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Alfredo Pironti

Publications and source records attributed to Alfredo Pironti.

6 recordsLinked to original sources

CARONTE: a Physics-Informed Extreme Learning Machine-Based Algorithm for Plasma Boundary Reconstruction in Magnetically Confined Fusion Devices

In this work, we propose a novel physics informed neural network based algorithm for real time plasma boundary reconstruction in tokamak devices. The approach is based on a single Extreme Learning Machine network used to solve the homogeneous Grad Shafranov equation, which is required to identify the plasma boundary. This architecture enables the real time training of the network parameters using the available magnetic sensor data and, consequently, dynamically adapting the network output to the evolving plasma equilibrium. We demonstrate that, the network performs accurate plasma boundary reconstruction for complex configurations, outperforming well established methods, such as the algorithm used for decades at the Joint European Torus, the world's largest tokamak, until it ceased operation in 2023. Indeed, compared to the latter, the proposed solution better generalizes the poloidal flux function, without requiring algorithm retuning across different plasma equilibria. The proposed neural network reconstructor demonstrates also greater robustness with respect to noise on the magnetic measurements. Moreover, this method takes advantage of the generalization power of neural networks but without the need for extensive, time consuming training based on a huge amount of experimental data, making its implementation on existing devices straightforward.

physics.plasm-ph

Assessing the Finite-Time Stability of Nonlinear Systems by means of Physics-Informed Neural Networks

In this paper, the problem of assessing the Finite-Time Stability (FTS) property for general nonlinear systems is considered. First, some necessary and sufficient conditions that guarantee the FTS of general nonlinear systems are provided; such conditions are expressed in terms of the existence of a suitable Lyapunov-like function. Connections of the main theoretical result of given in this article with the typical conditions based on Linear Matrix Inequalities (LMI) that are used for Linear Time-Varying (LTV) systems are discussed. An extension to the case of discrete time systems is also provided. Then, we propose a method to verify the obtained conditions for a very broad class of nonlinear systems. The proposed technique leverages the capability of neural networks to serve as universal function approximators to obtain the Lyapunov-like function. The network training data are generated by enforcing the conditions defining such function in a (large) set of collocation points, as in the case of Physics-Informed Neural Networks. To illustrate the effectiveness of the proposed approach, some numerical examples are proposed and discussed. The technique proposed in this paper allows to obtain the required Lyapunov-like function in closed form. This has the twofold advantage of a) providing a practical way to verify the considered FTS property for a very general class of systems, with an unprecedented flexibility in the FTS context, and b) paving the way to control applications based on Lyapunov methods in the framework of Finite-Time Stability and Control.

math.OC

Vertical stabilization of tokamak plasmas via Extremum Seeking

In this paper we propose a vertical stabilization~(VS) control system for tokamak plasmas based on the extremum seeking (ES) algorithm. The gist of the proposed strategy is to inject an oscillating term in the control action and exploit a modified ES algorithm in order to bring to zero the average motion of the plasma along the unstable mode. In this way, the stabilization of the unstable vertical dynamic of the plasma is achieved. The approach is validated by means of both linear and nonlinear simulations of the overall~ITER tokamak magnetic control system, with the aim of demonstrating robust operation throughout the flat-top phase of a discharge and the capability of reacting to a variety of disturbances.

physics.plasm-ph

Finite-Time stabilization of linear systems with unknown control direction via Extremum Seeking

In this paper the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum seeking algorithm. We propose to use a suitable oscillatory input to modify the system dynamics, at least in an average sense, so as to satisfy a Differential Linear Matrix Inequality (DLMI) condition which in turns guarantees that the system's state remains inside a prescribed time varying hyper-ellipsoid in the state space. The finite-time stability (FTS) of the averaged dynamics implies the FTS of the original system, as the distance between the original and the averaged dynamics can be made arbitrarily small by choosing a sufficiently high value of the dithering frequency used by the extremum seeking algorithm. An estimate of the necessary minimum dithering/mixing frequency is provided, and the effectiveness of the proposed finite-time stabilization approach is analysed by means of numerical examples.

math.OC

Asymptotic analysis of the Friedkin-Johnsen model when the matrix of the susceptibility weights approaches the identity matrix

In this paper we analyze the Friedkin-Johnsen model of opinions when the coefficients weighting the agent susceptibilities to interpersonal influence approach 1. We will show that in this case, under suitable assumptions, the model converges to a quasi-consensus condition among the agents. In general the achieved consensus value will be different to the one obtained by the corresponding DeGroot model

cs.SI

Input-Output Finite-Time Stability

This paper introduces the extension of Finite-Time Stability (FTS) to the input-output case, namely the Input-Output FTS (IO-FTS). The main differences between classic IO stability and IO-FTS are that the latter involves signals defined over a finite time interval, does not necessarily require the inputs and outputs to belong to the same class of signals, and that quantitative bounds on both inputs and outputs must be specified. This paper revises some recent results on IO-FTS, both in the context of linear systems and in the context of switching systems. In the final example the proposed methodology is used to minimize the maximum displacement and velocity of a building subject to an earthquake of given magnitude.

eess.SY