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Scale-Free Control for Complex Physical Network Systems

Periodic Reporting for period 4 - Scale-FreeBack (Scale-Free Control for Complex Physical Network Systems)

Reporting period: 2021-03-01 to 2022-08-31

Scale-FreeBack proposes a new paradigm by approaching the problem of control of large-scale complex systems with a new holistic vision, and novel design methods ensuring the scalability of the whole chain (modelling, observation, and control). For this purpose, we have first proposed appropriate scale-free dynamic modeling approaches breaking down the network system complexity, and then, based on such simplifications, to devise control algorithms specifically tailored for such models. Scale-free control refers here to the ability of a control algorithm to be easily scaled to system networks of arbitrary dimensions.

Scale-FreeBack takes advantage of the new opportunities presented by the latest large-scale sensing technologies to design scalable control algorithms applicable to a large class of large-scale cyber-physical interconnected networks. In addition to the purely theoretical aspects, the Scale-FreeBack team also came up with some innovative control solutions for improving traffic management, and epidemic spreading networks.

Scale-FreeBack has shown to go beyond traditional control approaches by first focusing on developing appropriate mathematical scale-free dynamic modeling approaches used for breaking down the complexity of network systems, and then building estimation and control algorithms specifically tailored to these models. We have applied and validate those algorithms and ideas to many systems of major important socio-economic interest including: predicting traffic systems, COVID spreading attenuation policies, synchronization of spintronic oscillators, and electromobility.
Scale-free modeling and aggregation. Here we deal with the problem of how to find a scale-free abstraction out of an arbitrary network and how to use this abstraction to benefit of the scale-free properties in term of control. We devised an algorithm, called MergeToScaleFree. It allows finding a partition of an arbitrary network resulting in a scale-free abstraction. This algorithm has been applied on large-scale networks such as the urban traffic network of Grenoble (20 000 nodes), and on a direct application of this algorithm in the context of epidemic spreading. Within the ERC, we have also explored several edges of the problem of modeling urban traffic networks: 2-D fluid macroscopic models for traffic models. Besides we developed a new boundary control design for large-scale urban traffic systems represented by an aggregated model PDE models. Finally, we have also validating of the 2D traffic models with real data coming from the GTL-ville experimental platform which is open to the general public http://gtlville.inrialpes.fr

State-state estimation over scale-free networks. Here we deal with the problem of estimating the average state of certain sectors in a large-scale network, but also its variance. The method has been applied to the problem of thermal monitoring of large buildings. This technique along with a simple on/off control policy for regulation saves around 25.32% of the energy.

We have devised a new method for on-line vehicle density reconstruction in large-scale traffic networks. For that, we have used flows and FCD speed measurements to jointly reconstruct density and flow in the entire network. A sensor radar networks has been installed in the city of Grenoble. It allows us to validate the proposed methodology, and to provide public information for the analysis of the city traffic conditions (road occupancy, energy vehicle consumption, vehicle emissions, and pollution diffusion). A demonstrator of these results are implemented in the GTL-Ville platform http://gtlville.inrialpes.fr

Control methods for scale-free network. We devised a very innovative solution to control large-scale systems: we have introduced the “continuation method” transforming spatially distributed ODE systems into continuous PDE. Most of the systems we encounter in real life consist of such a large number of particles that the direct analysis of their interaction is impossible. The method was illustrated by multiple examples including transport equations, Kuramoto equations and heat diffusion equations, an alternative solution to Hilbert's 6th problem. Several applications of the method have been worked out. Thy include: general linear networks, laser chains, traffic systems, and rings of spintronic oscillators.

Proof-of-Concept: road networks. Proof-of-concept studies are conducted by performing field tests at our data collection center (GTL-Ville), and simulations are performed to test the validity of our models, using a large-scale micro-simulator. The equipment available at the GTL-Ville is used to test our findings on a representative network using real-life data. This project considers a 1 km x 1.4 km zone of the Grenoble downtown, in which different traffic data is to be recollected in real time. GTL-Ville platform http://gtlville.inrialpes.fr
See attached Fig1-6 showing screen shots from the web-platform
We devise an algorithm, called MergeToScaleFree, and allows finding a partition of an arbitrary network resulting in a scale-free abstraction. For the first time in the control arena an algorithm for such model aggregation is proposed. In a different approach we have proposed Aggregated Scale-Free Models for large-scale traffic system. The main progress beyond the state of the art is the derivation of a two-dimensional PDE describing how the flow along the network is propagate via a continuum distribution. The model then is able to predict shock, advection waves in the 2-D plane and multi-directions. For the first time, this type of model has been validated using real data from the GTL-Ville.

We have introduced a new concept of scale-free detectability, and the mathematical conditions for a network to have such that the average state of some area can be estimated. In simple terms, scale-free detectability means that the average states estimation becomes exact as the degree of the aggregated nodes grows. In addition to this, we have studied some resilience property when some of nodes in the network are broken, or the suited scale-free detectability condition is not satisfied.

Traffic density, traveling time and vehicle emission estimation in large-scale traffic networks. We have proposed a density and flow reconstruction. Experimental rea-time validation using the GLT platform has been realized in a selected area of Grenoble Downtown.

We devised a very innovative solution to control large-scale systems: we have introduced the “continuation method” transforming spatially distributed ODE systems into continuous PDE. As a main example a continuation of a Newtonian system of interacting particles was performed, thus obtaining the Euler equations for compressible fluids and thereby providing an original alternative solution to Hilbert's 6th problem.

Images attached to the Summary for publication: PDF from the 5 min presentation at TRA.
First results in Agrregation towards SF graph
Figure 4 - Travel times overview
Figure 2 - Fluidity index
Fig1 screen -raw data coverage
Figure 6 - Historical display
Scale-FreeBack vision
Targets toward new approach for Large scale traffic control
Density recustruction set up
Figure 3 – Partitions’ representation
Real-time Data collection and snap shots of the GTL-Ville interface
Results of 2-D Traffic models and comparison with micro simulator
Figure 5 - Density heat-map
pitch event at TRA'18