Non-linear missile guidance synthesis using control Lyapunov functions

2005 ◽  
Vol 219 (2) ◽  
pp. 77-87 ◽  
Author(s):  
P Gurfil
Keyword(s):  
Lyapunov Functions ◽  
Three Dimensional ◽  
Performance Measure ◽  
Line Of Sight ◽  
Missile Guidance ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Non Linear ◽  
Non Linear Systems ◽  
Fixed Line

This paper derives a new non-linear guidance law aimed at interception of highly manoeuvring targets. The guidance law is developed based on the theory of control Lyapunov functions (CLFs), a methodology for universal stabilization of non-linear systems which is also inverse optimal with respect to some performance measure. The three-dimensional guidance dynamics are formulated in a fixed-line-of-sight coordinate system, yielding matching between the target and missile accelerations. Closed-form expressions for the CLF guidance commands are given. Simulation shows that the new guidance scheme significantly outperforms augmented proportional navigation in short-range engagements.

A generalized design method for three-dimensional guidance laws

2016 ◽  
Vol 231 (1) ◽  
pp. 47-60 ◽  
Author(s):  
Sheng Sun ◽  
Di Zhou ◽  
Jingyang Zhou ◽  
Kok Lay Teo
Keyword(s):  
Lyapunov Function ◽  
Sliding Mode ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Generalized Function ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Target Acceleration ◽  
Guidance Laws ◽  
Proportional Navigation Guidance

The true proportional navigation guidance law, the augmented proportional navigation guidance law, or the adaptive sliding-mode guidance law, is designed based on the planar target-to-missile relative motion dynamics. By a proper construction of a nonlinear Lyapunov function for the line-of-sight angular rates in the three-dimensional guidance dynamics, it is shown that the three guidance laws mentioned above are able to ensure the asymptotic convergence of the angular rates as they are directly applied to the three-dimensional guidance environment. Furthermore, considering the missile autopilot dynamics as a first-order lag, we design three-dimensional nonlinear guidance laws by using the backstepping technique for three cases: (1) the target does not maneuver; (2) the information of target acceleration can be acquired; and (3) the target acceleration is not available but its bound is known a priori. In the first step of the backstepping design of the control law, there is no need to cancel the nonlinear coupling terms in the three-dimensional guidance dynamics in such way that the final expressions of the proposed guidance laws are significantly simplified. Thus, the proposed nonlinear Lyapunov function for the line-of-sight angular rates is a generalized function for designing three-dimensional guidance laws. Simulation results of a missile interception mission show that the proposed guidance laws are highly effective.

3D Nonlinear Guidance Law for Bank-to-Turn Missile

2011 ◽  
Vol 317-319 ◽  
pp. 727-733
Author(s):  
Shuang Chun Peng ◽  
Liang Pan ◽  
Tian Jiang Hu ◽  
Lin Cheng Shen
Keyword(s):  
Three Dimensional ◽  
Lyapunov Theory ◽  
Line Of Sight ◽  
Rate Model ◽  
Guidance Law ◽  
Terminal Constraints ◽  
Guidance Laws ◽  
3D Guidance ◽  
Guidance Model ◽  
Vector Description

A new three-dimensional (3D) nonlinear guidance law is proposed and developed for bank-to-turn (BTT) with motion coupling. First of all, the 3D guidance model is established. In detail, the line-of-sight (LOS) rate model is established with the vector description method, and the kinematics model is divided into three terms of pitching, swerving and coupling, then by using the twist-based method, the LOS direction changing model is built for designing the guidance law with terminal angular constraints. Secondly, the 3D guidance laws are designed with Lyapunov theory, corresponding to no terminal constraints and terminal constraints, respectively. And finally, the simulation results show that the proposed guidance law can effectively satisfy the guidance precision requirements of BTT missile.

Two composite guidance laws based on the backstepping control and disturbance observers with autopilot lag

2019 ◽  
Vol 41 (10) ◽  
pp. 2957-2969 ◽  
Author(s):  
Chaoyuan Man ◽  
Zhenxing Zhang ◽  
Shihua Li
Keyword(s):  
Disturbance Observer ◽  
Three Dimensional ◽  
Simulation Studies ◽  
Missile Guidance ◽  
Nonlinear Disturbance Observer ◽  
First Order ◽  
Guidance Law ◽  
Control Scheme ◽  
Backstepping Controller ◽  
Guidance Laws

A composite three-dimensional (3D) missile guidance law is proposed for manoeuvering targets with the consideration of the first-order autopilot dynamics without any linearization. This guidance law consists of a backstepping controller and a feedforward compensation based on disturbance observers. In this control scheme, the unknown target acceleration is regarded as part of the lumped disturbance, estimated by a disturbance observer, and then feedforward compensated. The backstepping controller is introduced to deal with unmatched disturbances. Moreover, both the nonlinear disturbance observer (NDOB) and the generalized proportional integral observer (GPIO) are employed in the derivation. Simulation studies demonstrate the effectiveness of the proposed guidance law, and compare the guidance performance of the two composite guidance laws with different disturbance observers.

