Giacomo Innocenti

Dynamical phases of the Hindmarsh-Rose neuronal model: Studies of the transition from bursting to spiking chaos

The dynamical phases of the Hindmarsh-Rose neuronal model are analyzed in detail by varying the external current I. For increasing current values, the model exhibits a peculiar cascade of nonchaotic and chaotic period-adding bifurcations leading the system from the silent regime to a chaotic state dominated by bursting events. At higher I-values, this phase is substituted by a regime of continuous chaotic spiking and finally via an inverse period doubling cascade the system returns to silence. The analysis is focused on the transition between the two chaotic phases displayed by the model: one dominated by spiking dynamics and the other by bursts. At the transition an abrupt shrinking of the attractor size associated with a sharp peak in the maximal Lyapunov exponent is observable. However, the transition appears to be continuous and smoothed out over a finite current interval, where bursts and spikes coexist. The beginning of the transition (from the bursting side) is signaled from a structural modification in the interspike interval return map. This change in the map shape is associated with the disappearance of the family of solutions responsible for the onset of the bursting chaos. The successive passage from bursting to spiking chaos is associated with a progressive pruning of unstable long-lasting bursts.

Topological identification in networks of dynamical systems

The paper deals with the problem of reconstructing the tree-like topological structure of a network of linear dynamical systems. A distance function is defined in order to evaluate the “closeness” of two processes and some useful mathematical properties are derived. Theoretical results to guarantee the correctness of the identification procedure for networked linear systems characterized by a tree topology are provided as well. The paper also suggests the approximation of a complex connected network with a tree in order to detect the most meaningful interconnections. The application of the techniques to the analysis of an actual complex network, i.e., to high frequency time series of the stock market, is extensively illustrated.

On the dynamics of chaotic spiking-bursting transition in the Hindmarsh–Rose neuron

The paper considers the neuron model of Hindmarsh-Rose and studies in detail the system dynamics which controls the transition between the spiking and bursting regimes. In particular, such a passage occurs in a chaotic region and different explanations have been given in the literature to represent the process, generally based on a slow-fast decomposition of the neuron model. This paper proposes a novel view of the chaotic spiking-bursting transition exploiting the whole system dynamics and putting in evidence the essential role played in the phenomenon by the manifolds of the equilibrium point. An analytical approximation is developed for the related crucial elements and a subsequent numerical analysis signifies the properness of the suggested conjecture.

Appliance operation scheduling for electricity consumption optimization

This paper concerns the problem of optimally scheduling a set of appliances at the end-user premises. The users energy fee varies over time, and moreover, in the context of smart grids, the user may receive a reward from an energy aggregator if he/she reduces consumption during certain time intervals. In a household, the problem is to decide when to schedule the operation of the appliances, in order to meet a number of goals, namely overall costs, climatic comfort level and timeliness. We devise a model accounting for a typical household user, and present computational results showing that it can be efficiently solved in real-life instances.

Optimization models for consumer flexibility aggregation in smart grids: The ADDRESS approach

This paper addresses the problem of optimal management of consumer flexibility in an electric distribution system. Aggregation of a number of consumers clustered according to appropriate criteria, is one of the most promising approaches for modifying the daily load profile at nodes of an electric distribution network. Modifying the daily load profile is recognized as one of the strongest needs both for safe and efficient operation of the network. The paper proposes an optimization approach allowing the aggregator, i.e., the operator which manages the aggregated consumers, to gather flexibility and generate bids for the energy market, with the aim of maximizing its revenue. It is shown that this problem can be solved through mixed integer linear programming. Numerical simulation results are provided for validating the proposed approach.

Reduced complexity models in the identification of dynamical networks: Links with sparsification problems

In many applicative scenarios it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as economics, neuroscience and biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function operating a trade-off between accuracy and complexity in the final model. We address the problem of reducing the complexity by fixing a certain degree of sparsity, and trying to find the solution that ¿better¿ satisfies the constraints according to the criterion of approximation.

Lego-bike: A challenging robotic lab project to illustrate rapid prototyping in the mindstorms/simulink integrated platform

LEGO© Mindstorms is a widely spread affordable education robotic platform, that has recently gained native support from the Mathworks© simulation environment Simulink. The pros and cons of the integrated Mindstorms/Simulink framework are actually illustrated through a complex model based control design project featuring a self‐stabilized bicycle, that represents a proper example of the rapid prototyping capability of the platform. The importance of such an integration is discussed taking into account the history and the results of the LEGO‐based learning activities held at the Control Systems Laboratory of the University of Florence for graduate and undergraduate courses.

Brief paper: Modeling the topology of a dynamical network via Wiener filtering approach

The paper considers the problem of determining a suitable link structure for a set of networked interdependent processes, then providing a simplified description for their unknown underlying topology, also giving useful insights about their mutual influences. There are many scenarios where this problem has a prominent relevance. Indeed, it is often possible to measure the outputs of a large number of systems which are not independent, with no a priori knowledge of what the interconnections are. Examples can be found in fields as diverse as Economics, Biology, Ecology and Neural Sciences. The main idea of this work is to provide both a qualitative and quantitative description of the links among the processes in terms of modeling errors, assuming no a priori knowledge about the network features. To this aim, Wiener filtering and graph theory are exploited in a linear framework, in order to reconstruct a suitable connected and acyclic scheme for the internal connections of the whole system. Moreover, we show the consistency of the proposed technique, when the underlying network is actually connected and acyclic, proving that the structure obtained through the identification method coincides with the actual one and that this goal cannot be achieved via simple Wiener filtering. An application to real data illustrates the effectiveness of the suggested approach.

Pedestrian Dead Reckoning Based on Frequency Self-Synchronization and Body Kinematics

A novel pedestrian dead reckoning method conceived to be used with sensors freely positioned not too far from the waist level is presented. Attitude and heading reference systems already built in in nowadays inertial measurements units (IMUs) are exploited to cast the sampled data into a global reference coordinate system, where human gait analysis can be used to figure out the motion related to each single step. In particular, vertical accelerations are processed by means of a phase locked loop to detect the pace and the steps, and then the step length is computed exploiting an empirical piecewise linear relationship with the pace, while the geometrical features of the planar acceleration are used to estimate the stride heading, based on the waist kinematics. Experiments show the good results of the proposed algorithm when using both a low-cost IMU embedded in a smartphone and a more expensive stand-alone device, highlighting the method robustness with respect to the implementing hardware.

A Novel Dissipativity-Based Control for Inexact Nonlinearity Cancellation Problems

When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and then designing a linear controller for the remaining linear dynamics. By canceling the original nonlinearity via a first feedback loop, global linearization can be achieved. However, when the controller is not capable of exactly canceling the nonlinearity, such control strategy may provide unsatisfactory performance or even induce instability. Here, the interplay between accuracy of nonlinearity approximation, quality of state estimation, and robustness of linear controller is investigated and explicit conditions for stability are derived. An alternative controller design based on such conditions is proposed and its effectiveness is compared with standard methods on a benchmark system.