INVERSE PASSIVE LEARNING OF AN INPUT OUTPUT-MAP THROUGH UPDATE-SPLINE-SMOOTHING

This paper presents a robust method of learning passively a one-dimensional input-output-map when receiving only indirect information about the correct input-output-map (e.g., only the sign of the deviation between the actual estimated output value and the correct output value is obtained). This information is obtained for only one input-output combination per updating cycle. The approach is to increment or decrement step by step the output values of the actually stored map and then to apply global or local cubic spline smoothing in order to avoid ''adaptation holes'' at points which are never updated or less frequently updated than other points. This method works with noisy measurements as well as slowly time-varying systems. Even continuous changes of the desired input-output-relation do not result in instability. Problems of convergence and stability are treated and design rules are given.