DISCRETE-TIME FEEDBACK ERROR LEARNING WITH TIME-DELAY
Keywords:
Discrete-time system, time-delay system, feedback error learning, strictly positive, realness, learning control, adaptive controlAbstract
In this study, a theoretical foundation on the Discrete-Time Feedback Error Learning (DTFEL) method is extended. This is analogous to the original continuous-time version Feedback Error Learning (FEL) method which is proposed as a control model of cerebellum in the field of computational neuroscience. The DTFEL method has been developed because a digital controller is now replacing an analog one and the FEL method can not be applied to this type of controller directly. However, the validity of the stability of DTFEL has been proved based on the strictly positive realness. From the viewpoint of adaptive control, this is very restricted because some required assumptions can not be satisfied by real systems. Additionally, it is stated that the stability of the system is guaranteed by selecting a sufficiently large positive constant feedback gain. However, from the viewpoint of the control system design, it is not clear how large the feedback gain should be, since such largeness depends on unknown parameters. This study proposes another scheme for the DTFEL method which does not require any positive real conditions. This can be done by utilizing the error signal more effectively. Removing the positive realness leads to a proof of the stability of the DTFEL with the time-delay system.
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