A three-dimensional diffrential game missile guidance law using neural networks

2001 ◽  
Author(s):  
Min-Jea Tahk ◽  
Han-Lim Choi ◽  
Hun-Gu Lee ◽  
Yonmook Park
Keyword(s):  
Neural Networks ◽  
Three Dimensional ◽  
Missile Guidance ◽  
Guidance Law

scholarly journals Attack behaviour in naïve Gyrfalcons is modelled by the same guidance law as in Peregrines, but at a lower guidance gain

2021 ◽  
pp. jeb.238493
Author(s):  
Caroline H. Brighton ◽  
Katherine E. Chapman ◽  
Nicholas C. Fox ◽  
Graham K. Taylor
Keyword(s):  
High Speed ◽  
Angular Rate ◽  
Species Level ◽  
Line Of Sight ◽  
Proportional Navigation ◽  
Evolutionary Origins ◽  
Guidance Law ◽  
Flight Morphology ◽  
Aerial Hunting ◽  
The Individual

The aerial hunting behaviours of birds are strongly influenced by flight morphology and ecology, but little is known of how this relates to the behavioural algorithms guiding flight. Here we use GPS loggers to record the attack trajectories of captive-bred Gyrfalcons (Falco rusticolus) during their maiden flights against robotic aerial targets, which we compare to existing flight data from Peregrines (Falco peregrinus). The attack trajectories of both species are well modelled by a proportional navigation (PN) guidance law, which commands turning in proportion to the angular rate of the line-of-sight to target, at a guidance gain. However, naïve Gyrfalcons operate at significantly lower values of N than Peregrines, producing slower turning and a longer path to intercept. Gyrfalcons are less manoeuvrable than Peregrines, but physical constraint is insufficient to explain the lower values of N we found, which may reflect either the inexperience of the individual birds or ecological adaptation at the species level. For example, low values of N promote the tail-chasing behaviour that is typical of wild Gyrfalcons and which apparently serves to tire their prey in a prolonged high-speed pursuit. Likewise, during close pursuit of typical fast evasive prey, PN will be less prone to being thrown off by erratic target manoeuvres at low guidance gain. The fact that low-gain PN successfully models the maiden attack flights of Gyrfalcons suggests that this behavioural algorithm is embedded in a guidance pathway ancestral to the clade containing Gyrfalcons and Peregrines, though perhaps with much deeper evolutionary origins.

scholarly journals Impact Time Control Cooperative Guidance Law Design Based on Modified Proportional Navigation

Aerospace ◽  
2021 ◽  
Vol 8 (8) ◽  
pp. 231
Author(s):  
Zhanyuan Jiang ◽  
Jianquan Ge ◽  
Qiangqiang Xu ◽  
Tao Yang
Keyword(s):  
Constant Velocity ◽  
Three Dimensional ◽  
Estimation Method ◽  
Time Varying ◽  
Two Dimensional ◽  
Proportional Navigation ◽  
Impact Time ◽  
Time Control ◽  
Guidance Law ◽  
Cooperative Guidance

The paper proposes a two-dimensional impact time control cooperative guidance law under constant velocity and a three-dimensional impact time control cooperative guidance law under time-varying velocity, which can both improve the penetration ability and combat effectiveness of multi-missile systems and adapt to the complex and variable future warfare. First, a more accurate time-to-go estimation method is proposed, and based on which a modified proportional navigational guidance (MPNG) law with impact time constraint is designed in this paper, which is also effective when the initial leading angle is zero. Second, adopting cooperative guidance architecture with centralized coordination, using the MPNG law as the local guidance, and the desired impact time as the coordination variables, a two-dimensional impact time control cooperative guidance law under constant velocity is designed. Finally, a method of solving the expression of velocity is derived, and the analytic function of velocity with respect to time is given, a three-dimensional impact time control cooperative guidance law under time-varying velocity based on desired impact time is designed. Numerical simulation results verify the feasibility and applicability of the methods.

Evaluation of Guidance Laws Performance Sing Genetic Algorithm

2014 ◽  
Vol 598 ◽  
pp. 723-730
Author(s):  
Mohamed Zakaria ◽  
Talaat Ibrahim ◽  
Alaa El Din Sayed Hafez ◽  
Hesham Abdin
Keyword(s):  
Genetic Algorithm ◽  
Differential Geometry ◽  
Standard Deviation ◽  
Optimization Process ◽  
Line Of Sight ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Simulation Results ◽  
Miss Distance ◽  
Guidance Laws

Several conditions affect the performance of guidance law like target parameters or delayed line of sight rate. A variable navigation ratio is used to enhance the performance of guidance law. In this paper a Genetic Algorithm is used to formulate different forms of variable gains and measure the miss distance. An optimization process is running to find the minimum miss distance. The average values and standard deviation of miss distance for all genetic algorithm individuals are calculated to measure the performance and robustness of guidance law. Two guidance laws are considered proportional navigation (PN) and differential geometry (DG). The simulation results show that the proportional navigation is superior to differential geometry performance in the presence of delayed line of sight rate.

Sign in / Sign up

Export Citation Format

Share Document