Counter-terrorism is a global task that every nation is concerned about. To improve operations against terrorism, many nations carry out counter-terroristic operations not only by themselves but also in cooperation with other nations. In this paper, we propose an extended the Kaplan-Kress-Szechtman model to cope with multi-party counter-terrorism. The optimal control problem for this model is studied. Our main tool is Pontryagin’s maximal principle. The optimal intelligence level and individual reinforcement of each party are found. The numerical results show that counter-terrorism operations in cooperative models are more effective than that in single models.
CaulkinsJGrassDFeichtingerG, et al. Optimizing counter-terror operations: Should one fight fire with fire or water. Comput Oper Res2008; 35: 1874–1885.
2.
DeitchmanS.A Lanchester model of guerilla warfare. Oper Res1962; 10: 818–827.
3.
SchafferM.Lanchester models of guerrilla engagements. Oper Res1968; 16: 457–488.
4.
KressMSzechtmannR.Why defeating insurgencies is hard: the effect of intelligence in counter insurgency operations - a best case scenario. Oper Res2009; 57: 578–585.
5.
KaplanEHMintzAMishalS, et al. What happened to suicide bombings in Israel? Insights from a terror stock model. Stud Conflict Terror2005; 28: 225–235.
6.
TaylorJ.Lanchester-type models of warfare and optimal control. Nav Res Logist Q1974; 21: 70–106.
7.
LinKYMackayLJ.The optimal policy for the one-against-many heterogeneous Lanchester model. Oper Res Lett2014; 42: 473–477.
8.
ChenXJiangNJingY, et al. Differential game model and its solutions for force resource complementary via lanchester square law equation. Milan: International Federation of Automatic Control (IFAC), 2011.
9.
ChenXJiangNJingY, et al. Optimal control of a class of warfare dynamic systems based on Lanchester (2,2) attrition model. In: 27th Chinese control and decision conference (CCDC), China, 2015, pp.1263–1267. Piscataway, NJ: IEEE.
10.
FeichtingerGNovakAWrzaczekS. Optimizing counter-terroristic operations in an asymmetric Lanchester model. In: 15th IFAC workshop on control applications of optimization, Rimini, Italy, 13–16 September 2012. Amsterdam: Elsevier.
