Topics in Cooperative Control.
PhD thesis, National University of Ireland Maynooth.
The main themes of this thesis are networked dynamic systems and related cooperative
control problems. We shall contribute a number of technical results to the stability theory
of switched positive systems, and present a new cooperative control paradigm that leads to
several cooperative control schemes which allow multi-agent systems to achieve a common
goal while, at the same time, satisfying certain local constraints. In this context, we also
discuss a number of practical applications for our results.
On a very abstract level, we first investigate the stability of an unforced dynamic system
or network that switches between different configurations. Next, a control input is included
to regulate the aggregate behaviour of the network. Lastly, looking at a particular instance
of this problem setting, an estimation component is added to the mix.
To be more specific, we first derive a number of necessary and sufficient, easily verifiable
conditions for the existence of common co-positive linear Lyapunov functions for switched
positive linear systems. This is particularly useful given the classic result that, roughly,
existence of such functions is sufficient for exponential stability of the switched system
under arbitrary switching. Such switched systems may represent a networked dynamic
system that switches between different configurations.
Next, we develop several cooperative control schemes for networked, dynamic multi-
agent systems. Several decentralised algorithms are devised that allow the network to
achieve what may be called implicit, constrained consensus: Constrained in the sense
that the aggregate behaviour of the network (assumed to be a function of the totality of its
states) should assume a prescribed value; implicit in the sense that the consensus is not
to be reached on the states directly, but on values that are a function of the states. This
can be used to assure inter-agent fairness in some sense, which makes this result relevant
to a large class of real-world problems. Initially, three algorithms will be given that work
in a variety of settings, including non-linear and uncertain settings, time-changing and
asymmetric network topologies, as well as asynchronous state updates. For these results,
the general assumption is that the aggregate behaviour of the network is made accessible to
each node so that it can be incorporated into the control algorithm.
Then, a somewhat more specific application is addressed, namely (algebraic) connec-
tivity control in wireless networks. This is a setting where the aggregate behaviour (the
network’s connectivity level, roughly an algebraic measure of how well information can
flow through the network) has to be estimated first before it can be regulated. To that end,
a fully decentralised scheme is developed that allows the connectivity level to be estimated
locally in each node. This estimate is then used to inform a decentralised scheme to adjust
the nodes’ interconnections in order to drive the network to the desired connectivity level.
Finally, three further real-world applications are discussed that rely on the results pre-
sented in this thesis.
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