Fifth Term

Period: 01/05/2024 – 31/07/2025

SECTION 1 – GENERAL TRENDS OF THE PROJECT

Brief summary of the project

With reference to the work packages/tasks reported in The invited session on Plasma modeling and control in magnetically confined fusion devices has been held at the Joint 9th IFAC Symposium on System Structure and Control, 19th IFAC Workshop on Time Delay Systems and 2nd IFAC Workshop on Control of Complex System. The session has been organized by the members of the TRAINER project: Sara Dubbioso, Federico Fiorenza and Domenico Frattolillo. The following contributions related to the TRAINER project have been presented

A. Antonione, G. Carannante, K. Cindric, M. Ferrari, G. De Tommasi, "Control system development and testing for the electron beam current of ITER European gyrotrons";
S. Dubbioso, G. De Tommasi, N. Ferron, C. Galperti, G. Manduchi, S. Marchioni, A. Mele, A. Pironti, "Hardware-in-the-loop validation of an Extremum Seeking-based system for vertical stabilization of tokamak plasmas".

The following contribution to the 31st IEEE Symposium on Fusion Engineering ( has been prepared and presented in June 2025:

A. Antonione, G. Carannante, M. Ferrari, F. Sanchez, G. De Tommasi, "Data-driven mode loss detection for the emitted radio-frequency beam of ITER gyrotrons".

The following contribution to the 51st EPS Conference on Plasma Physics has been prepared and presented in July 2025:

N. Isernia, O. Ficker, B. Stefanoska, D. Kabirov-Leontieva, V. Fernández Pacheco, G. Ferrari, V. Yanovskiy, M. Imrisek, P. Vondracek, E. Matveeva, F. Villone, "Evaluating energy fluxes during COMPASS disruption".
The following contribution to the 30th IAEA Fusion Energy Conference has been prepared:

M. Mattei, L. E. di Grazia, D. Frattolillo, “Intra-shot Tools for Plasma Scenario Optimization and Magnetic Control”

The following journal version of the contributions presented at SOFT 2024 have been published online on Fusion Engineering and Desing:

L. E. di Grazia, E. Fable, M. Mattei, M. Siccinio, F. Maviglia, H. Zohm, "Burn control strategies using plasma elongation in DEMO";
P. Zumbolo, R. Albanese, A. G. Chiariello, A. Iaiunese, A. Lampasi, M. Neri, R. Martone, "Energy optimization of the EFCC power supply in DTT scenarios"
S. Dubbioso, D. Ottaviano, F. Fiorenza, G. De Tommasi, N. Ferron, G. Manduchi, E. Acampora, R. Ambrosino, "Rapid prototyping of control modules for the DTT Plasma Control System";
S. Dubbioso, G. De Tommasi, C. Galperti, F. Felici, S. Marchioni, A. Mele, A. Merle, A. Tenaglia, "Simulation validation of an Extremum Seeking-based Vertical Stabilization system for TCV";
D. Frattolillo, L. E. di Grazia, M. Mattei, F. Pesamosca, "Magnetic control strategies to reduce first wall heat loads in ITER";
L. E. di Grazia, M. Mattei, A. Pironti, "An Extended Kalman Filter approach for tokamak plasma equilibrium reconstruction".

The following journal contribution have been published:

D. Frattolillo, A. Mele, C. Galperti, L. E. di Grazia, M. Mattei, S. Coda, G. De Tommasi, A. Pironti, A. Tenaglia, P. de Vries, L. Pangione, L. Zabeo, "Implementation of an ITER-relevant QP-based Current Limit Avoidance algorithm in the TCV tokamak", Plasma Physics and Controlled Fusion, vol. 67, no. 5, pp. 055017, May 2025.
M. Neri, P. Zumbolo, R. Albanese, "Accurate plasma boundary calculation using linear triangular finite elements," Computational Physics, vol. 311, pp. 109574, June 2025.
L. E. di Grazia, C. Vincent, M. Mattei, F. Felici, L. Kogan, A. Mele, "Iterative learning optimization and control of MAST-U breakdown and early ramp-up scenarios," Optimization and Engineering, 2025.
G. Tartaglione, M. Ariola, L. E. Di Grazia, “A hybrid model-based and learning-based approach for the plasma magnetic control in DEMO”, International Journal of Dynamics and Control, 13(6), 2025.

Table 1 - TRAINER work packages and tasks.

