Cyber-Physical Systems

120 Cyber-Physical Systems: From Theory to Practice

quantity vector given the current one, or E(r[k +1]|r[k]). Specifically, we will view the stochastic

flow network as linear,ifE(r[k +1]|r[k]) is a purely linear function of r[k] for all k or equivalently

if E(r[k +1]|r[k]) = Q[k]r[k] for a fixed matrix Q[k] (which does not depend on r[k]) for each k.

Some remarks on linear stochastic flow networks are needed:

1. The condition for linearity does not require that the P[k] be independent of r[k], only that

the conditional mean of the next quantity vector is a linear function of the current one. One

example in Section 5.3.2 shows that even some dynamics ...