SUMMARYThis paper proposes a design approach of continuous sliding mode control of uncertain systems, the uncertainty being norm bounded. The two steps of the design methodology are investigated. The existence step, in which we choose the sliding surface that gives good behaviour during the sliding mode, is formulated as a pole assignment of linear uncertain system in a sector through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization. In the reaching step, we propose a continuous nonlinear control strategy ensuring a bounded motion about the ideal sliding mode, thus approximating the ideal dynamic behaviour in the presence of uncertainty. Finally, the validity and the applicability of this approach are illustrated by a flight stabilization benchmark example.

A novel neural architecture for prediction in industrial control: the 'Double Recurrent Radial Basis Function network' (R2RBF) is introduced for dynamic monitoring and prognosis of industrial processes. Three applications of the R2RBF network on the prediction values confirmed that the proposed architecture minimizes the prediction error. The proposed R2RBF is excited by the recurrence of the output looped neurons on the input layer which produces a dynamic memory on both the input and output layers. Given the learning complexity of neural networks with the use of the back-propagation training method, a simple architecture is proposed consisting of two simple Recurrent Radial Basis Function networks (RRBF). Each RRBF only has the input layer with looped neurons using the sigmoid activation function. The output of the first RRBF also presents an additional input for the second RRBF. An unsupervised learning algorithm is proposed to determine the parameters of the Radial Basis Function (RBF) nodes. The K-means unsupervised learning algorithm used for the hidden layer is enhanced by the initialization of these input parameters by the output parameters of the RCE algorithm.

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