Adaptive feedback control of wall modes in tokamaks

The goal of this study is to stabilize the resistive wall modes (RWM) in tokamaks with adaptive stochastic feedback control. This is the first ever attempt at adaptive stochastic feedback optimal control of RWM in tokamaks. Both adaptive optimal state feedback and adaptive output feedback control have been studied. The adaptive optimal state feedback control design successfully stabilizes a slowly time-evolving RWM in a tokamak in a time scale of 4 times the inverse of the growth rate of the RWM. The stabilized system output for the time-invariant model is twice the system noise level. For the time-varying model, it is several times larger than the time-invariant case. The adaptive stochastic output feedback can also stabilize the slowly time-evolving RWM. It can do this in a time about 3 times that of the inverse of the growth rate of the RWM. The stabilized system output is twice as large as that of the state feedback case. In order to avoid the bottleneck encountered in the various sequential computations with big matrices in the feedback algorithms, neural network control has been proposed. It has been used to implement the adaptive stochastic output feedback control. It can stabilize the RWM instability in a time of 3 times the inverse of the growth rate of the RWM. The stabilized wall modes have the steady state output similar to the output feedback case. The developed algorithms, state feedback, output feedback, neural network control, can be readily applied to other plasma instabilities.