Constrained Synchronization of Multi-Agent Systems Using Distributed MPC and Invariant Families of Terminal Sets

In this paper, we present a synchronizing DMPC scheme that employs two ingredients: (i) a cost function that penalizes the deviation of the MPC control input from an unconstrained synchronization control law based on algebraic graph theory and (ii) an invariant family of constraints admissible terminal sets for MASs in closed-loop with an unconstrained synchronization control law. We prove that the developed DMPC scheme with a shrinking prediction horizon guarantees finite-time controllability to a family of invariant terminal sets and recursive feasibility. Compared to existing LMI methods for computing a family of constraints admissible invariant sets, we reduce conservatism by exploiting specific graph properties common to MASs. The developed DMPC algorithm for achieving constrained synchronization is tested in different benchmark examples, including balancing capacitor voltages for modular multilevel converters and harmonic oscillators, yielding faster synchronization.