints

This paper proposes an optimal impact angle control guidance law for homing missiles with a narrow field-of-view of the seekers. As groundwork for designing a guidance law, we first present a general guidance structure that can achieve any terminal constraint of the line-of-sight rate based on the optimal control theory. We configure the desired profile of the line-of-sight rate using a saturation function whose exact form is determined to satisfy the required boundary conditions. By combining the line-of-sight rate profile with the optimal guidance structure, we develop a guidance law that achieves an impact angle interception with the field-of-view constraint. Herein, as the entire guidance structure is derived based on exact kinematics without any approximation, the proposed law ensures the accurate impact angle interception for various engagement scenarios. This precise consideration of the engagement kinematics also accurately ensures the energy optimality of preventing the excessive use of control inputs when homing. To evaluate the performance of the proposed method, numerical simulations with various engagement scenarios are conducted, and the results demonstrate that the proposed law allows missiles to accurately intercept their targets with the desired impact angles and without violating the prescribed field-of-view constraint.

Look Angle Constrained Impact Angle Control Guidance Law for Homing Missiles With Bearings-Only Measurements

This paper presents an impact angle control guidance law that confines the missile look angle during homing in order to not exceed a seeker's field-of-view limit. A sliding surface variable whose regulation guarantees the interception of a stationary target at the desired impact angle is designed, and the guidance law is derived to make the surface variable go to the sliding mode. Using a magnitude-limited sigmoid function in the surface variable, the proposed law prohibits the look angle from exceeding the specified limit during the entire homing. This capability to confine the missile look angle is valuable when a seeker's field-of-view is restricted, since imposing the terminal impact angle constraint demands the missile to fly a curved trajectory. Furthermore, the proposed law can be implemented under bearings-only measurements because the command does not involve any information of the relative range and line-of-sight rate. Numerical simulations are conducted to demonstrate the validity of the proposed law. The result shows that the proposed guidance law accomplishes the impact angle constraint without violating the prescribed look angle limit although it only uses the information of bearing angles.

A new adaptive finite time nonlinear guidance law to intercept maneuvering targets

A new adaptive nonlinear guidance law for homing missiles to intercept maneuvering targets in terminal phase is proposed. This guidance law generates smooth acceleration commands and is able to stabilize the relative lateral velocity in a desired finite time. The proposed guidance law uses bounds of the target acceleration and jerk and is consisting of two adaptive terms. It is proved that the first adaptive term of the proposed guidance law converges to the target acceleration normal to the line of sight. Finite time stability of the guidance loop is proved by using Lyapunov stability theorem. Numerical simulations are performed to illustrate the proposed guidance law potential.

Trajectory reshaping based guidance with impact time and angle constraints

This study presents a novel impact time and angle constrained guidance law for homing missiles. The guidance law is first developed with the prior-assumption of a stationary target, which is followed by the practical extension to a maneuvering target scenario. To derive the closed-form guidance law, the trajectory reshaping technique is utilized and it results in defining a specific polynomial function with two unknown coefficients. These coefficients are determined to satisfy the impact time and angle constraints as well as the zero miss distance. Furthermore, the proposed guidance law has three additional guidance gains as design parameters which make it possible to adjust the guided trajectory according to the operational conditions and missile’s capability. Numerical simulations are presented to validate the effectiveness of the proposed guidance law.

A guidance law with finite time convergence considering autopilot dynamics and uncertainties

Taking into consideration both the autopilot dynamics and uncertainties, this paper proposes a finite time convergent guidance law for homing missile to intercept a maneuvering target. Firstly, an exact observer (differentiator) is employed to estimate the target maneuvers in finite time. Then, a finite time convergent guidance law is designed based on the existing finite time sliding-mode control theory. It is proved that the line-of-sight (LOS) angular rate converges to zero in finite time under the proposed guidance law. Compared with the existing finite time guidance laws, this guidance law can compensate for the effects of the autopilot dynamics and uncertainties, and the information used for feedback control is much easier to obtain. Finally, simulation results show that our scheme, as a finite time convergent algorithm, has strong robustness to bounded disturbances.

Augmented Polynomial Guidance With Impact Time and Angle Constraints

In this paper, a new impact time and impact angle control guidance law for homing missiles against a stationary target is proposed. To derive a state feedback command for the proposed law with terminal constraints on the impact time and angle, we introduce a polynomial function of the guidance command with three unknown coefficients, one of which is determined to achieve the impact time requirement. The others are determined to satisfy the terminal impact angle constraint, as well as the zero miss distance. Because the proposed guidance law has arbitrary guidance gains, it is possible to shape the intercept trajectory and acceleration command profile by choosing proper gains in relation to the missile's capability, operational conditions, and so on.

