Distributed PI Control in Multi-Agent Systems: From Anti-Windup to Topology

Abstract: In this thesis, we study the impact of input saturation on multiagentsystems, which are controlled by the recently developed DAPI (DistributedAveraging Proportional Integral) control scheme. We are alsostudying modern anti-windup synthesis for these systems. Specically,we are constructing anti-windup compensators through a method thatminimizes an upper bound of the L2-gain globally for asymptotically stablecontrol systems. Both static and dynamic anti-windup compensatorsare constructed. Numerical examples of a water tank and a microgrid areconsidered. It is veried in simulations that the constructed compensatorssuccessfully prevent windup caused by actuator saturation, and that thedynamic compensator has better performance. The performance of thesecompensators are also compared with the classical anti-windup method,called back calculation.During our study of anti-windup compensators, we found a partiallyrelated problem, which is also included in the thesis. The problem is toarrange the edge weights in a multi-agent system such that the L2-gainis minimized. This problem does not include input saturation but theconnection is the minimization of an upper bound of the L2-gain and themulti-agent systems. For the considered class of multi-agent systems, weestablish a connection between the algebraic connectivity and an upperbound of the L2-gain.