Optimal cooperative guidance with guaranteed miss distance in three-body engagement

2016 ◽  
Vol 232 (3) ◽  
pp. 492-504 ◽  
Author(s):  
Feng Fang ◽  
Yuan-Li Cai
Keyword(s):  
Linear Quadratic ◽  
Control Effort ◽  
Guidance Law ◽  
Cooperative Guidance ◽  
The One ◽  
Three Body ◽  
The Cost ◽  
Miss Distance ◽  
Penalty Weight ◽  
Guidance Laws

The three-body engagement where a target aircraft protects itself by using a cooperative defender missile to intercept an attacking missile is investigated. It is formulated as a constrained linear quadratic optimal problem. Two different optimal cooperative guidance laws for the target and defender are proposed in two cooperation schemes. Since any control effort to reduce the miss distance to smaller than missile’s lethal radius is wasted, the guidance laws are derived to achieve an upper bound on the missile–defender miss distance. In the two-way cooperation scheme, the target and the defender act as a team. How the target makes a trade-off between aiding the defender and evading the missile is investigated by considering both the missile–target zero-effort miss distance and the control effort into the cost function. Without the penalty weight on the missile–target zero-effort miss distance, the two-way minimum control effort guidance laws are available. In the one-way cooperation scheme, the target uses a known evasion strategy independently. The optimal cooperative guidance law is derived for minimizing the control effort of the defender. Simulation results show that these proposed guidance laws can provide a specified missile–defender miss distance and save the control effort compared with the zero-miss-distance guidance law. Two-way cooperation scheme outperforms one-way cooperation scheme.

Application of optimal control law to laser guided bomb

2018 ◽  
Vol 122 (1251) ◽  
pp. 785-797
Author(s):  
Takieddine Mouada ◽  
Milos V. Pavic ◽  
Bojan M. Pavkovic ◽  
Sasa Z. Zivkovic ◽  
Mirko S. Misljen
Keyword(s):  
Noise Removal ◽  
Control Law ◽  
State Variables ◽  
Linear Quadratic ◽  
State Variable ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
Miss Distance ◽  
Guidance Laws

ABSTRACTThe paper presents a laser guided bomb guidance law based on the linear quadratic differential game theory, where a case of two perpendicular planes with two state variables in each plane has been considered. The Kalman filtering method has been used for noise removal from the measured signals and for estimation of the missing state variable values needed for the optimal guidance law. Optimisation has been conducted with respect to minimisation of the performance index. Comparative analysis of different guidance laws is done. A statistical analysis is performed to obtain the terminal miss distance in dependence on total flight time.

scholarly journals Adaptive Estimation and Cooperative Guidance for Active Aircraft Defense in Stochastic Scenario

Sensors ◽  
2019 ◽  
Vol 19 (4) ◽  
pp. 979 ◽  
Author(s):  
Feng Fang ◽  
Yuanli Cai ◽  
Zhenhua Yu
Keyword(s):  
Adaptive Estimation ◽  
Posteriori Probability ◽  
Multiple Model ◽  
Linear Quadratic ◽  
Control Effort ◽  
A Posteriori Probability ◽  
Active Defense ◽  
Cubature Kalman Filter ◽  
Cooperative Guidance ◽  
Guidance Laws

The active aircraft defense problem is investigated for the stochastic scenario wherein a defending missile (or a defender) is employed to protect a target aircraft from an attacking missile whose pursuit guidance strategy is unknown. For the purpose of identifying the guidance strategy, the static multiple model estimator (sMME) based on the square-root cubature Kalman filter is proposed, and each model represents a potential attacking missile guidance strategy. Furthermore, an estimation enhancement approach is provided by using pseudo-measurement. For each model in the sMME, the model-matched cooperative guidance laws for the target and defender are derived by formulating the active defense problem as a constrained linear quadratic problem, where an accurate defensive interception and the minimum evasion miss distance are both considered. The proposed adaptive cooperative guidance laws are the result of mixing the model-matched optimal cooperative guidance laws in the criterion of maximum a posteriori probability in the framework of the sMME. By adopting the adaptive cooperative guidance laws, the target can facilitate the defender’s interception with the attacking missile with less control effort. Also, simulation results show that the proposed guidance laws increase the probability of successful target protection in the stochastic scenario compared with other defensive guidance laws.

