Michel Gevers

Julien M. Hendrickx, Michel Gevers, Alexandre S. Bazanella

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear transfer functions and are excited by known external excitation signals and/or unknown noise signals. A major research question concerns the identifiability of the whole network - topology and all transfer functions - from the measured node signals and external excitation signals. So far all results on this topic have assumed that all node signals are measured. This paper presents the first results for the situation where not all node signals are measurable, under the assumptions that (1) the topology of the network is known, and (2) each node is excited by a known external excitation. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. A practical outcome is that, under those assumptions, a network can often be identified using only a small subset of node measurements.

Michel Gevers, Alexandre Sanfelice Bazanella, Gian Vianna da Silva

We present a new and simple method for the identification of a single transfer function that is embedded in a dynamical network. In existing methods the consistent identification of the desired transfer function relies on the positive definiteness of the spectral density matrix of the vector of all node signals, and it typically requires knowledge of the topology of the whole network. The positivity condition is on the internal signals and therefore can not be guaranteed a priori, in addition it is far from necessary. The new method of this paper provides simple conditions on which nodes to excite and which nodes to measure in order to produce a consistent estimate of the desired transfer function. Just as importantly, it requires knowledge of the local topology only.

Alexander De Cock, Michel Gevers, Johan Schoukens

Optimal input design is an important step of the identification process in order to reduce the model variance. In this work a D-optimal input design method for finite-impulse-response-type nonlinear systems is presented. The optimization of the determinant of the Fisher information matrix is expressed as a convex optimization problem. This problem is then solved using a dispersion-based optimization scheme, which is easy to implement and converges monotonically to the optimal solution. Without constraints, the optimal design cannot be realized as a time sequence. By imposing that the design should lie in the subspace described by a symmetric and non-overlapping set, a realizable design is found. A graph-based method is used in order to find a time sequence that realizes this optimal constrained design. These methods are illustrated on a numerical example of which the results are thoroughly discussed. Additionally the computational speed of the algorithm is compared with the general convex optimizer cvx.

Alexandre S. Bazanella, Michel Gevers, Julien M. Hendrickx et al.

Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear time-invariant transfer functions and are possibly excited by known external excitation signals and/or unknown noise signals. So far all results on the identifiability of the whole network have assumed that all node signals are measured. Under this assumption, it has been shown that such networks are identifiable only if some prior knowledge is available about the structure of the network, in particular the structure of the excitation. In this paper we present the first results for the situation where not all node signals are measurable, under the assumptions that the topology of the network is known, that each node is excited by a known signal and that the nodes are noise-free. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. An important outcome of our research is that, under those assumptions, a network can often be identified using only a small subset of node measurements.