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The time optimal pursuit-evasion-capture (PEC) game problem for two spacecraft with continuous constant thrust is studied, which is a typical and considerable game scenario in practice. Progressive Shooting Method (PSM) is proposed to solve the PEC game in this paper. The method solves the problem in two stages. First-shooting settles a simplified problem by substituting CW dynamics to simple dynamics, while second-shooting settles the original problem with the results of first-shooting. For first-shooting, an analytic initial guess construction method based on prior information is proposed, in which vague adjoint variables are expressed by quantities with clear physical meanings. Through qualitative analysis for the optimal trajectory, the quantities are approximately estimated and then analytic expressions of an initial guess are constructed. The proposed method provides an instructive way to deal with the difficulty that an initial guess is hard to provide for an optimal control problem based on indirect-method. Numerical results show that a PEC game can be solved by the proposed method with well convergence and high computational efficiency.

PurposeThe purpose of this paper is to examine the attitude control problem of a certain and big flexible satellite with unmodeled dynamics and unknown bounded disturbances and control input saturation; and to present a design method of robust adaptive controllers (RACs).Design/methodology/approachFirst, using the Lyapunov stability theory, it is shown that the proposed adaptive controller can guarantee the stability of the nonlinear system. Then, the parameters regulation method of the RAC is introduced. Finally, an RAC is designed for the object satellite model consisted of all the error‐source models.FindingsThe simulation results are compared with other results that are derived by using the typical PID controller. It is proved that the designed RAC has some properties of quickly response, high steady‐state precision and strong robustness.Originality/valueThe paper is of value in presenting a design method of RACs aiming at the object satellite with uncertainties and control input saturation.

A robust adaptive controller is presented for the control system of Inter-Satellite Linkage (ISL) antenna acquisition and tracking, which faces with the uncertainties of un-modeled dynamics and unbounded disturbance and the control input constraints. The stability is proved by using Lyapunov stabilization theory. The simulation results show that the robust adaptive controller can satisfy all the design requirements, especially the control accuracy is amazingly high contrast to the required accuracy. Furthermore, robust stability of the controller for un-modeled dynamics, uncertainties of parameters and the external disturbance was verified.