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Mathematical Problems in Engineering
Volume 2014, Article ID 481347, 7 pages
Research Article

Modeling and Optimal Control of a Class of Warfare Hybrid Dynamic Systems Based on Lanchester Attrition Model

1School of Sciences, Linyi University, Linyi, Shandong 276005, China
2School of Automobile Engineering, Linyi University, Linyi, Shandong 276005, China

Received 13 December 2013; Revised 2 March 2014; Accepted 4 March 2014; Published 3 April 2014

Academic Editor: Rongni Yang

Copyright © 2014 Xiangyong Chen and Ancai Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For the particularity of warfare hybrid dynamic process, a class of warfare hybrid dynamic systems is established based on Lanchester equation in a battle, where a heterogeneous force of different troop types faces a homogeneous force. This model can be characterized by the interaction of continuous-time models (governed by Lanchester equation), and discrete event systems (described by variable tactics). Furthermore, an expository discussion is presented on an optimal variable tactics control problem for warfare hybrid dynamic system. The optimal control strategies are designed based on dynamic programming and differential game theory. As an example of the consequences of this optimal control problem, we take the (2, 1) case and solve the optimal strategies in a (2, 1) case. Simulation results show the feasibility of warfare hybrid system model and the effectiveness of the optimal control strategies designed.