Error Learning Method

In this study, a new theoretical foundation for the Discrete-Time Feedback Error Learning (DTFEL) method is proposed. This method is analogous to the original Continuous-Time Feedback Error Learning (FEL) originally proposed as a control model of the cerebellum in the field of computational neuroscience. DTFEL is superior to FEL since it is applicable for digital controllers which are commonly used nowadays. Based on the strictly positive realness, the stability of DTFEL has been validated. However, from the viewpoint of adaptive control, this condition is restricted since some required assumptions cannot be satisfied in real systems, such as the direct input-output transmission gain is required to be large. Moreover, the stability of the system is guaranteed by selecting a sufficiently large positive constant feedback gain, which is a vague requirement from the viewpoint of control system design. This study proposes another scheme for the DTFEL method which does not require any positive real condition and overcomes the direct input-output transmission gain requirement. This can be achieved by utilizing the error signal more effectively.