Computation of Least-Conservative State-Constraint Sets for Decentralized MPC with Dynamic and Constraint Coupling

We address the problem of synthesizing state-constraint sets for a fully decentralized Model Predictive Control (MPC) scheme. We consider linear time-invariant discrete time systems, with subsystems possibly coupled in both dynamics and state constraints. For each individual subsystem we employ a set-based framework to compute the state-constraint sets, that are used to synthesize local tube-based MPC controllers. The offline problem that computes the constraint sets explicitly ensures that the feasible regions of the MPC controllers are non-empty, and whenever the controllers are feasible, the overall system constraints are satisfied with the least conservativeness possible. We demonstrate the closed-loop performance of the decentralized scheme, assessed with respect to centralized MPC, using a numerical example.