Alexandre Sanfelici Bazanella

Eduardo Mapurunga, Alexandre Sanfelici Bazanella

In this work we evaluate the excitation and measurement patterns (EMP) for networks with tree topology. We investigate guidelines for the selection of the minimal EMPs, i.e. those with the least number of excited and measured nodes combined, for which the accuracy obtained, in terms of the trace of the asymptotic covariance matrix, is optimal. We introduce the concept of partial information matrix as a means to systematically obtain the information matrix for any dynamic network. For a specific tree class, called cross, we show that the accuracy of a particular module depends on the magnitude of the parameters to be estimated. Furthermore, when all factors are equal, it is best to excite. %we show that for small magnitudes of this parameter, it is best to excite. We extend a topological condition for branches under which the accuracy of a particular module of the network is independent of the other parameters from the tree. We provide a numerical analysis showing that our guidelines could be used as a selection tool for minimal EMPs for tree networks.

Alexandre Sanfelici Bazanella, Tristão Garcia

Ordinary differential equations (ODE's) are a cornerstone of systems and control theory. Accordingly, they are standard material in undergraduate programs in engineering and there is abundant didactic literature about this topic. Yet, the solution methods and formulas prescribed in this didactic literature are unclear about the assumptions behind their derivation and thus about the limits of their applicability. Specifically, smoothness of the input is rarely discussed, even though it is a critical property to define the character of the solutions and the validity of the methods and formulas prescribed. On the other hand, the relationships with the state space representation (SSR) of linear systems is absent from this same literature and only marginally discussed in more advanced texts. In this paper we detail these gaps left behind in the didactic literature, then we provide a formal delimitation of the boundaries of the standard solutions and methods for linear ODE's. Our analysis relies on some key properties of state space representations, so we establish the formal connections between ODEs and SSR's, defining an equivalence between the two that is absent in the literature and is of conceptual interest by itself.