Monotonic Recurrent Bounded Derivative Neural Network

Neural networks applied in control loops and safety-critical domains have to meet hard requirements. First of all, a small approximation error is required, then, the smoothness and the monotonicity of selected input-output relations have to be taken into account and finally, for some processes, time dependencies in time series should be induced into the model. If not then the stability of the control laws can be lost. In the following paper authors present new Monotonic Recurrent Bounded Derivative Network (RBDN) on the basis of the Bounded Derivative Network (BDN) [1]. Authors compared invented network with other known networks, investigated the influence of the back connection in recurrent network, stability and monotonicity of the new recurrent network. This paper is also an attempt to incorporate Input/Output monotonicity into the recurrent network nodes (weights). 1 Bounded Derivative Neural Network Following the work [1] consider multi layer perceptron. This class of networks consists of multiple layers of computational units, usually interconnected in a feed-forward way. Each neuron in one layer has directed connections to the neurons of the subsequent layer. In many applications the units of these networks apply a hyper tangent function as an activation function (see Eq.1): General equation of the MLP is given in Eq.(1).