Adaptive Distributed Parameter and Input Estimation in Plasma Tokamak Heat Transport

Abstract

: In this paper, the adaptive estimation of spatially varying diffusion and source term coefficients for a linear parabolic partial differential equation describing tokamak plasma heat transport is considered. An estimator is defined in the infinite-dimensional framework having the system state and the parameters' estimate as its states. Our scheme allows to estimate constant, spatially distributed and spatio-temporally distributed parameters as well as input with known upper bounds in time. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite-dimensional, the Galerkin finite-dimensional technique is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach.

Estimation of Heat Source Term and Thermal Diffusion in Tokamak Plasmas Using a Kalman Filtering Method in the Early Lumping Approach

“…Simulation results on both simulated and experimental data attest the efficiency of the chosen methodology to handle parameter and input estimation for heat transport in tokamak plasmas. However, if the basis dimensions constraint can be covered using late lumping methods (as we have done in [49] and [50]), the problem of the noise measurement effect was not addressed in this paper. This is beyond the scope of our present work since we dealt with filtered measurements using correlation electron cyclotron emission diagnostics (see [46] and references therein).…”

Retraction statement: Adaptive distributed parameter and input estimation in linear parabolic PDEs

“…Figures 2 and 3 show that using the adaptive estimator (19) and (20) and the adopted tuning gains, the parameters ( e , b) and the input S profiles are reconstructed efficiently. Note that the efficiency of the distributed sensing version of this estimator was tested using experimental data in [28] and gave good performance.…”

“…However, the effect of noisy measurements was not investigated. This will be addressed in our future works where the case of space-varying and time-varying parameters presented in [28,29] but using interior-point measurements will also be considered.…”