Optimization in an asymmetric Lanchester (n, 1) model

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. © The Author(s) 2019.