Decentralised Interpolating Control: A Periodic Invariance Approach

This paper presents a decentralised periodic interpolating control (dpIC) scheme for the constrained control of interconnected systems, which employs periodic invariance and vertex reachability of target sets. Periodic invariance allows the state of the system to leave a candidate set temporarily but return into the set in a finite number of steps. We consider a periodic invariant set with low-complexity (e.g. rectangle, hexagon for planar systems) to replace the expensive controllable invariant outer set. This set is defined within the controllable stabilising region of each subsystem and a reachability problem is solved off-line for each vertex of the outer set to provide an admissible control sequence that steers the system state back into the original target set after a finite number of steps. dpIC is effectuated between such periodic invariant sets for each subsystem and the local maximal admissible inner set by means of an inexpensive linear programming problem, which is solved on-line at the beginning of each periodic control sequence. dpIC is demonstrated on the problem of stabilising a platoon of vehicles. Copyright (C) 2020 The Authors.