Cooperative Multiple-Model Adaptive Guidance for an Aircraft Defending Missile

A cooperative guidance law, for a defender missile protecting an aerial target from an incoming homing missile, is presented. The filter used is a nonlinear adaptation of a multiple model adaptive estimator, in which each model represents a possible guidance law and guidance parameters of the incoming homing missile. Fusion of measurements from both the defender missile and protected aircraft is performed. A matched defender’s missile guidance law is optimized to the identified homing missile guidance law. It utilizes cooperation between the aerial target and the defender missile. The cooperation stems from the fact that the defender knows the future evasive maneuvers to be performed by the protected target and thus can anticipate the maneuvers it will induce on the incoming homing missile. Moreover, the target performs a maneuver that minimizes the control effort requirements from the defender. The estimator and guidance law are combined in a multiple model adaptive control configuration. Simulation results show that combining the estimations with the proposed optimal guidance law, that utilizes cooperation between the defending missile and protected target, yields hit-to-kill closed loop performance with very low control effort. This facilitates the use of relatively small defending missiles to protect aircrafts from homing missiles.

Optimal Intercept Missile Guidance Strategies with Autopilot Lag

In the linear-quadratic pursuit-evasion game, the pursuer (interceptor) wishes to minimize the terminal miss, whereas the evader (target) wishes to maximize it. Therefore, the optimal strategy of the interceptor is derived against the anticipated worst possible strategy of the target. If the interceptor has a lag, the current approach is to include this lag directly in the system dynamics, which are known to both players. In this problem formulation, the optimal cost could easily go to infinity, which means that the target will win the game. This is expected, because the target has knowledge about interceptor's lag. To ensure the existence of an interceptor strategy, the weighting on the terminal miss has to be chosen small enough so that the optimal cost will remain finite. However, this manipulation prevents the target from maximizing the terminal miss and effectively constrains the target strategy. Therefore, the interceptor strategy is derived against the worst-case target strategy that is not really the worst case. In this paper, it is shown that this interceptor strategy performs poorly in realistic situations where the target tries to maximize the terminal miss. Instead, two new interceptor strategies are derived against target strategies that are determined without knowledge about the interceptor's lag. These two optimal interceptor strategies improve the game-theoretic guidance law for homing missiles by correctly taking into account the autopilot lag.

3D Nonlinear H2/H∞ Adaptive Guidance Law for Homing Missiles

This paper explores the effectiveness of nonlinear H2/H∞ optimal guidance design applied to a realistic missile guidance problem with target models. Extended the concept of augmented proportional navigation (APN), a newly-developed technique is applied and solutions are obtained for guidance designs of missile system combine the traditional H2 quadratic performance criterion for noise rejection with the H∞ performance criterion for the maximum robustness against the error of maneuvering target estimated.

Tunable H∞ robust guidance law for homing missiles

The proposed robust guidance control law can attain satisfactory robust performance for pursuing an unpredictable maneuvering target. Sufficient condition analysis is also carried out for the proposed guidance control law with tunable parameters. The proposed method not only need not touch the hard-solved Hamilton–Jacobi partial differential inequality but also guarantees that the line-of-sight distance between homing missile and maneuvering target can quickly converge to zero. A previously-implemented simulation discussed elsewhere is performed using the guidance control law to illustrate the efficiency of the proposed design.

Nonlinear rule-based controller for missile terminal guidance

The design of a rule-based guidance law for homing missiles onto targets is presented. The stability of the missile-target dynamics is proven. Unlike conventional approaches that solve the Hamilton–Jacobi partial differential inequality associated with the missile guidance problem, the proposed guidance law is based on heuristic fuzzy rules. Furthermore, the proposed missile guidance control law guarantees that the missile can reach the impact region and destroy the target. An example is used to illustrate the application of the proposed design method.

Synthesis of optimal feedback guidance law for homing missiles using neural networks

Most existing missiles are guided by proportional navigation guidance (PNG) law, but PNG is a particular case for LQ guidance rule with two main assumptions of small line-of-sight angles and negligible acceleration along the line-of-sight. However, most missile engagements exceed these limits because of high tangential and normal accelerations. Unfortunately, it is not possible to determine the feedback guidance law for non-linear systems such as homing missiles in real-time. We use artificial neural networks to synthesize feedback laws for homing missiles with non-linear state equations. We first obtain an open-loop optimal numerical solution for non-linear state equations and then use these data to train a feed-forward multilayer neural network in an off-line session. The network is then used effectively in a real-time for feedback guidance method. Simulation results show that this neural networks guidance method can efficiently produce an optimal feedback law in spite of relatively simple network architecture. Copyright © 2000 John Wiley & Sons, Ltd.

Synthesis of optimal feedback guidance law for homing missiles using neural networks

Synthesis of optimal feedback guidance law for homing missiles using neural networks

Motion Tracking Sliding-Mode Guidance of a Homing Missile with Bearings-Only Measurements.

