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Learning strategy for optimal fuzzy control

Publication . Salgado, Paulo; Igrejas, Getúlio

In this paper, a new scheme of fuzzy optimal control for discrete-time nonlinear systems based on the Pontryagin’s Minimum Principle is proposed. Using back propagation from the final co-state error and gradient descent, a method which allows training an adaptive fuzzy inference system to estimate values for the co-state variables converging to the optimal ones is devised. This approach allows finding a solution to the optimal control problem on-line by training the system, rather than by pre-computing it. Finally, this optimal approach is applied to nonlinear control benchmark problems. The results demonstrate the effectiveness of the approach towards achieving the optimal control objective.

2007Conference object

Open access

Decomposition of a greenhouse TS-Fuzzy model by clustering process

Publication . Salgado, Paulo; Igrejas, Getúlio

This paper presents a fuzzy c-means clustering method for decompose a T-S fuzzy system. This technique is used to organize the fuzzy greenhouse climate model into a new structure more interpretable, as in the case of the physical model. This new methodology was tested to split the inside greenhouse air temperature and humidity flat fuzzy models into fuzzy sub-models. These fuzzy sub-models are compared with its counterpart’s physical sub-models. This algorithm is applied to the T-S fuzzy rules. The results are several clusters of rules where each cluster is a new fuzzy sub-system. This is a generalized Probabilistic Fuzzy C-Means (PFCM) algorithm applied to TS-Fuzzy System clustering. This allows automatic organization of one fuzzy system into a multimodel Hierarchical Structure.

2007Conference object

Open access

Time series prediction by perturbed fuzzy model

Publication . Salgado, Paulo; Gouveia, Fernando; Igrejas, Getúlio

This paper presents a fuzzy system approach to the prediction of nonlinear time series and dynamical systems based on a fuzzy model that includes its derivative information. The underlying mechanism governing the time series, expressed as a set of IF–THEN rules, is discovered by a modified structure of fuzzy system in order to capture the temporal series and its temporal derivative information. The task of predicting the future is carried out by a fuzzy predictor on the basis of the extracted rules and by the Taylor ODE solver method. We have applied the approach to the benchmark Mackey-Glass chaotic time series.

2007Conference object

Open access

Clustering algorithms for fuzzy rules decomposition

Publication . Salgado, Paulo; Igrejas, Getúlio

This paper presents the development, testing and evaluation of generalized Possibilistic fuzzy c-means (FCM) algorithms applied to fuzzy sets. Clustering is formulated as a constrained minimization problem, whose solution depends on the constraints imposed on the membership function of the cluster and on the relevance measure of the fuzzy rules. This fuzzy clustering of fuzzy rules leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of a flat fuzzy system results a set of decomposed sub-systems that will be conveniently linked into a Hierarchical Prioritized Structures.

2007Conference object

Open access

Clustering of TS-fuzzy system

Publication . Igrejas, Getúlio; Salgado, Paulo

This paper presents a fuzzy c-means clustering method for partitioning symbolic interval data, namely the T-S fuzzy rules. The proposed method furnish a fuzzy partition and prototype for each cluster by optimizing an adequacy criterion based on suitable squared Euclidean distances between vectors of intervals. This methodology leads to a fuzzy partition of the TS-fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of TS-fuzzy system the result is a set of additive decomposed TS-fuzzy sub-systems. In this work a generalized Probabilistic Fuzzy C-Means algorithm is proposed and applied to TS-Fuzzy System clustering.

2007Conference object

Open access