Spectral identification of networks with inputs

We consider a network of interconnected dynamical systems. Spectral network identification consists in recovering the eigenvalues of the network Laplacian from the measurements of a very limited number (possibly one) of signals. These eigenvalues allow to deduce some global properties of the network, such as bounds on the node degree. Having recently introduced this approach for autonomous networks of nonlinear systems, we extend it here to treat networked systems with external inputs on the nodes, in the case of linear dynamics. This is more natural in several applications, and removes the need to sometimes use several independent trajectories. We illustrate our framework with several examples, where we estimate the mean, minimum, and maximum node degree in the network. Inferring some information on the leading Laplacian eigenvectors, we also use our framework in the context of network clustering.Comment: 8 page

Prediction error identification of linear dynamic networks with rank-reduced noise

Dynamic networks are interconnected dynamic systems with measured node signals and dynamic modules reflecting the links between the nodes. We address the problem of \red{identifying a dynamic network with known topology, on the basis of measured signals}, for the situation of additive process noise on the node signals that is spatially correlated and that is allowed to have a spectral density that is singular. A prediction error approach is followed in which all node signals in the network are jointly predicted. The resulting joint-direct identification method, generalizes the classical direct method for closed-loop identification to handle situations of mutually correlated noise on inputs and outputs. When applied to general dynamic networks with rank-reduced noise, it appears that the natural identification criterion becomes a weighted LS criterion that is subject to a constraint. This constrained criterion is shown to lead to maximum likelihood estimates of the dynamic network and therefore to minimum variance properties, reaching the Cramer-Rao lower bound in the case of Gaussian noise.Comment: 17 pages, 5 figures, revision submitted for publication in Automatica, 4 April 201

Network Reconstruction from Intrinsic Noise

This paper considers the problem of inferring an unknown network of dynamical systems driven by unknown, intrinsic, noise inputs. Equivalently we seek to identify direct causal dependencies among manifest variables only from observations of these variables. For linear, time-invariant systems of minimal order, we characterise under what conditions this problem is well posed. We first show that if the transfer matrix from the inputs to manifest states is minimum phase, this problem has a unique solution irrespective of the network topology. This is equivalent to there being only one valid spectral factor (up to a choice of signs of the inputs) of the output spectral density. If the assumption of phase-minimality is relaxed, we show that the problem is characterised by a single Algebraic Riccati Equation (ARE), of dimension determined by the number of latent states. The number of solutions to this ARE is an upper bound on the number of solutions for the network. We give necessary and sufficient conditions for any two dynamical networks to have equal output spectral density, which can be used to construct all equivalent networks. Extensive simulations quantify the number of solutions for a range of problem sizes. For a slightly simpler case, we also provide an algorithm to construct all equivalent networks from the output spectral density.Comment: 11 pages, submitted to IEEE Transactions on Automatic Contro

Local module identification in dynamic networks with correlated noise: the full input case

The identification of local modules in dynamic networks with known topology has recently been addressed by formulating conditions for arriving at consistent estimates of the module dynamics, typically under the assumption of having disturbances that are uncorrelated over the different nodes. The conditions typically reflect the selection of a set of node signals that are taken as predictor inputs in a MISO identification setup. In this paper an extension is made to arrive at an identification setup for the situation that process noises on the different node signals can be correlated with each other. In this situation the local module may need to be embedded in a MIMO identification setup for arriving at a consistent estimate with maximum likelihood properties. This requires the proper treatment of confounding variables. The result is an algorithm that, based on the given network topology and disturbance correlation structure, selects an appropriate set of node signals as predictor inputs and outputs in a MISO or MIMO identification setup. As a first step in the analysis, we restrict attention to the (slightly conservative) situation where the selected output node signals are predicted based on all of their in-neighbor node signals in the network.Comment: Extended version of paper submitted to the 58th IEEE Conf. Decision and Control, Nice, 201

System Identification of multi-rotor UAVs using echo state networks

Controller design for aircraft with unusual configurations presents unique challenges, particularly in extracting valid mathematical models of the MRUAVs behaviour. System Identification is a collection of techniques for extracting an accurate mathematical model of a dynamic system from experimental input-output data. This can entail parameter identification only (known as grey-box modelling) or more generally full parameter/structural identification of the nonlinear mapping (known as black-box). In this paper we propose a new method for black-box identification of the non-linear dynamic model of a small MRUAV using Echo State Networks (ESN), a novel approach to train Recurrent Neural Networks (RNN)

Identification of Invariant Sensorimotor Structures as a Prerequisite for the Discovery of Objects

Perceiving the surrounding environment in terms of objects is useful for any general purpose intelligent agent. In this paper, we investigate a fundamental mechanism making object perception possible, namely the identification of spatio-temporally invariant structures in the sensorimotor experience of an agent. We take inspiration from the Sensorimotor Contingencies Theory to define a computational model of this mechanism through a sensorimotor, unsupervised and predictive approach. Our model is based on processing the unsupervised interaction of an artificial agent with its environment. We show how spatio-temporally invariant structures in the environment induce regularities in the sensorimotor experience of an agent, and how this agent, while building a predictive model of its sensorimotor experience, can capture them as densely connected subgraphs in a graph of sensory states connected by motor commands. Our approach is focused on elementary mechanisms, and is illustrated with a set of simple experiments in which an agent interacts with an environment. We show how the agent can build an internal model of moving but spatio-temporally invariant structures by performing a Spectral Clustering of the graph modeling its overall sensorimotor experiences. We systematically examine properties of the model, shedding light more globally on the specificities of the paradigm with respect to methods based on the supervised processing of collections of static images.Comment: 24 pages, 10 figures, published in Frontiers Robotics and A

A Neural Network Method for Efficient Vegetation Mapping

This paper describes the application of a neural network method designed to improve the efficiency of map production from remote sensing data. Specifically, the ARTMAP neural network produces vegetation maps of the Sierra National Forest, in Northern California, using Landsat Thematic Mapper (TM) data. In addition to spectral values, the data set includes terrain and location information for each pixel. The maps produced by ARTMAP are of comparable accuracy to maps produced by a currently used method, which requires expert knowledge of the area as well as extensive manual editing. In fact, once field observations of vegetation classes had been collected for selected sites, ARTMAP took only a few hours to accomplish a mapping task that had previously taken many months. The ARTMAP network features fast on-line learning, so the system can be updated incrementally when new field observations arrive, without the need for retraining on the entire data set. In addition to maps that identify lifeform and Calveg species, ARTMAP produces confidence maps, which indicate where errors are most likely to occur and which can, therefore, be used to guide map editing