Year: 2011
Type: dissertation
Abstract: The main themes of this thesis are networked dynamic systems and related cooperative\ncontrol problems. We shall contribute a number of technical results to the stability theory\nof switched positive systems, and present a new cooperative control paradigm that leads to\nseveral cooperative control schemes which allow multi-agent systems to achieve a common\ngoal while, at the same time, satisfying certain local constraints. In this context, we also\ndiscuss a number of practical applications for our results.\nOn a very abstract level, we first investigate the stability of an unforced dynamic system\nor network that switches between different configurations. Next, a control input is included\nto regulate the aggregate behaviour of the network. Lastly, looking at a particular instance\nof this problem setting, an estimation component is added to the mix.\nTo be more specific, we first derive a number of necessary and sufficient, easily verifiable\nconditions for the existence of common co-positive linear Lyapunov functions for switched\npositive linear systems. This is particularly useful given the classic result that, roughly,\nexistence of such functions is sufficient for exponential stability of the switched system\nunder arbitrary switching. Such switched systems may represent a networked dynamic\nsystem that switches between different configurations.\nNext, we develop several cooperative control schemes for networked, dynamic multi-\nagent systems. Several decentralised algorithms are devised that allow the network to\nachieve what may be called implicit, constrained consensus: Constrained in the sense\nthat the aggregate behaviour of the network (assumed to be a function of the totality of its\nstates) should assume a prescribed value; implicit in the sense that the consensus is not\nto be reached on the states directly, but on values that are a function of the states. This\ncan be used to assure inter-agent fairness in some sense, which makes this result relevant\nto a large class of real-world problems. Initially, three algorithms will be given that work\nin a variety of settings, including non-linear and uncertain settings, time-changing and\nasymmetric network topologies, as well as asynchronous state updates. For these results,\nthe general assumption is that the aggregate behaviour of the network is made accessible to\neach node so that it can be incorporated into the control algorithm.\nThen, a somewhat more specific application is addressed, namely (algebraic) connec-\ntivity control in wireless networks. This is a setting where the aggregate behaviour (the\nnetwork’s connectivity level, roughly an algebraic measure of how well information can\nflow through the network) has to be estimated first before it can be regulated. To that end,\na fully decentralised scheme is developed that allows the connectivity level to be estimated\nlocally in each node. This estimate is then used to inform a decentralised scheme to adjust\nthe nodes’ interconnections in order to drive the network to the desired connectivity level.\nFinally, three further real-world applications are discussed that rely on the results pre-\nsented in this thesis.
Author: Florian Knorn
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1040735863