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The optimal control and its limited version namely the model predictive control represent one of the most important nonlinear control alternatives nowadays. The success of them are also proven in many practical applications. These can provide for several industrial applications the optimal trajectory calculation as well as calculation of the real-time control signal. One successful version of this is Generalized Predictive Control (GPC). A big advantage of these control algorithms is that they solutions are able to take into account the limitations of the inputs, and the states. In some cases, it is important to know the mathematical model chosen and the complete state information. Otherwise, the model can be estimated during the operation. Our study shows through the control of the cathode heating of a high power electron beam device the self-tuning adaptive control thus constructed. Using a suitable dynamic model and an extended Kalman estimator, we determine the estimated temperature of the two cathodes during operation and the saturation electron current, which ensures the maximum cathode life. The practical application was tested on a CTW 5/60 type

Az optimális és modell prediktív irányítások áttekintése és valós idejű alkalmazása, különös tekintettel az állapotbecslők használatára