Guidance against maneuvering targets using Lyapunov optimizing feedback control

This paper proposes a variation of the pure proportional navigation guidance law, called augmented pure proportional navigation, to account for target maneuvers, in a realistic nonlinear engagement geometry, and presents its capturability analysis. These results are in contrast to most work in the literature on augmented proportional navigation laws that consider a linearized geometry imposed upon the true proportional navigation guidance law. Because pure proportional navigation guidance law is closer to a realistic implementation of proportional navigation than true proportional navigation law, and any engagement process is predominantly nonlinear, the results obtained in this paper are more realistic than any available in the literature. Sufficient conditions on speed ratio, navigation gain, and augmentation parameter for capturability, and boundedness of lateral acceleration, against targets executing piecewise continuous maneuvers with time, are obtained. Further, based on a priori knowledge of the maximum maneuver capability of the target, a significant simplification of the guidance law is proposed in this paper. The proposed guidance law is also shown to require a shorter time of interception than standard pure proportional navigation and augmented proportional navigation. To remove chattering in the interceptor maneuver at the end phase of the engagement, a hybrid guidance law using augmented pure proportional navigation and pure proportional navigation is also proposed. Finally, the guaranteed capture zones of standard and augmented pure proportional navigation guidance laws against maneuvering targets are analyzed and compared in the normalized relative velocity space. It is shown that the guaranteed capture zone expands significantly when augmented pure proportional navigation is used instead of pure proportional navigation. Simulation results are given to support the theoretical findings.

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.

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.

Our former studies has shown the general superiority of augmented proportional navigation over conventional proportional navigation. However, there were some exceptions where the latter has shown a better performance than the former. The farther study result showed that, the conventional proportional navigation is favorable against the aircraft in-coplane maneuver, while augmented proportional navigation is superior to the former against the aircraft out-of-coplane maneuver, even in cases where a fairly large time lag exists in the target acceleration estimation. Motivated by the fact, a new missile guidance algorithm which switches between conventional and augmented proportional navigation depending on the kind of the aircraft maneuver is studied and the performance is evaluated by simulations. The result shows the general superiority of this guidance algorithm over existent conventional or augmented proportional navigation guidance.

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.

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

In this paper, a new guidance law for a missile against an accelerating and turning target is presented. When a missile axial acceleration is constant and a target is maneuvering with a constant acceleration, there exists a rectilinear collision course. The guidance laws presented guide a missile so as to fly along the collision course. First, two theoretical guidance laws are derived from the idea based on proportional navigation. Since it is very difficult, however, to realize these theoretical guidance laws on most existing tactical missiles, this paper also shows a method for simply implementing them. The performance of the guidance laws presented is compared with that of proportional navigation or augmented proportional navigation using simulation studies of a simple model of a short range air-to-air missile. The simulation results show that the guidance laws presented are far superior in performance to proportional navigation or augmented proportional navigation.

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 PD nonlinear dynamic inverse guidance law finite time convergence is proposed for the problem of UAV's collision avoidance in this paper. First, a proportional-derivative nonlinear dynamic inverse guidance law, which can be applied to multiple initial angles and speeds, is designed to ensure the security of UAV's collision avoidance. In addition, the stability of guidance law is proved by the circle criterion, and stability conditions are used to design coefficients of guidance law. In order to analysis the performance of this guidance law, a simulation system based on 6-DOF UAV is established. The results conclusively demonstrate that the maneuvering range of collision avoidance is smaller than the collision avoidance method based on traditional nonlinear dynamic inverse guidance.

Two new algorithms for homing missile guidance and estimation in the two-dimensional intercept problem are proposed based on the assumption that certain targets execute evasive maneuvers orthogonal to their velocity vectors. The objectives of both algorithms are to estimate the engagement states in the presence of unknown target accelerations and guide the interceptor to hit the target based on these state estimates. Both algorithms are the integration of a fllter in cascade with a guidance law but constructed using difierent philosophies. One algorithm constructs the fllter that estimates the target acceleration and the guidance law based on a target model in which the magnitude of the target acceleration vector is assumed to be a sinusoidal function. The other algorithm constructs the fllter by blocking the dynamic efiect of the target acceleration and constructs the guidance law based on the anticipated worst possible target acceleration. These two algorithms form an interesting design trade between the inherent estimation lag and increased estimation uncertainty.

An improved three dimensional adaptive robust guidance law is proposed for the passive homing guidance in which only line-of-sight angular rate can be measured when target maneuvered. The nonlinear control system of missile is designed according to relative motion model of missile and target, which regards coupling and target acceleration as interference. Then a sliding surface and control law is designed based on approximate parallel approaching principle and variable structure control theory. The self-learning ability of RBF neural network is used to approximate the uncertain nonlinear time-varying functions in the control law online. Finally, the network weights adaptive law is proposed according to Lyapunov theory. This method can assure the excellent adaptive ability and robustness of the system. Simulation results indicate that the guidance law is better than traditional proportional navigation and variable structure guidance law in performance.

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.

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.

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

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