Data issued of most real-world applications are evolving; they change constantly over time. In such applications, it is difficult to induce correctly a model (classifier) using traditional classification methods. Thus, it is important to use an adapted classification method to build a classifier and to update its parameters as new data is available. In this paper, we propose an adaptive classification approach based on the Fuzzy K-Nearest Neighbours (FKNN) method to monitor online evolving systems. The developed method, named semi-supervised Dynamic FKNN, comprises the following phases. In the first phase (detection phase), a class evolution can be detected and confirmed after the classification of each new pattern. Then in the second phase (adaptation phase), the parameters of the evolved class are updated incrementally. In the last phase (validation phase) the adapted classes are validated in order to keep only the representative ones. This approach is illustrated using an example of system which switches between several functioning modes.
This paper presents stability conditions for Takagi-Sugeno (T-S) uncertain descriptors. These are based on a fuzzy Lyapunov approach and a non-PDC (Parallel Distributed Compensation) control scheme. To design the fuzzy controller, the stability conditions are derived into LMIs. Moreover, in order to reduce once more the conservatism of the proposed stability conditions, a relaxation scheme, allowing rewriting the triple summation structure, is introduced for T-S descriptors. A designed example illustrates the efficiency of the proposed approaches.
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