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REFERENCE LINKING PLATFORM OF KOREA S&T JOURNALS
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Journal of the Korea Society for Industrial and Applied Mathematics
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The Korean Society for Industrial and Applied Mathematics
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Volume & Issues
Volume 19, Issue 4 - Dec 2015
Volume 19, Issue 3 - Sep 2015
Volume 19, Issue 2 - Jun 2015
Volume 19, Issue 1 - Mar 2015
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A TUTORIAL ON LINEAR QUADRATIC OPTIMAL GUIDANCE FOR MISSILE APPLICATIONS
TAHK, MIN-JEA ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 217~234
DOI : 10.12941/jksiam.2015.19.217
In this tutorial the theoretical background of LQ optimal guidance is reviewed, starting from calculus of variations. LQ optimal control is then introduced and applied to missile guidance to obtain the basic form of LQ optimal guidance laws. Extension of LQ optimal guidance methodology for handling weighted cost function, dynamic lag associated with the missile dynamics and the autopilot, constrained impact angle, and constrained impact time is also described with a brief discussion on the asymptotic properties of the optimal guidance laws. Furthermore, an introduction to polynomial guidance and generalized impactangle-control guidance, which are closed related with LQ optimal guidance, is provided to demonstrate the current status of missile guidance techniques.
OPTIMAL IMPACT ANGLE CONTROL GUIDANCE LAWS AGAINST A MANEUVERING TARGET
RYOO, CHANG-KYUNG ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 235~252
DOI : 10.12941/jksiam.2015.19.235
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.
IMPACT-TIME-CONTROL GUIDANCE LAWS FOR COOPERATIVE ATTACK OF MULTIPLE MISSILES
JEON, IN-SOO ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 253~270
DOI : 10.12941/jksiam.2015.19.253
Two major simultaneous attack strategies have been introduced, as one of cooperative attack of multiple missiles. One strategy is an undesignated time attack, in which the missiles communicate among themselves to synchronize the arrival times by reducing the mutual differences of times-to-go of multiple missiles during the homing. The other is a designated time attack, in which a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. For this individual homing, Impact-Time-Control Guidance (ITCG) law is required. After introducing cooperative proportional navigation (CPN) for the first strategy, this article presents a new closed-form ITCG guidance solution for the second strategy. It is based on the linear formulation, employing base trajectories driven by PNG with various navigation constants. Nonlinear simulation of several engagement situations demonstrates the performance and feasibility of the proposed ITCG law.
GUIDANCE LAW FOR IMPACT TIME AND ANGLE CONTROL WITH CONTROL COMMAND RESHAPING
LEE, JIN-IK ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 271~287
DOI : 10.12941/jksiam.2015.19.271
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.
OPTIMAL IMPACT ANGLE CONSTRAINED GUIDANCE WITH THE SEEKER`S LOCK-ON CONDITION
PARK, BONG-GYUN ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 289~303
DOI : 10.12941/jksiam.2015.19.289
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.
POLYNOMIAL FUNCTION BASED GUIDANCE FOR IMPACT ANGLE AND TIME CONTROL
KIM, TAE-HUN ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 305~325
DOI : 10.12941/jksiam.2015.19.305
In this paper, missile homing guidance laws to control the impact angle and time are proposed based on the polynomial function. To derive the guidance commands, we first assume that the acceleration command profile can be represented as a polynomial function with unknown coefficients. After that, the unknown coefficients are determined to achieve the given terminal constrains. Using the determined coefficients, we can finally obtain the state feedback guidance command. The suggested approach to design the guidance laws is simple and provides the more generalized optimal solutions of the impact angle and time control guidance.
ANALYSIS ON GENERALIZED IMPACT ANGLE CONTROL GUIDANCE LAW
LEE, YONG-IN ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 327~364
DOI : 10.12941/jksiam.2015.19.327
In this paper, a generalized guidance law with an arbitrary pair of guidance coefficients for impact angle control is proposed. Under the assumptions of a stationary target and a lag-free missile with constant speed, necessary conditions for the guidance coefficients to satisfy the required terminal constraints are obtained by deriving an explicit closed-form solution. Moreover, optimality of the generalized impact-angle control guidance law is discussed. By solving an inverse optimal control problem for the guidance law, it is found that the generalized guidance law can minimize a certain quadratic performance index. Finally, analytic solutions of the generalized guidance law for a first-order lag system are investigated. By solving a third-order linear time-varying ordinary differential equation, the blowing-up phenomenon of the guidance loop as the missile approaches the target is mathematically proved. Moreover, it is found that terminal misses due to the system lag are expressed in terms of the guidance coefficients, homing geometry, and the ratio of time-to-go to system time constant.
LINEAR QUADRATIC OPTIMAL GUIDANCE WITH ARBITRARY WEIGHTING FUNCTIONS
LEE, CHANG-HUN ;
Journal of the Korea Society for Industrial and Applied Mathematics, volume 19, issue 3, 2015, Pages 365~386
DOI : 10.12941/jksiam.2015.19.365
In this article, the linear quadratic (LQ) optimal guidance laws with arbitrary weighting functions are introduced. The optimal guidance problems in conjunction with the control effort weighed by arbitrary functions are formulated, and then the general solutions of these problems are determined. Based on these investigations, we can know a lot of previous optimal guidance laws belong to the proposed results. Additionally, the proposed results are compared with other results from the generalization standpoint. The potential importance on the proposed results is that a lot of useful new guidance laws providing their outstanding performance compared with existing works can be designed by choosing weighting functions properly. Accordingly, a new optimal guidance law is derived based on the proposed results as an illustrative example.