Tube-based stochastic model predictive control for spacecraft close proximity under external uncertainty

In this work, we present a tube-based stochastic model predictive control (SMPC) method for nonlinear discrete-time systems subject to unbounded disturbances. The covariance-based probability invariant set (PIS) is formulated by an affine feedback law determined online. The nonlinear chance constraint is first approximated by linear form and then recursively tightened as the optimization algorithm converges. The solution to the original stochastic optimal control problem in tube SMPC is generated by successively solving a series of deterministic semi-definite cone programs. Besides, the recursive feasibility for tube SMPC is established with mild assumption. The efficiency of algorithm is verified by an experiment on six degree of freedom (DOF) spacecraft close proximity under external disturbances.