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Abnormal and Singular Solutions in the Target Guarding Problem with Dynamics

  • Matthew W. HarrisEmail author
Article
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Abstract

The topic of this paper is a two-player zero-sum differential game known as the target guarding problem. After a brief review of Isaacs’ original problem and solution, a problem with second-order dynamics and acceleration control is considered. It is shown that there are four solution classes satisfying the necessary conditions. The four classes are (i) abnormal and non-singular, (ii) normal and non-singular, (iii) normal and pursuer singular, (iv) normal and evader singular. The normal and totally singular case is ruled out. Closed-form solutions are provided for cases ii–iv. The order of singularity in all cases is infinite. Thus, the problem exhibits many interesting properties: normality, abnormality, non-singularity, infinite-order singularity, and non-uniqueness. A practical example of each class is provided.

Keywords

Abnormality Singularity Differential games Target guarding 

Notes

Acknowledgements

On the occasion of his retirement as editor of the Journal of Optimization Theory and Applications, I thank Dr. David G. Hull for his service to the journal and The University of Texas. More importantly, I thank him for his personal mentorship and friendship, and I wish him the best.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanical and Aerospace EngineeringUtah State UniversityLoganUSA

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