[WP0] – Development of a fast control-oriented nonlinear plasma equilibrium code

[T0.1] – Development of a fast version of a plasma equilibrium code to be executed within the Simulink environment and of an approximate parameter varying linear model of the plasma/tokamak dynamics

[WP1] – Development of DRL control agents for basic magnetic control problems

[T1.1] – Development of a first version of DDPG agents for the basic magnetic control problems (i.e. Plasma Current Control and Vertical Stabilization) by exploiting both single linear models and parameter varying linear model of the plasma response to model the environment

[T1.2] – Refinement of the agents developed by [T1.1], by exploiting the fast nonlinear equilibrium code

[T1.3] – Assessment of the possibility of developing a DDPG agent to solve problem the Plasma Shape Control problem

[WP2] – Development of data-driven plasma parameters estimators for adaptive model-free plasma vertical stabilization

[T2.1] – Development of the data-driven estimator of the plasma growth rate

[T2.2] – Development of an Extremum-seeking based VS system and assess the possibility to integrate it with the growth rate estimator developed by [T2.1]

[WP3] - Development of DRL-based tuning procedures to improve the robustness of model-based magnetic control algorithms

[T3.1] – Optimization of the controller gains for the plasma current, shape and VS system exploiting DDPG algorithms and fast nonlinear simulations with the nonlinear equilibrium code

[WP4] – Dissemination

[T4.1] – Dissemination

Names of the operational units involved in the implementation of the project

Research Unit (RU) University of Naples “Federico II” – led by the Principal Investigator, Prof. Gianmaria De Tommasi
RU University of Naples “Parthenope” – led by Prof. Marco Ariola

Description of the achievement of the objectives connected to the project and related outcomes

The project activities of the considered timeframe were mainly related to:

further validation of the control-oriented models developed by Task 0.1 on the TCV tokamak (Switzerland). The developed models have been used to design a current-limit avoidance systems based on online Quadratic Programming (QP) optimization.
- further validation of the control-oriented models developed by Task 0.1 on the MAST-U spherical tokamak (United Kingdom). The developed models have been used to deploy an iterative learning optimization and control of the breakdown and early ramp-up;
further validation of the control-oriented models developed by Task 0.1 on the EAST tokamak (People’s Republic of China). The developed models have been used:
- to deploy an iterative learning optimization and control of the breakdown and early ramp-up;
- to design a PF current controller that integrates also the control of the plasma current (i.e., an ITER-like solution).
development of a DDPG agent for vertical stabilization by using the parameter varying linear model of the plasma response;

Description of the carried out activities which are in compliance with the DNSH, Open Access principles as well as with gender, generational principles and with those of Equal opportunities;

No specific compliance with the DNSH, Open Access principles as well as with gender, generational principles, and with those of Equal opportunities has been experienced in the considered timeframe.

Description of the actions aimed at informing and disseminating knowledge

The main activities performed in the considered timeframe are:

participation (as contributors to invited and regular sessions) to the following conferences:
1. 31st IEEE Symposium on Fusion Engineering (SOFE 2025), Cambridge, Massachusetts (USA), June 2025;
2. 2nd IFAC Workshop on Control of Complex Systems (COSY'25), Gif-sur-Yvette, France, July 2025;
3. 51st EPS Conference on Plasma Physics, Vilnius, Lithuania, July 2025.
publication of papers on the following international journals:
1. Fusion Engineering and Design
2. Plasma Physics and Controlled Fusion
3. Computational Physics
4. Optimization Engineering
update of the contents of the website https://trainer.dieti.unina.it/.

SECTION 2 – PROGRESS OF ACTIVITIES

With regard to the specific timeframe, it is below provided:

Detailed description of activities carried out by each operational unit with a focus on the timeframe for their implementation

In the specific timeframe, Federico II RU has mainly focused on:

the validation of the Extremum Seeking-based VS (ES-VS) on the TCV internal simulator; this activity partially succeeded, but it is still ongoing, since the some bug fixing is still needed to integrated ES-VS algorithm in the TCV simulation platform;
the assessment of the performance of the proposed ES-VS on the EAST tokamak. EAST researcher provided a Simulink version of their magnetic control system. The assessment is ongoing;
the experimental validation of the Iterative Learning Control (ILC) procedures implemented using plasma models developed in WP0. In particular the ILC procedure was applied to optimize a complete ramp-up in MAST-U where the new ramp-up had interesting fallouts regarding the reduction of IRE phenomena. Preliminary experiments were also done in EAST;
the test of a fixed boundary equilibrium procedure and the related linearized plasma response model on various devices, comparing the results with those obtained with CREATE-NL+ and CREATE-L codes. A procedure for the magnetic field calculations with second order accuracy using linear finite elements in the presence of magnetic media has been proposed and presented as contribution to the COMPUMAG Conference. An innovative approach to the analysis and the optimization of 3D magnetic fields in tokamaks has been proposed and a contribution to the “ET Cagliari 2025 symposium” (ETCA) has been presented in the considered timeframe.

