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ANALYSIS ON GENERALIZED IMPACT ANGLE CONTROL GUIDANCE LAW 广义冲击角控制制导律分析
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.327
Yong-In Lee
{"title":"ANALYSIS ON GENERALIZED IMPACT ANGLE CONTROL GUIDANCE LAW","authors":"Yong-In Lee","doi":"10.12941/JKSIAM.2015.19.327","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.327","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"26 1","pages":"327-364"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86952850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
OPTIMAL IMPACT ANGLE CONTROL GUIDANCE LAWS AGAINST A MANEUVERING TARGET 针对机动目标的最优冲击角控制制导律
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.235
C. Ryoo
{"title":"OPTIMAL IMPACT ANGLE CONTROL GUIDANCE LAWS AGAINST A MANEUVERING TARGET","authors":"C. Ryoo","doi":"10.12941/JKSIAM.2015.19.235","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.235","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"36 1","pages":"235-252"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91291242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
LINEAR QUADRATIC OPTIMAL GUIDANCE WITH ARBITRARY WEIGHTING FUNCTIONS 具有任意加权函数的线性二次最优制导
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.365
Chang-hun Lee
{"title":"LINEAR QUADRATIC OPTIMAL GUIDANCE WITH ARBITRARY WEIGHTING FUNCTIONS","authors":"Chang-hun Lee","doi":"10.12941/JKSIAM.2015.19.365","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.365","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"53 1 1","pages":"365-386"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89099736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
POLYNOMIAL FUNCTION BASED GUIDANCE FOR IMPACT ANGLE AND TIME CONTROL 基于多项式函数的冲击角制导与时间控制
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.305
Tae-Hun Kim
{"title":"POLYNOMIAL FUNCTION BASED GUIDANCE FOR IMPACT ANGLE AND TIME CONTROL","authors":"Tae-Hun Kim","doi":"10.12941/JKSIAM.2015.19.305","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.305","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"70 1","pages":"305-325"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89169159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
GUIDANCE LAW FOR IMPACT TIME AND ANGLE CONTROL WITH CONTROL COMMAND RESHAPING 带控制命令整形的冲击时间和角度控制制导律
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.271
Jin-Ik Lee
{"title":"GUIDANCE LAW FOR IMPACT TIME AND ANGLE CONTROL WITH CONTROL COMMAND RESHAPING","authors":"Jin-Ik Lee","doi":"10.12941/JKSIAM.2015.19.271","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.271","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"5 1","pages":"271-287"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75475551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A TUTORIAL ON LINEAR QUADRATIC OPTIMAL GUIDANCE FOR MISSILE APPLICATIONS 关于导弹应用的线性二次最优制导的教程
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.217
M. Tahk
{"title":"A TUTORIAL ON LINEAR QUADRATIC OPTIMAL GUIDANCE FOR MISSILE APPLICATIONS","authors":"M. Tahk","doi":"10.12941/JKSIAM.2015.19.217","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.217","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"29 1","pages":"217-234"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75554624","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
IMPACT-TIME-CONTROL GUIDANCE LAWS FOR COOPERATIVE ATTACK OF MULTIPLE MISSILES 多导弹协同攻击的冲击时控制导律
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.253
In-Soo Jeon
{"title":"IMPACT-TIME-CONTROL GUIDANCE LAWS FOR COOPERATIVE ATTACK OF MULTIPLE MISSILES","authors":"In-Soo Jeon","doi":"10.12941/JKSIAM.2015.19.253","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.253","url":null,"abstract":"Two major simultaneous attack strategies have been introduced, as one of cooper- ative attack of multiple missiles. One strategy is an undesignated time attack, in which the mis- siles 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 coopera- tive 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, employ- ing 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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"46 1","pages":"253-270"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88726376","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
OPTIMAL IMPACT ANGLE CONSTRAINED GUIDANCE WITH THE SEEKER`S LOCK-ON CONDITION 导引头锁定条件下最优冲击角约束制导
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-09-25 DOI: 10.12941/JKSIAM.2015.19.289
Bong-Gyun Park
{"title":"OPTIMAL IMPACT ANGLE CONSTRAINED GUIDANCE WITH THE SEEKER`S LOCK-ON CONDITION","authors":"Bong-Gyun Park","doi":"10.12941/JKSIAM.2015.19.289","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.289","url":null,"abstract":"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.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"86 1","pages":"289-303"},"PeriodicalIF":0.6,"publicationDate":"2015-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90052249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
EFFICIENT LATTICE REDUCTION UPDATING AND DOWNDATING METHODS AND ANALYSIS 高效格约简更新和降龄方法及分析
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-06-25 DOI: 10.12941/JKSIAM.2015.19.171
Jaehyun Park, Y. Park
{"title":"EFFICIENT LATTICE REDUCTION UPDATING AND DOWNDATING METHODS AND ANALYSIS","authors":"Jaehyun Park, Y. Park","doi":"10.12941/JKSIAM.2015.19.171","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.171","url":null,"abstract":"In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov´asz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"1 1","pages":"171-188"},"PeriodicalIF":0.6,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72699824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
GLOBAL THRESHOLD DYNAMICS IN HUMORAL IMMUNITY VIRAL INFECTION MODELS INCLUDING AN ECLIPSE STAGE OF INFECTED CELLS 体液免疫病毒感染模型中的全局阈值动力学，包括感染细胞的蚀期
IF 0.6
Journal of the Korean Society for Industrial and Applied Mathematics Pub Date : 2015-06-25 DOI: 10.12941/JKSIAM.2015.19.137
A. Elaiw
{"title":"GLOBAL THRESHOLD DYNAMICS IN HUMORAL IMMUNITY VIRAL INFECTION MODELS INCLUDING AN ECLIPSE STAGE OF INFECTED CELLS","authors":"A. Elaiw","doi":"10.12941/JKSIAM.2015.19.137","DOIUrl":"https://doi.org/10.12941/JKSIAM.2015.19.137","url":null,"abstract":"In this paper, we propose and analyze three viral infection models with humoral immunity including an eclipse stage of infected cells. The incidence rate of infection is represented by bilinear incidence and saturated incidence in the first and second models, respectively, while it is given by a more general function in the third one. The neutralization rate of viruses is giv0en by bilinear form in the first two models, while it is given by a general function in the third one. For each model, we have derived two threshold parameters, the basic infection reproduction number which determines whether or not a chronic-infection can be established without humoral immunity and the humoral immune response activation number which determines whether or not a chronic-infection can be established with humoral immunity. By constructing suitable Lyapunov functions we have proven the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the threshold parameters and on the general functions which are sufficient for the global stability of the equilibria of the model. We have performed some numerical simulations for the third model with specific forms of the incidence and neutralization rates and have shown that the numerical results are consistent with the theoretical results.","PeriodicalId":41717,"journal":{"name":"Journal of the Korean Society for Industrial and Applied Mathematics","volume":"1 1","pages":"137-170"},"PeriodicalIF":0.6,"publicationDate":"2015-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80432797","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
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