• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.235-252
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• 2015

Optimal impact angle control guidance law and its variants for intercepting a maneuvering target are introduced in this paper. The linear quadratic(LQ) optimal control theory is reviewed first to setup framework of guidance law derivation, called the sweep method. As an example, the inversely weighted time-to-go energy optimal control problem to obtain the optimal impact angle control guidance law for a fixed target is solved via the sweep method. Since this optimal guidance law is not applicable for a moving target due to the angle mismatch at the impact instant, the law is modified to three different biased proportional navigation(PN) laws: the flight path angle control law, the line-of-sight(LOS) angle control law, and the relative flight path angle control law. Effectiveness of the guidance laws are verified via numerical simulations.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.3
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• pp.240-245
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• 2005

In this paper, planar waypoint guidance synthesis for UAVs using the LQ optimal impact-angle-control guidance law is proposed. We prove that the energy-optimal control problem with the constraint of passing through the waypoints is equivalent to the problem of finding the optimal pass angles on each waypoint of the optimal impact-angle-control law. The optimal pass angles can be obtained as a numerical solution of the simple pass angle optimization problem that requires neither input parameterization nor constraints. The trajectory obtained by applying the optimal impact-angle-control law with these optimal pass angles becomes energy optimal.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.289-303
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• 2015

In this paper, an optimal guidance law with terminal angle constraint considering the seeker's lock-on condition, in which the target is located within the field-of-view (FOV) and detection range limits at the end of the midcourse phase, is proposed. The optimal solution is obtained by solving an optimal control problem minimizing the energy cost function weighted by a power of range-to-go subject to the terminal constraints, which can shape the guidance commands and the missile trajectories adjusting guidance gains of the weighting function. The proposed guidance law can be applied to both of the midcourse and terminal phases by setting the desired relative range and look angle to the final interception conditions. The performance of the proposed guidance law is analyzed through nonlinear simulations for various engagement conditions.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.68 no.1
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• pp.172-181
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• 2019

This paper deals with the problem of generating the energy optimal trajectory which is intended to enhance the target tracking performance of a passive homing missile. Noticing that the essence of passive target tracking is the range estimation problem, the target information gathered by passive measurements can be readily analyzed by introducing the range estimator designed in line-of-sight(LOS) frame. Moreover, for the linear filter structure of the suggested range estimator, the cost function associated with the target information is clearly expressed as a function of the line-of-sight rate. Based on this idea, the optimal missile trajectory maximizing the target information is obtained by solving the saddle point problem for an indefinite quadratic cost which consists of the target information and the energy. It is shown that, different from the previous heuristic approaches, the guidance command producing the optimal passive homing trajectory is produced by the modified proportional navigation guidance law whose navigation constant is determined by the weighting coefficient for target information cost.

• Journal of the Korea Institute of Military Science and Technology
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• v.1 no.1
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• pp.211-218
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• 1998

As a part of trajectory modulation to increase system survivability and terminal effectiveness, impact angle control is required in the terminal phase of tactical missile systems. The missile systems are not allowed to have high altitude to reduce probability of detection by sensors of missile defense systems. In this paper, an analytic form of a time-optimal control law is suggested in the case of constrained missile maneuverability and impact angle under the assumption of a zero-lag autopilot. The control law is obtained by establishing optimal missile-target engagement geometry in the vertical plane. Extension of the law for missiles with autopilot response lags requiring a numerical solution is studied by introducing an iterative algorithm for optimal switching time determination of which the initial switching instants are obtained from the analytic solution. Also suggested is a closed-form impact angle control law derived by an energy-optimal approach. The performances of the proposed guidance laws are evaluated by a series of computer runs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.3
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• pp.271-287
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• 2015

In this article, a more generalized form of the impact time and angle control guidance law is proposed based on the linear quadratic optimal control methodology. For the purpose on controlling an additional constraint such as the impact time, we introduce an additional state variable that is defined to be the jerk (acceleration rate). Additionally, in order to provide an additional degree of freedom in choosing the guidance gains, the performance index that minimizes the control energy weighted by an arbitrary order of time-to-go is considered in this work. First, the generalized form of the impact angle control guidance law with an additional term which is used for the impact time control is derived. And then, we also determine the additional term in order to achieve the desired impact time. Through numbers of numerical simulations, we investigate the superiority of the proposed guidance law compared to previous guidance laws. In addition, a salvo attack scenario with multiple missile systems is also demonstrated.

• Proceedings of the KIEE Conference
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• 2002.11c
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• pp.122-125
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• 2002

The optimal guidance has advantages of accuracy and economic energy consumption but it is difficult to implement due to its dependence on the target information such as the relative range, the relative velocity and the acceleration of target. This paper uses optimal guidance and sliding-mode guidance to obtain a new guidance method. The suggested method shows robustness against target maneuvers, good dynamic performance, energy saving of missile and terminal accuracy. Its effectiveness is demonstrated by the simulation results.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.36 no.9
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• pp.884-890
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• 2008

A new guidance law to reach circular target area with grazing angle constraint is proposed as one of midcourse guidance laws of unmanned air vehicles. The purpose of the law is to control the grazing angle between the velocity vector of the vehicle and the line of sight to the aiming point, the center of the circular target area, when the vehicle passes any point on the circle. The optimal solution is derived based on the optimal control theory minimizing a range weighted control energy subject to the nonlinear dynamic equations of the vehicle approaching to the circular target area with grazing angle constraint. The major properties including a convergence of the solution are examined and the performance of the law applied to some typical scenarios is shown by the numerical simulation.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.590-595
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• 1992

An integrated guidance scheme for guided weapon system is described in this paper. Against conventional guidance methods, this method combines an autopilot and a guidance law. The controller is designed using LQ regulator whose performance index is different from other optimal guidance laws. Since dynamics of the system is considered in the derivation, the controller performance is improved. By simulation, the suggested method shows better performance in minimum distance sense than conventional guidance schemes such as Bang Bang guidance or Pursuit Guidance. Since the suggested method provides smooth rudder deflection in contrast to the conventional method, the load on a energy source of the system can be greatly lessened.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.37 no.11
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• pp.1104-1111
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• 2009

In the low altitude, mission of the aircraft is restricted by a variety of threats such as anti-air missiles and terrain obstacles. Especially, aircraft have always a risk of ground collision near terrain. In this study, to effectively solve this problem, we developed the flight path generation algorithm that is considered the terrain avoidance. In this flight path generation algorithm, waypoints that should be passed by the UAV are selected first. The waypoints are located in the middle of the terrain obstacles. Then, physically meaningful waypoints sets are classified by Dijkstra algorithm. The optimal waypoint guidance law based on the optimal control theory is applied to produce trajectory candidates. And finally the minimum control energy trajectory is determined.