On Problems Of Warfare Command Decision Making And Game Based On Lanchester Equations

Warfare command decision making and game problems are the core of the science of armed forces command and control. From the view point of quantitative analysis, Lanchester equation, which can be considered as the first mathematical equation to de-scribe and forecast quantitatively the development process and trend of battle, has become one of the most widely used methods to research warfare command decision making and game problems. Research on warfare command problems based on Lanchester equation also become one important branch of the military strategy and system engineering, and it opened up a new field for researching the war with the modern mathematical methods. Therefore, the investigations of decision making and game problems for warfare systems based on Lanchester equations have important theoretical and practical significance.This dissertation focuses on warfare command control strategy design for several classes of warfare systems based on Lanchester equations. By using the method of dif-ferential game, nonlinear optimization technologies and the related important principles and methods, some optimal strategies for winning and some optimal control strategies are designed respectively, and the detailed design procedures of control alternatives are provided. Numerical examples and simulations illustrate the advantages and effectiveness of the proposed approaches. The main contents of this dissertation are composed of the following five parts:Firstly, the warfare command decision making problem for winning is addressed, when the total combat capability of the attacking side is not superior to the defending side. For this problem, the warfare systems are established based on Lanchester equation, and the corresponding warfare command stratagems, which can transform the battlefield situation, are proposed and analyzed quantitatively by considering the influence of warfare information factor. The application examples in military conflicts show the feasibility and effectiveness of the proposed model and the warfare command stratagems for winning. The research results may provide a theoretical reference for warfare command decision making.Secondly, for a class of warfare systems with the reinforcements, the optimal deci-sion making problems for winning is discussed. The definitions of the empty type winning strategy and non-empty type winning strategy are proposed based on a defined winning theory of warfare systems. By means of Lanchester equation, the sufficient conditions of the existence of two warfare strategies are presented. Nonlinear optimization technology is used to solve the corresponding optimal decision making problems for winner, and the optimal warfare strategies are obtained. It not only ensures that the victory of the decision maker in conflicts, but also the maximum value of index performance is obtained. Finally, numerical examples show the feasibility of the proposed optimal winning strategies.Thirdly, the warfare command game problem for determining the optimal reinforce-ment strategies between two opposing forces in military conflicts is investigated. Under some moderate tactics assumptions, an optimization model is established to solve the game problem based on Lanchester square law equation. By applying the optimal control and differential game theory, an optimum condition is presented. Furthermore, a practical method is developed to obtain the optimal reinforcement strategies. Finally, an appli-cation example is included to demonstrate the feasibility and effectiveness of the game model and the approach.Fourthly, considering the particularity of operational hybrid dynamic process, a class of corresponding warfare hybrid dynamic systems is established using Lanchester equa-tion. Under some reasonable assumptions, the problem of building the optimal variable tactics of warfare hybrid dynamic system is investigated, and its solving method is given based on differential game theory. Finally, a numerical example shows the feasibility of warfare hybrid system and the effectiveness of the solving method of optimal variable tactics problem.Fifthly, considering the particularity of operational hybrid dynamic process, the problem of building the optimal control of warfare hybrid dynamic system is investigated on the condition of fixed variable tactics sequences, and its solving method is given based on dynamic programming principle and differential game theory. Finally, a numerical ex-ample shows the feasibility of warfare hybrid system and the effectiveness of the optimal control strategies designed. The research results may provide theoretical reference for warfare command decision making and game.Finally, the results of the dissertation are summarized and further research topics are pointed out.