Abstract
In this paper the stability-related properties of Long Short-Term Memory (LSTM) networks are analyzed, and their use as the model of the plant in the design of Model Predictive Controllers (MPC) is investigated. First, sufficient conditions guaranteeing Incremental Input-to-State stability (dISS) of LSTM are derived, and it is shown that this property can be enforced during the training of the network. Then, the design of an observer with guaranteed convergence of the state estimate to the true one is addressed, the observer is then embedded in a MPC scheme designed for the solution of the tracking problem. The resulting closed-loop scheme is proved to be asymptotically stable. The training algorithm and control scheme are tested numerically on the simulator of a pH reactor, the reported results confirm the effectiveness of the proposed approach.
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URL
https://arxiv.org/abs/1910.04024