Cooperative guidance law for active aircraft defense with intercept angle constraint

2020 ◽  
pp. 095441002096509
Author(s):  
Min He ◽  
Xiaofang Wang ◽  
Hai Lin ◽  
Nianyuan Xiao ◽  
Zonglin Du
Keyword(s):  
Time Constraint ◽  
Feasible Region ◽  
Motion Model ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Cooperative Guidance ◽  
Nonlinear Relative Motion ◽  
Three Body ◽  
Miss Distance ◽  
The Given

In this paper, the three-body engagement scenario is considered where a target aircraft fires a defender missile to intercept the attacker missile. A cooperative guidance law with the intercept angle constraint for both of the defender missile and target has been presented. With the assumption that the attacker missile uses augmented proportional navigation guidance law, the nonlinear relative motion model of target-attacker-defender engagement is built. Considering the requirement of miss distance and satisfying the intercept angle constraint, the function index is established. The cooperative guidance law is derived based on optimal control theory. Moreover, given initial launch condition, the feasible intercept angle region of defender is analyzed, considering the limited maneuverability of defender and target and the intercept time constraint which means the attacker must be intercepted by the defender prior to hitting the target. Similarly, the feasible launch region of defender is obtained with the given designated intercept angle, variable overload of defender and target, and intercept time constraint. The simulation results further demonstrate that within the feasible region of designated intercept angle and launching condition, the defender can intercept the attacker with designated intercept angle successfully despite of the limited maneuverability. Compared with conventional uncooperative situation, the target-defender cooperation could significantly reduce the maneuverability requirements for the defender.

New Guidance Law Design with Multiple Object Constraints for Guided Rocket-Propelled Missile

2014 ◽  
Vol 709 ◽  
pp. 256-262
Author(s):  
Xiao Ju Duan ◽  
Xiao Zhong Xue ◽  
Peng Yun Liu
Keyword(s):  
Aerodynamic Drag ◽  
Optimization Methods ◽  
Linear Quadratic ◽  
New Approach ◽  
Guidance Law ◽  
Multiple Object ◽  
Flight Path Angle ◽  
Miss Distance ◽  
Guidance Laws ◽  
Mixed Framework

A new approach is designed to the guidance of rocket-propelled missile with multiple object constraints. It allows the rocket-propelled missile to reach its target with a close to zero falling angle at a least time-of-flight (TOF). Instead of deriving the optimum guidance law by a series of linear quadratic optimization methods which results in guidance laws being complex, the new guidance law adopts a mixed framework composed of a modified PN guidance command and a TOF guidance command. The modified PN guidance is designed based on measured state information including missile position, flight-path angle and acceleration, which yields zero-miss-distance and zero-falling-angle. The TOF guidance command is determined in quadratic multinomial with respect to TOF error that is estimated with missile velocity reduction due to aerodynamic drag. Simulation results are presented to show that the proposed guidance law performs favorably in multiple object constraints.

An LQ Approach to Active Control of Vibrations in Helicopters

1996 ◽  
Vol 118 (3) ◽  
pp. 482-488 ◽  
Author(s):  
Sergio Bittanti ◽  
Fabrizio Lorito ◽  
Silvia Strada
Keyword(s):  
Optimal Control ◽  
Active Control ◽  
Linear Quadratic ◽  
Control Effort ◽  
Vibration Effect ◽  
Suitable Definition ◽  
Lq Optimal Control ◽  
The One ◽  
Definition Of ◽  
And Control

In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

scholarly journals Cooperative Guidance of Seeker-Less Missiles for Precise Hit

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Jianbo Zhao ◽  
Fenfen Xiong
Keyword(s):  
Linear Quadratic ◽  
Control Cost ◽  
Proportional Navigation ◽  
Two Stage ◽  
Maximum Acceleration ◽  
Linear Quadratic Optimal Control ◽  
Position Information ◽  
Precise Position ◽  
Guidance Law ◽  
Cooperative Guidance

