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It is therefore of interest to explore alternative approaches. We show that the surge tank controller design problem naturally fits a differential games framework, proposed by Dupuis and McEneaney, for controlling a system to confine the state to a safe region of the state space. We show furthermore that the differential game arising in this way can be solved by decomposing it into a collection of (one player) optimal control problems. We discuss the implications of this decomposition technique, for the solution of other controller design problems possessing some features of the surge tank controller design problem.

Echo State Networks (ESNs) have been recently proposed as a special class of recurrent neural networks (RNNs), which help to avoid the possibility of vanishing gradient associated with RNNs, and also computational less complex. On-line training of ESNs has previously been implemented using an RLS-type algorithm. Our approach aims at avoiding the numerical disadvantages inherent to the RLS algorithm by switching to a simpler and less computationally-intensive gradient descent algorithm. Simulations performed on benchmark AR, nonlinear and chaotic signals suggest that the performance of ESNs in single-step and multistep-ahead prediction is not sacrificed by the proposed method.

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