To design plasma magnetic control systems in modern tokamaks one needs models of the plasma. These models are linear parameter varying (LPV) because of relatively small variations of outputs of the feedback loops around scenarios and may be obtained by first-principle equations, identification approach or by their combinations. The challenge of obtaining models of plasma in the tokamak becomes more complicated by the existence of plasma position and poloidal field control loops with diagnostics and actuators which are needed as inner cascades for plasma current and shape control in particular on the Globus-M2 tokamak (Ioffe Inst., St. Petersburg, RF). The plasma equilibrium is reconstructed on the base of magnetic measurements outside the plasma by Picard iterations, moving filaments or neural networks, and linear plasma models are developed around the equilibrium with the help of the Kirchhoff’s law and force balance. In order to ensure the operability of plasma current and shape feedback control systems, the identification approach (controlled plant model design on the base of experimental input-output signals) is planned to be used. The basic methods of the identification are supposed to be applied as follows: subspaces, wavelets, linear matrix inequalities (LMIs), adaptive state observers, and dynamical neural networks which are able to automatically adjust their states to an unknown plant (elements of artificial intelligence). The solutions of the identification problem will be compared with the models obtained by the first principles with the aim to get the sufficient accuracy of coincidence. The approaches to be developed of getting tokamak plasma models may be applied to any vertically elongated operating tokamak such as Globus-M2 (RF), Damavand (Iran), D-IIID (US), ST40 (GB), ASDEX U (Germany), TCV (Switzerland).

We propose a new approach to filtering under arbitrary bounded exogenous disturbances based on reducing this problem to an optimization problem. The approach has a low computational complexity since only Lyapunov equations are solved at each iteration. At the same time, it possesses advantages essential from an engineering-practical point of view, namely, the possibilities to limit the filter matrix and to construct optimal filter matrices separately for each coordinate of the system’s state vector. A gradient method for finding the filter matrix is presented. According to the examples, the proposed recurrence procedure is rather effective and yields quite satisfactory results. This paper continues the series of research works devoted to feedback control design from an optimization perspective.

The direction of developing plasma magnetic control systems in D-shaped tokamaks with its actuality and scientific novelty is presented. Shortly the poloidal systems of ITER and DEMO are characterized. The new imitation computer digital platform for modeling plasma magnetic control systems in real time for application in physical experiments is described. The preliminary results of testing the plasma magnetic control system for the Globus-M2 tokamak (Ioffe Institute, S-Petersburg, Russia) on the target computer of the platform are given. The digital twin of the imitation platform is characterized. The methodology of risk minimization is presented.

An adaptive state-feedback control system for a class of linear systems with piecewise-constant unknown parameters is proposed. The solution ensures a global exponential stability of a closed-loop system under condition that a regressor is finitely exciting after each parameters switch, and does not require neither any knowledge of a plant input matrix, nor the switching time instants. The obtained theoretical results are corroborated by numerical simulations.

Abstract: The paper is devoted to a method for constructing exact solutions of evolutionary differential equations with two space variables.The method uses the theory of symmetries of completely integrable distributions. As an example, we consider a linear parabolic equation that arises in filtration theory, thermodynamics, and mathematical biology. Dynamics are calculated for this equation and classes of their exact solutions are constructed.