Control of Average and Deviation in Large-Scale Linear Networks

Abstract

This paper deals with the problem of controlling the average state of a large-scale linear network to a constant reference value. We design an output-feedback controller such that no information about state vector or system matrices is needed. For this controller to have arbitrary positive gains, it is sufficient that only a sign condition on system matrices should be satisfied. To assure that the states of the network are close to the average state, the problem of deviation minimization is solved in addition, using a novel extremum seeking algorithm.

Boundary Control for Stabilization of Large-Scale Networks through the Continuation Method

“…Essentially the same process can be applied to the equation ( 8) to get the PDE version. For every term in the summation in (8) we can write…”

“…Taking high orders of continuation in ( 16) gives a highorder PDE which is difficult to work with. Thus it makes sense to take the smallest order which provides preservation of stability properties of (8). Having in mind the discussion above, in this paper we will use d = 2, restricting our analysis only to the systems for which c 2 > 0 such that instability is not artificially introduced.…”

“…Note that ( 22) is a space-dependent multidimensional generalization of (8). Also we assume that ghost cells are added to the system (22) to ensure boundary conditions as in Section IV.…”

“…Mostly, the methods of network analysis "forget" information about positions, relying only on interaction topology. Among examples of methods of this type, there is model reduction, in particular clustering of the original network depending on the topology [5], [6] or reduction towards the average state [7], [8].…”

A Continuation Method for Large-Scale Modeling and Control: from ODEs to PDE, a Round Trip

“…Probably the most known approach of this type is a model reduction technique which transforms a network into a smaller one while conserving the properties and the dynamics, see [5], [6]. Also the reduction towards the average state was studied in [7], [8].…”