Aiming to solve the optimal control problem for the pursuit-evasion game with a space non-cooperative target under the condition of incomplete information, a new method degenerating the game into a strong tracking problem is proposed, where the unknown target maneuver is processed as colored noise. First, the relative motion is modeled in the rotating local vertical local horizontal (LVLH) frame originated at a virtual Chief based on the Hill-Clohessy-Wiltshire relative dynamics, while the measurement models for three different sensor schemes (i.e., single LOS (line-of-sight) sensor, LOS range sensor and double LOS sensor) are established and an extended Kalman Filter (EKF) is used to obtain the relative state of target. Next, under the assumption that the unknown maneuver of the target is colored noise, the game control law of chaser is derived based on the linear quadratic differential game theory. Furthermore, the optimal control law considering the thrust limitation is obtained. After that, the observability of the relative orbit state is analyzed, where the relative orbit is weakly observable in a short period of time in the case of only LOS angle measurements, fully observable in the cases of LOS range and double LOS measurement schemes. Finally, numerical simulations are conducted to verify the proposed method. The results show that by using the single LOS scheme, the chaser would firstly approach the target but then would lose the game because of the existence of the target’s unknown maneuver. Conversely, the chaser can successfully win the game in the cases of LOS range and double LOS sensor schemes.

Date of publication xxxx 00, 0000, date of current version xxxx 00, 0000.

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The stability of grid-connected inverters is very sensitive to varying grid impedance, especially in the weak grid condition. In this paper, based on the Lyapunov method and with the micro-grid impedance identification, an active damping adaptive control strategy is proposed to guarantee local asymptotic stability for an LCL inverter system. First, using the backstepping design and taking the state variable errors as new variables, an appropriate Lyapunov function is constructed, so that the asymptotic stability control law can be obtained. Then, with this asymptotic stability controller, taking the varying impedance into account, an adaptive controller is developed using the Lyapunov direct method. Hence, the controller presented here can assure asymptotic stability, the system performance can also be improved instantly according to the adaptive control, and the expected stability and performance can also be achieved. Finally, the feasibility of the proposed control strategy was verified via a simulation and an experiment.INDEX TERMS LCL grid-connected inverter, asymptotic stability, backstepping method, Lyapunov function

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