Optimization of Planar Low-Thrust Orbit Transfer Maneuver via Fuzzy Optimal Control Approach

In this paper, minimum-time low-thrust planar orbit transfer problem is solved by fuzzy optimal control. Trajectory dynamic restricting assumptions and using analytical averaging method, the governing equations of orbit transfer problem in its desired form with constant acceleration magnitude is achieved. Then, using Euler discretization method, the whole differential dynamic equations, performance function and transversality conditions are represented in a discrete form. Calling membership function concept of fuzzy environment, this algorithm transfers classical optimal control including performance index and trajectory transversality conditions associated with uncertanities to fuzzy environment. Thereafter, introducing slack variables all the inequalities change to equality conditions. Applying Bellman-Zadeh approach, optimal control problem turns to parameter optimization problem which then is solved by Lagrange multipliers technique. Finally, solving the set of nonlinear algebraic equations made by optimality necessary conditions simultaneously is achieved by nonlinear programming method. Numerical fuzzy optimal control results are validated with available analytical results which show the priorities of this method in orbit transfer trajectory optimization in presence of uncertainities. FOC approach is categorized into direct methods for solving optimal control problems, while it is far from their defects e.g. curse of dimensionality and burdensome computational load so that it applies fuzzy approach and expert knowledge to simply solve the problems.