Modeling and Optimal Control of a Class of Warfare Hybrid Dynamic Systems Based on Lanchester (n, 1) Attrition Model

For the particularity of warfare hybrid dynamic process, a class of warfare hybrid dynamic systems is established based on Lanchester equation in a (n, 1) battle, where a heterogeneous force of n 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.