Reduced-complexity interpolating control with periodic invariant sets

A low-complexity interpolating control scheme based on the concept of periodic invariance is proposed. Periodic invariance allows the state trajectory to leave the controllable invariant set temporarily but return into the set in a finite number of steps. A periodic set with easy representation is considered to reduce the expensive computation of the controllable invariant set. Since this set is not a traditional invariant set, a vertex reachability problem of target sets is solved off-line for each vertex of the set and provides a contractive control sequence that steers the system state back into the original set. Online, the periodic interpolating control (pIC) scheme allows to transition between such periodic invariant sets and an inner set endorsed with positive invariance properties. Proofs of recursive feasibility and asymptotic stability of the pIC are given. A numerical example demonstrates that pIC provides similar performance compared to more expensive optimisation-based schemes.