The results show that differential game can be transferred to the matrix form of the game,and players' equilibrium strategies can be solved simply through system dynamics simulation.

The mathematical thought reflected in these researches were, actually, different from modern Game theory, but, still, it showed the possibility of dealing with Game problems with mathematic tools, and meanwhile, the thought of differential game theory in the early time was included in these researches, which in a way inspired the establishment of Game theory.

Mathematical model using differential game theory for collision avoidance was formulated. The collision avoidance problem on urgent situation was converted into differential games problem.

Analysis Method for Nash Strategy of Linear Time Variant Quadratic Differential Game via Wavelets (Ⅱ) —Convergence of the Wavelet Approximation Solution

The numerical problem for the saddle point strategy of linear quadratic differential game is studied. A new method is proposed based on the multi scale multi resolution approximation feature of wavelets.

This paper studies the convergence problem of the wavelet approximation analysis method. For Nash strategy of linear time variant quadratic differential game, we prove that the wavelet approximation solution of Nash strategy converge to the accurate solution. The order of error estimation is given based on the multi_scale multi_resolution approximation feature of wavelets.

Genetic algorithm was also carried out to optimize guidance performance by using MATLAB.Third, this thesis thoroughly had also studied the three-dimensional differential game guidance law.

It is widely applied in various fields such as control theory and differential game theory, mathematic economics and decision theory, nonlinear optimal theory, biology mathematic, physics and topology, functional analysis, convex analysis and nonsmooth analysis, differential equation and differential inclusions and so on.

In the second case, taking the minimum of the terminal miss-distance and control energy consumption as the performance index, the optimal guidanc law has been derived from differential game theory. These optimal guidance laws have included the other guidance laws which didn't consider the blind area.

By using a two-person zero-sum differential game method, an adaptive control law is constructed basing on the combination of H ∞ robust control law and parameter estimate.

Based on the concept of two person zero sum differential game, the sufficient conditions for the existence of an H ∞ state feedback controller to guarantee the robust stability and disturbance attenuation level is obtained, and the solution is given in terms of Hamilton Jacobi Isaacs equation.

A differential game of pursuit of an evader by m dynamic pursuers under simple motion is studied.

A differential game with cost defined by the distance between the evader and his nearest pursuer at the game completion instant is studied.

On some sufficient conditions for optimality of the pursuit time in the differential game with multiple pursuers

Studies are made of continuous methods of the deviation in one differential game on the plane with a nonconvex terminal set.

The problem under study can serve as an example of the nondegenerate differential game with a nonconvex terminal set, in which the attempt fails to assure the deviation with the aid of feedback control methods described by continuous mappings.

In this paper, first of all, a brief history of the beginning and development of the differential games in the earlier stage is stated. Furthermore, as fundamental examples, a kind of two-person zero sum differential games and one of the qualitative differential games are presented, from which one can be more concretly to understand the properties of those researched in differential games.Some problems at present are also introduced, such as the games of pursuit in air-to-air combat,...

In this paper, first of all, a brief history of the beginning and development of the differential games in the earlier stage is stated. Furthermore, as fundamental examples, a kind of two-person zero sum differential games and one of the qualitative differential games are presented, from which one can be more concretly to understand the properties of those researched in differential games.Some problems at present are also introduced, such as the games of pursuit in air-to-air combat, the application of differential games in system engineering and the leader-follower strategy,the differential games with imperfect information , differential games with time lag , positional differential games, and the method of functional analysis in solving differential game problems, etc. Of course, these are not the all problems of today.More than 40 literatures are listed for further research.

In this paper a method of synthesis of optimal guidance law by use of differential games and by means of an example considered only kinematical factor of a missile and a target is presented. By using two approaches, in this paper, it is illustrated that in specifically case the result obtained can be reduced to 2-dimensional properlional navigation. Finally, from these results a formula for evaluation of the time for terminal control saturation of homing guide is also given.

An optimal guidance law which considers kinetic factors of missile and target via first order inertial loop in three dimensional space is studied on the basis of the theory of differential games. An optimal feedback guidance law is given in vector form, and the control rigidity parameter"k"is introduced into the feedback gain. The "k" is a scalar with determinate physical meaning. It represents responded characteristics and controllability of the system. Hence, in addition to being a function of time the...

An optimal guidance law which considers kinetic factors of missile and target via first order inertial loop in three dimensional space is studied on the basis of the theory of differential games. An optimal feedback guidance law is given in vector form, and the control rigidity parameter"k"is introduced into the feedback gain. The "k" is a scalar with determinate physical meaning. It represents responded characteristics and controllability of the system. Hence, in addition to being a function of time the feedback gain is related with the characteristics of the system. So it is possible to develop the certain relations of the feedback gain to other parameters such as Ts, Ks,ξs as well as H, M etc. by further studying on the parameter"k". Therefore, an improvement for the effect of the guidance law can be obtained, In other words, since the control rigidity"k" is introduced, a new synthesis mean is provided to the further studying on the guidance law.Finally, several problems are discussed in brief: first, the degeneration of the optimal guidance law proposed is discussed under certain conditions; then, for the convenience of realization, a suboptimal guidance law is given in finite rigidity case by means of further simplification; and also the controllability of the system is illustrated essentially. In addition, the case of ξ≠1 is considered in Appendix.