Sum-Of-Norms MPC for Linear Periodic Systems with Application to Spacecraft Rendezvous

In this paper, an MPC solution is devised for linear time-periodic optimal regulation problems requiring the minimization of a sum of vector norms. Such type of problems arise for instance in aerospace applications, in which it is desired to trade-off fuel consumption and state regulation performance, while limiting as much as possible the control activation time. Closed-loop stability is guaranteed by embedding in the design a terminal set and a terminal cost, both of which are periodically time-varying. Differently from quadratic MPC, the terminal cost is in the form of a weighted 2-norm. A systematic method to construct such a function is presented. The proposed design is demonstrated on a spacecraft rendezvous case study with periodic dynamics.