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.

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.

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.

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.

Trajectory shaping guidance law design using constraint-combining multiplier

2021 ◽  
pp. 095441002098637
Author(s):  
Min-Guk Seo ◽  
Chang-Hun Lee ◽  
Tae-Hun Kim
Keyword(s):  
Design Method ◽  
Impact Angle ◽  
State Variables ◽  
Flight Trajectory ◽  
Potential Significance ◽  
Guidance Law ◽  
Terminal Constraints ◽  
The Impact ◽  
Guidance Laws ◽  
Impact Angle Constraint

A new design method for trajectory shaping guidance laws with the impact angle constraint is proposed in this study. The basic idea is that the multiplier introduced to combine the equations for the terminal constraints is used to shape a flight trajectory as desired. To this end, the general form of impact angle control guidance (IACG) is first derived as a function of an arbitrary constraint-combining multiplier using the optimal control. We reveal that the constraint-combining multiplier satisfying the kinematics can be expressed as a function of state variables. From this result, the constraint-combining multiplier to achieve a desired trajectory can be obtained. Accordingly, when the desired trajectory is designed to satisfy the terminal constraints, the proposed method directly can provide a closed form of IACG laws that can achieve the desired trajectory. The potential significance of the proposed result is that various trajectory shaping IACG laws that can cope with various guidance goals can be readily determined compared to existing approaches. In this study, several examples are shown to validate the proposed method. The results also indicate that previous IACG laws belong to the subset of the proposed result. Finally, the characteristics of the proposed guidance laws are analyzed through numerical simulations.

scholarly journals Suboptimal Regulation of a Class of Bilinear Interconnected Systems with Finite-Time Sliding Planning Horizons

2008 ◽  
Vol 2008 ◽  
pp. 1-26 ◽  
Author(s):  
M. de la Sen ◽  
Aitor J. Garrido ◽  
J. C. Soto ◽  
O. Barambones ◽  
I. Garrido
Keyword(s):  
Control Law ◽  
State Variables ◽  
Linear Quadratic ◽  
Equivalent Representation ◽  
Quadratic Performance Index ◽  
Matrix Sequence ◽  
Control Scheme ◽  
Quadratic Performance ◽  
System Equations ◽  
Riccati Matrix

This paper focuses on the suboptimization of a class of multivariable discrete-time bilinear systems consisting of interconnected bilinear subsystems with respect to a linear quadratic optimal regulation criterion which involves the use of state weighting terms only. Conditions which ensure the controllability of the overall system are given as a previous requirement for optimization. Three transformations of variables are made on the system equations in order to implement the scheme on an equivalent linear system. This leads to an equivalent representation of the used quadratic performance index that involves the appearance of quadratic weighting terms related to both transformed input and state variables. In this way, a Riccati-matrix sequence, allowing the synthesis of a standard feedback control law, is obtained. Finally, the proposed control scheme is tested on realistic examples.

Design and Instruction Solution of an Optimal Guidance Law for Ship-Air Missile beyond Visual Range

2012 ◽  
Vol 433-440 ◽  
pp. 3831-3836
Author(s):  
Yong Tao Zhao ◽  
Yun An Hu
Keyword(s):  
Control Variable ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Guidance Law ◽  
The Earth ◽  
Optimal Guidance ◽  
Quadratic Optimal Control ◽  
Simulation Results ◽  
Visual Range ◽  
Terminal Guidance

For the case of ship-air missile intercepting the low target beyond visual range by ship-ship coordination, the instruction solution model was presented and an optimal guidance law was designed considering the effect of the curvature of the earth. In the midcourse and terminal guidance segment, the optimal guidance law was designed through applying the concept of the pseudo control variable and the theory of the linear quadratic optimal control. The information of the target was described in the launch coordinates through coordinate transformation to realize the instruction solution for the designed guidance law. The simulation results show that the model of the instruction solution is correct and the designed guidance law is feasible.

scholarly journals Evasion-Pursuit Strategy against Defended Aircraft Based on Differential Game Theory

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Qilong Sun ◽  
Minghui Shen ◽  
Xiaolong Gu ◽  
Kang Hou ◽  
Naiming Qi
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Optimal Strategies ◽  
Open Loop ◽  
Active Defense ◽  
Guidance Law ◽  
Optimal Guidance ◽  
Differential Game Theory ◽  
One To One ◽  
The One

The active defense scenario in which the attacker evades from the defender and pursues the target is investigated. In this scenario, the target evades from the attacker, and the defender intercepts the attacker by using the optimal strategies. The evasion and the pursuit boundaries are investigated for the attacker when the three players use the one-to-one optimal guidance laws, which are derived based on differential game theory. It is difficult for the attacker to accomplish the task by using the one-to-one optimal guidance law; thus, a new guidance law is derived. Unlike other papers, in this paper, the accelerations of the target and the defender are unknown to the attacker. The new strategy is derived by linearizing the model along the initial line of sight, and it is obtained based on the open-loop solution form as the closed-loop problem is hard to solve. The results of the guidance performance for the derived guidance law are presented by numerical simulations, and it shows that the attacker can evade the defender and intercept the target successfully by using the proposed strategy.

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.

Biased optimal guidance law with specified velocity rendezvous angle constraint

2015 ◽  
Vol 119 (1220) ◽  
pp. 1287-1299 ◽  
Author(s):  
X. Xu ◽  
Y. Liang
Keyword(s):  
High Speed ◽  
Terminal Phase ◽  
Maneuvering Target ◽  
Guidance Law ◽  
Terminal Time ◽  
Optimal Guidance ◽  
Simulation Results ◽  
Miss Distance ◽  
Simplified Mathematical Model ◽  
Distance Setting

Abstract In order to increase the effectiveness of interceptor missile, velocity rendezvous angle control is required in the terminal phase. The purpose of this paper is to obtain an optimal guidance law which can achieve specified velocity rendezvous angle as well as zero terminal miss distance. A biased optimal guidance law based on a simplified mathematical model is deduced for interceptors engaging against invasion aircraft. Different from previous literatures on this issue, the presented guidance law suitable for intercepting high-speed maneuvering target. Another advantage is, under centimeter level miss distance setting, the guidance law needs smaller guidance command near the terminal time, which can successfully avoid command saturation. Simulation results demonstrate the effectiveness of the presented guidance law.

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.

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