This paper studies two pursuit-evasion problems under distance conditions in frame of differential game. In particular, a zero-sum differential game with the objective of distance and a nonzero-sum differential game with objective of both distance and azimuth adjustment are presented. The two players in the games are described by a nonlinear dynamics model subject to both speed and acceleration constraints in the two-dimensional plane. Instead of numerical solutions, the explicit equilibrium solutions of these two differential games are given under the condition that the distance between two players is larger than a certain value. Finally, the simulation results of these two differential games under typical cases demonstrate the effectiveness of our method.

In this paper, the attitude tracking and load relief control problems against wind disturbances and uncertain aerodynamics as well as the engine thrust of launch vehicles are studied. Firstly, a framework of Compensated Acceleration Feedback based Active Disturbance Rejection Control (CAF-ADRC) is established to achieve both desired attitude tracking and load relief performances. In particular, the total disturbance that includes the effects caused by both aero-coefficient perturbations and disturbances is estimated by constructing an Extended State Observer (ESO) to achieve attitude tracking. Furthermore, combined with the normal acceleration due to the engine thrust, the accelerometer measurement is also compensated to enhance the load relief effect. Secondly, the quantitative analysis of ESO and the entire closed-loop system are studied. It can be concluded that the desired attitude tracking and load relief performances can be achieved simultaneously under the proposed approach. Besides, tuning laws of the proposed approach are systematically given, which are divided into ESO, Proportional Derivative (PD) and Compensated Acceleration Feedback (CAF) modules. Moreover, the performances under CAF-ADRC approach can be better than those under CAF based PD (CAF-PD) approach by tuning load relief gain. Finally, the approach presented is applied to a typical control problem of launch vehicles with wind disturbances and parameter uncertainties.