Gianfranco Parlangeli

Gianfranco Parlangeli, Giuseppe Notarstefano

In this paper we investigate the reachability and observability properties of a network system, running a Laplacian based average consensus algorithm, when the communication graph is a path or a cycle. More in detail, we provide necessary and sufficient conditions, based on simple algebraic rules from number theory, to characterize all and only the nodes from which the network system is reachable (respectively observable). Interesting immediate corollaries of our results are: (i) a path graph is reachable (observable) from any single node if and only if the number of nodes of the graph is a power of two, $n=2^i, i\in \natural$, and (ii) a cycle is reachable (observable) from any pair of nodes if and only if $n$ is a prime number. For any set of control (observation) nodes, we provide a closed form expression for the (unreachable) unobservable eigenvalues and for the eigenvectors of the (unreachable) unobservable subsystem.

Giovanni Indiveri, Gianfranco Parlangeli

The issue of single range based observability analysis and observer design for the kinematics model of a 3D vehicle subject to a constant unknown drift velocity is addressed. The proposed method departs from alternative solutions to the problem and leads to the definition of a linear time invariant state equation with a linear time varying output that can be used to globally solve the original nonlinear state estimation problem with a standard Kalman filter. Simple necessary and sufficient observability conditions are derived. Numerical simulation examples are described to illustrate the performance of the method.