Abstract
Recurrent Neural Networks (RNNs) are increasingly being used for model identification, forecasting and control. When identifying physical models with unknown mathematical knowledge of the system, Nonlinear AutoRegressive models with eXogenous inputs (NARX) or Nonlinear AutoRegressive Moving-Average models with eXogenous inputs (NARMAX) methods are typically used. In the context of data-driven control, machine learning algorithms are proven to have comparable performances to advanced control techniques, but lack the properties of the traditional stability theory. This paper illustrates a method to prove a posteriori the stability of a generic neural network, showing its application to the state-of-the-art RNN architecture. The presented method relies on identifying the poles associated with the network designed starting from the input/output data. Providing a framework to guarantee the stability of any neural network architecture combined with the generalisability properties and applicability to different fields can significantly broaden their use in dynamic systems modelling and control.
Highlights
Neural networks are becoming increasingly popular in the fields of dynamic modelling, time series forecasting and control
When tuning the Deep Neural Networks (DNNs) architecture described in Section 3.2.2, the tuned parameters are:
A new procedure to compute the poles of a generalised DNN architecture is proposed
Summary
Neural networks are becoming increasingly popular in the fields of dynamic modelling, time series forecasting and control. Deep Neural Networks (DNNs) are employed in control applications when the traditional model based approach lacks design efficiency or is deemed unfeasible This could be due to the model of the system being very complex, due to a time-varying environment or when the control solution is too cumbersome to compute due to a large action space [1]. When big datasets are available, machine learning algorithms show comparable performance to advanced control techniques such as the combination of real-time optimization and model predictive control [2]. Despite their advantages, data-driven control systems cannot rely on the traditional stability theory used for model based approaches [2]. The lack of stability proofs jeopardises the use of the DNN in safety-critical system identification and control applications in which stability assessment and quantification are of paramount importance
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