In the same timeframe, Parthenope RU has worked on the development of a DDPG agent for vertical stabilization by using the Linear Parameter Varying (LPV) model of the plasma response developed in T0.1. A new training procedure, based on the parameter varying linear model, was proposed to design a DDPG agent able to stabilize the vertical position of the plasma during the ramp-up phase.

The control architecture shown in Figure 1 has been tested and validated for an ITER case study with a LPV model that allows us to schedule different linear models as a function of the plasma current.

The RL agent was designed and trained to compute the voltage provided by the fast converter acting on the imbalance circuit, whose task is to supply the current needed for vertical stabilization. The control system calculates the control action by processing the estimates of the vertical position and speed of the plasma centroid, and the plasma current.

For the training of the agent, we considered random simulations of Vertical Displacement Event (VDE) in the range . The simulations were carried out using the LPV model of the plasma response; in this way each simulation was characterized by a random plasma current in the range . A quadratic reward function was defined in order to stop in the shortest possible time the vertical movement of the plasma.

Figure 1 - Block diagram of the proposed DDPG-based vertical stabilization control system

In Figure 2 we show the results of two closed-loop simulations of a VDE of 5 cm at different values of plasma current, i.e. in the first simulation we considered a plasma current and in the second one . Numerical results show that the trained DDPG agent is able to properly slow down the plasma in both cases.

Figure 2 - Closed-loop simulation of a VDE of 5 cm at different values of plasma current. Numerical results show that the trained DDPG agent is able to properly slow down the plasma in both cases

Description of potential changes to what has been originally approved mentioning the impacts on the aim of the intervention, on the achievement of intermediate and long- term goals, on the proposed actions for improvement

No changes to what has been approved were required.

Description of potential challenges encountered and of the proposed actions for improvement

With regard to the specific timeframe, no major challenges or issues have been encountered.

Brief description of potential publications.

In the considered timeframe the following conference contributions were prepared and presented in the corresponding venues:

[IC1] A. Antonione, G. Carannante, M. Ferrari, F. Sanchez, G. De Tommasi, "Data-driven mode loss detection for the emitted radio-frequency beam of ITER gyrotrons," in 31^st IEEE Symposium on Fusion Engineering (SOFE 2025), Cambridge, Massachusetts, June 2025.
[IC3] N. Isernia, O. Ficker, B. Stefanoska, D. Kabirov-Leontieva, V. Fernández Pacheco, G. Ferrari, V. Yanovskiy, M. Imrisek, P. Vondracek, E. Matveeva, F. Villone, "Evaluating energy fluxes during COMPASS disruption," in 51^st EPS Conference on Plasma Physics, Vilnius, Lithuania, July 2025.

Moreover, the following journal papers have been published (some being the journal version of the contribution to the SOFT2024 conference):

SECTION 3 – COMMON INDICATORS

Below the updates on the indicator RRFCI 8 – “Number of researchers who work in research centres which are recipients of financial support (women; men; non-binary)” – as per the description in the guidelines included in the n. 34 MEF notification from the 17^th of October 2022.

Common indicators (RU University of Naples “Federico II”)	Planned value	Implemented value
Researchers who work in research centers which are recipients of financial support (women)	0,0	0,0
Researchers who work in research centers which are recipients of financial support (men)	1,2	1,09
Researchers who work in research centers which are recipients of financial support (non-binary)	0,0	0,0

Common indicators (RU University of Naples “Parthenope”)	Planned value	Implemented value
Researchers who work in research centers which are recipients of financial support (women)	0,0	0,0
Researchers who work in research centers which are recipients of financial support (men)	0,53	0,37
Researchers who work in research centers which are recipients of financial support (non-binary)	0,0	0,0

SECTION 4 – PREDICTIVE ANALYSIS AND FINAL COMMENTS

Below it is provided a description of the forecast scenario on the development of the project, any potential change which is deemed necessary for the future as well as comments on the document.

Predictive analysis

Attempt to test on TCV the ES-VS system are still ongoing and depends also on the TCV internal planning.

Parthenope RU proposed the first version of a data-driven vertical controller, which was trained by using the Linear Parameter Varying (LPV) model of the plasma response developed in T0.1. Early simulations show that the vertical controller is able to stabilize the vertical position of the plasma during the ramp-up phase. In the next months a further evaluation of the performance will be performed.

Final comments

The project is progressing as planned.

TRAINER - Tokamak plasmas daTa-dRiven identificAtIon and magNEtic contRol