Motion tracking sliding-mode control theory is utilized to design a homing-missile guidance law, which induces missile-target line-of-sight angular rate to track an arbitrarily given signal, such that observability for the target tracking with bearings-only measurements is enhanced. An adaptive two-step filter is used to estimate missile-target relative range, relative velocity, and target acceleration involved in the guidance law during the whole guidance period. Simulation studies indicate that the presented guidance law provides good performance for the filter, robustness to estimation errors, and good terminal effectiveness.

Three-dimensional nonlinear H∞ guidance law with maneuvering targets

Abstract This paper proposes a three-dimensional H ∞ robust guidance law for homing missiles with nonlinear kinematics in the homing phase. Unlike conventional approaches where target's acceleration is often assumed to be known or needs to be estimated in real time, the proposed 3D robust guidance law can achieve performance robustness in the absence of target's acceleration information. The most difficult and challenging task involved in applying nonlinear H∞ control theory is the solution of the associated Hamilton-Jacobi partial differential inequality (HJPDI). In this paper we show that the HJPDI of the three-dimensional missile guid ance problem can be solved analytically with simple manipulations. The numerical simulations show that the three-dimensional H ∞ robust guidance law exhibits strong robustness properties against disturbances from target's maneuvers.

Adaptive Sliding-Mode Guidance of a Homing Missile

Sliding-mode control is applied to design robust homing missile guidance law. The sufe cient and necessary condition for the sliding-mode motion of a linear time-varying system not to be affected by disturbances and the sufe cient condition for that motion not to be affected by parameter perturbations are given. An adaptive reaching law of sliding mode for a linear time-varying system is then presented and used to derive an adaptive sliding-mode guidance law. Theoretical analysis and simulation results show that the adaptive sliding-mode guidance law is robust against disturbances and parameter perturbations. Furthermore, the presented guidance law is simple to implement in practice.

Nonlinear H Robust Guidance Law for Homing Missiles

This paper proposes an H1 robust guidance law for homing missiles with nonlinear kinematics in the homing phase. Unlike conventional approaches where target’ s acceleration is often assumed to be known or needs to be estimated in real time, the proposed robust guidance law can achieve performance robustness in the absence of target’ s acceleration information and under variations of the initial conditions of engagement. The most dife cult and challenging task involved in applying nonlinear H1 control theory is the solution of theassociated Hamilton ‐ Jacobipartial differentialinequality.In thispaperweshowthattheHamilton ‐Jacobipartialdifferential inequality of the missile guidance problem can be solved analytically with simple manipulations. The numerical simulations show that the H1 robust guidance law exhibits strong robustness properties against disturbances from target’ s maneuvers and variations in initial engagement conditions.

Optimal pointing control of robotic manipulators with state inequality constraints

Yang, C. D., Yeh, F. B., and Chen, J. H., The Closed-Form Solution of Proportional Navigation, Journal of Guidance, Control, and Dynamics, Vol. 10, No. 2, 1987, pp. 216-218. Yang, C. D., Hsiao, F. B., and Yeh, F. G., Generalized Guidance Law for Homing Missiles, IEEE Transactions on Aerospace and Electronic Systems, Vol. 25, No. 2, 1989, pp. 197-212. 11 Yuan, P. J., and Chern, J. S., Ideal Proportional Navigation, Journal of Guidance, Control, and Dynamics, Vol. 15, No. 5, 1992, pp. 1161-1165. Yuan, P. J., and Chern, J. S., Analytical Study of Biased Proportional Navigation, Journal of Guidance, Control, and Dynamics, Vol. 15, No. 1, 1992, pp. 185-190.

Passive homing missile guidance law based on new target maneuver models

Abstract : By using more realistic a priori knowledge about the target motion, tracking of maneuvering targets for homing missiles is enhanced. Since certain targets are assumed to execute evasive maneuvers orthogonal to their velocity vector, a new stochastic dynamic target model is proposed where this orthogonality is embedded. Along with this new acceleration dynamic model, the orthogonality is also enforced by the addition of a fictitious auxiliary measurement. The target states are estimated by the modified gain extended Kalman filter (MGEKF), and the angular target maneuver rate is constructed on- line. A guidance law that minimizes a quadratic performance index subject to the assumed stochastic engagement dynamics that includes state dependent noise is derived. This guidance law is determined in closed form where the gains are an explicit function of the estimated target maneuver rate as well as time to go. The numerical simulation for the two-dimensional angle-only measurement case indicates that the proposed target model with the MGEKF leads to remarkable estimation of the target states. Furthermore, the effect on terminal miss distance using this new guidance scheme is given. Keywords: Kalman filter; Target estimation; Linear quadratic guidance law; Guidance law.