### Plasma modeling

The employment of models in the context of fusion plasma science and engineering has become of paramount importance since fusion devices are complex machines, whose operational states and behaviors depend on several controllable and non-controllable** interconnected subsystems **as, limiting the analysis to the magnetic control: the **plasma**, the **electromagnetic circuits**, the **passive conducting structures**, the **magnetic diagnostics. **

The coupling of these elements give rise to **high order, nonlinear systems** with a large number of instabilities, so there is consensus in the fusion community that **active control** will be one of the key enabling technologies, whence the need of accurate models derives.

In axisymmetric toroidal geometry, plasma dynamics is that of a fluid conductor whose behavior is regulated by the **Grad-Shafranov** (GS) equation describing the force balance between kinetic pressure and Lorentz force through a nonlinear elliptic PDE relation.

In representing the plasma, **discrete filamentary models** have traditionally proved less accurate with respect to FE free boundary plasma models that can solve the GS equation, and thus can model the current distribution inside the boundary with a high number of degrees of freedom.

A **dynamic filamentary model **for the plasma is studied that controls the degrees of freedom of the problem through SVD regularization combined within an iterative scheme, which allow the representation of the advanced configurations with strongly non-homogeneous current distribution while keeping the model compact.

The **optimization** of this dynamic model can be carried out with the specific goal of studying a two-scale state space discrete time model with time varying parameters that accounts for both the iterative convergence and the time evolution in the scenario. The problem can be posed as an optimization problem in the form of Tikhonov minimization, and particular attention will regards the choice of suitable regularization terms and cost functions.

### Optimal sensor selection

The input to the modeling activity is given by the **measurements** available in the plant. In particular, the accurate reconstruction of the plasma boundary location and shape is obtained from magnetic diagnostics through algorithms that allow the reconstruction of a continuous flux map from a set of **sparse measurement signals**, characterized by different error and noise patterns. At the same time, an ideal observer made of a continuous array of virtual sensor shows that the degrees of freedom of the system is limited to a few tens, stating that in principle a low number of signals is sufficient for the model building procedure.

The formalization of this selection problem can be studied, by posing a **functional optimization problem constrained to the physics** (and the shape) of the EM fields where the model variables are weights of the elements of a suitable base obtained from the minimization of the error in recovering a set of sensor measurements. It is particularly interesting to study how to obtain the regularization of the solution by matching **global descriptors** of the plasma resulting from current moment calculation.

Such a sensor system should be reliable and robust enough to guarantee the correctness and the repeatability of the model based reconstruction procedure for both real-time control and real-time machine monitoring. The sparse diagnostic systems basically forms a sensor networks, therefore it appears sensible to exploit the diverse spatial localization of sensors in order to design techniques for fault detection.

Strictly related to this, there is the problem of **measurement reconciliation** (or sensor fusion). This activity will focus on the distributed estimation of the same phenomenon features (i.e. the plasma behavior) from different vantage points (i.e. different sensor locations), and the employment of robust regression methodologies to provide a consistent set of measurements to set the base for an **adaptive-input optimal procedure**.