A novel cooperative guidance scenario is proposed that implements fire-and-forget attacks for seeker-less missiles with a cheap finder for stationary targets and without requiring real-time communication among missiles or precise position information. Within the proposed cooperative scenario, the classic leader-follower framework is utilized, and a two-stage cooperative guidance law is derived for the seeker-less missile. Linear-quadratic optimal control and biased proportional navigation guidance (PNG) are employed to develop this two-stage cooperative guidance law to minimize the control cost in the first stage and to reduce the maximum acceleration command in the second stage when the acceleration command is continuous. Simulations and comparisons are conducted that demonstrate the effectiveness and advantages of the proposed guidance law.

scholarly journals Retraction notice

SIMULATION ◽  
2015 ◽  
Vol 91 (8) ◽  
pp. NP1-NP1 ◽  
Keyword(s):  
Differential Game ◽  
Linear Quadratic ◽  
Guidance Control ◽  
Guidance Law ◽  
Retraction Notice ◽  
Guidance Laws

At the request of the Editor(s) and the Publisher and author(s), the following article “Differential Game Guidance Law for a Kinetic Kill Vehicle and Its Simulation” by Xing-Yuan Xu, Xiao-Na Song and Yuan-Li Cai. Simulation, first published June 10, 2015, DOI 10.1177/0037549715588839 . has been retracted. The Editor has judged that the paper plagiarized the following article, and the authors have agreed to their paper being retracted: “Linear Quadratic Guidance Laws for Imposing a Terminal Intercept Angle” by Vitaly Shaferman and Tal Shima, Journal of Guidance, Control, and Dynamics, Vol. 31, No. 5, DOI 10.2514/1.32836.

Generalized optimal impact-angle-control guidance with terminal acceleration response constraint

2017 ◽  
Vol 231 (14) ◽  
pp. 2515-2536 ◽  
Author(s):  
Hui Wang ◽  
Jiang Wang ◽  
Defu Lin
Keyword(s):  
General Expression ◽  
Impact Angle ◽  
Acceleration Response ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Terminal Constraints ◽  
Miss Distance ◽  
Guidance Laws ◽  
Impact Angle Constraint

To study the optimal impact-angle-control guidance problem with multiple terminal constraints, a generalized optimal impact-angle-control guidance law with terminal acceleration response constraint (GOIACGL-TARC) is proposed. In the deriving, a time-to-go − nth power weighted object function is adopted to derived the GOIACGL-TARC and a general expression of GOIACGL-TARC is presented. Based on the general expression of GOIACGL-TARC, three guidance laws, GOIACGL-TARC1/TACC0/TACC1 are proposed and the inheritance relationship between GOIACGL-TACC0/TACC1/TARC1 and the conventional optimal guidance law with impact angle constraint is demonstrated. Performance analysis of the proposed guidance laws shows that in the case of GOIACGL-TACC0, the terminal acceleration is not zero at n = 0 and only as n > 0, the terminal acceleration converges to zero; in the case of GOIACGL-TACC1 and GOIACGL-TARC1, GOIACGL-TARC1 can guarantee the acceleration response to reach the exactly zero value but GOIACGL-TACC1 cannot, which can only guarantee the acceleration command to reach the exactly zero value. It is pointed out that compared with the biased proportional navigation guidance law, GOIACGL-TARC1 has an outstanding guidance performance in acceleration response, miss distance, and terminal impact angle error.

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.

Time-energy optimal guidance strategy for realistic interceptor using pseudospectral method

2020 ◽  
Vol 42 (13) ◽  
pp. 2361-2371 ◽  
Author(s):  
Arunava Banerjee ◽  
Mashuq Nabi ◽  
T. Raghunathan
Keyword(s):  
Optimal Control ◽  
Pseudospectral Method ◽  
Two Dimensional ◽  
Energy Usage ◽  
Proportional Navigation ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Legendre Pseudospectral Method ◽  
The Cost ◽  
Guidance Laws

This paper proposes the use of Legendre pseudospectral method (PSM) to obtain the optimal guidance strategy for a two-dimensional interceptor problem. An optimal control problem is formulated that addresses the conflicting objective of minimizing the energy usage, along with minimizing the time taken by missile to capture the target. The PSM-based guidance strategy is compared with other conventional guidance laws such as pure proportional navigation (PPN) guidance law and also evolutionary algorithm inspired differential evolution tuned proportional navigation (DEPN) guidance law. A scheme by which the PSM guidance strategy can be applied online is also included in this paper. The cost function value and the interception time indicates the superiority of the PSM-based guidance strategy.

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