Fuzzy Control for Spacecraft Orbit Transfer with Gain Perturbations and Input Constraint

This paper presents the problem of fuzzy guaranteed cost tracking control for spacecraft orbit transfer with parameter uncertainties and additive controller gain perturbations and subject to input constraints, and guaranteed cost function. The goal is to perform a planar orbit transfer in a circular orbit, focusing on minimizing fuel usage while accounting for uncertainties in both the plant and controller. Spacecraft dynamics is based on the Keplerian two-body problem using polar coordinates, which allows long-distance maneuvers in circular orbit when the well-known Clohessy-Wiltshire (C-W) equation is restricted by limited-distance maneuvers. To approximate the nonlinearities in the dynamical equation of motion, a Takagi-Sugeno (T-S) fuzzy model is proposed and a linearized model is established for the output tracking problem of the orbit transfer process. Issue related to the absence of a single equilibrium point in the nonlinear system, a gain-scheduling technique based on multiple operating points is employed to develop the (T-S) fuzzy model through the fuzzy approach. Based on the parallel distributed compensation (PDC) approach, sufficient conditions for a fuzzy non-fragile guaranteed cost control are derived. Using the Lyapunov theory, the controller objectives are formulated through linear matrix inequality (LMIs) which allows the system to be transferred into a convex optimization problem. The designed controller effectively accomplishes the orbit transfer process with minimal fuel consumption and maintains the performance level below a specified upper bound. Numerical simulations are conducted to demonstrate the effectiveness of the proposed method.