Time Optimal Closed-Loop Fuzzy-Control St rategy for Nonlinear Lunar Lander Mission

In th is paper a closed-loop time-optimal con trol strategy for the non-lin ear lusuu: letuler mission is developed, generally, determination of closed-loop feedback control law is not usually feasible for many non-linear dynamic systems, in addition, there exist certain difficulties associated with the numericaldetermination of open-loop optimal control solution for non-lin ear systems , such as slow convergence rate and high sensitivity to initial guesst imates, besides, if one manages to overcome th eseinherentdifficulties, the determined optimal control strategy will be in an open -loop form, and thus, fully dependent on the initial condition , obviously, in this way perturbations and noise processes unll ma ke the optimal trajectory deviate from its ideal predicted values in any actual operating enuironmeni. our study focuses on th e planar traj ectory andcontrol optimization of a lunar lander spacecraf t as a viable example of nonlin ear dynamic system, a fuzzy algorithm is augmented to our variational formulation of the problem in an attempt to create a closed-loop fuzzy guidance logic, the training process of the fuzzy system is greatly reduced throuqb. the in troduction of a set of states related non-dimensional variables, simulationresults indicate that the developed meth odology can be successfully ut ilized in other flight scenarios with good robustness to the actuator and measurment system noise.