Computationally Efficient Set-based Predictive Control for Grid-tied Inverters

This paper presents a fast gradient projection model predictive control algorithm based on a sequence of 1-step controllable sets for controlling a grid-tied converter with an LCL filter. The proposed method uses a set membership constraint on the first state, which ensures finite time convergence to the terminal set. To use the fast gradient projection method to solve the finite-time optimal control problem with state constraints, we adopted an approach where the set membership constraint is transformed into the corresponding input constraint as a function of the current state. In this way, no significant additional computational load was introduced, allowing the MPC algorithm to be solved efficiently.