Towards lifelong learning of Recurrent Neural Networks for control design

Abstract

This paper proposes a method for lifelong learning of Recurrent Neural Networks, such as NNARX, ESN, LSTM, and GRU, to be used as plant models in control system synthesis. The problem is significant because in many practical applications it is required to adapt the model when new information is available and/or the system undergoes changes, without the need to store an increasing amount of data as time proceeds. Indeed, in this context, many problems arise, such as the well known Catastrophic Forgetting and Capacity Saturation ones. We propose an adaptation algorithm inspired by Moving Horizon Estimators, deriving conditions for its convergence. The described method is applied to a simulated chemical plant, already adopted as a challenging benchmark in the existing literature. The main results achieved are discussed.

On the stability properties of Gated Recurrent Units neural networks

“…In this Appendix, the algorithm here adopted to train the deep LSTM model (2), based on the so-called Truncated BackPropagation Through Time (TBPTT) [3], is briefly described. For more details, the interested reader is addressed to [28]. This procedure represents an intuitive way to address the training problem, i.e., the problem of finding the weights Φ ‹ that minimize the free-run simulation error over the training data.…”

“…The second term in ( 17) is a suitably designed regularization term that enforces the satisfaction of the δISS sufficient conditions (8), see [9], [28]. An example of such regularization function is a piecewise-linear function, i.e., ρpνq "…”

“…the number of inequalities, ε ν ą 0 is the constraint clearance, while π " π ą 0 represent the cost coefficients. More advanced regularization functions, such as the generalized piecewise function [28], can also be adopted. This iterative training procedure is eventually halted when the performances on validation set, i.e.…”

“…Finally, the performances of the trained model need to be objectively quantified on the independent test set. To this end, the FIT performance index r%s can be adopted [9], [28], which is defined as…”

“…In this context, being able to certify the model's Incremental Input-to-State Stability (δISS, [18]) allows the designer to synthesize control laws with closedloop stability guarantees [14], [19] and robust zero-error tracking of constant reference signals [20], [21]. As discussed in [9], this property is also beneficial in terms of model's robustness against input perturbations, consistency of modeling performances in spite of wrong initialization, and safety [22].…”