Learning model predictive control with long short-term memory networks

This article analyzes the stability-related properties of long short-term memory (LSTM) networks and investigates their use as the model of the plant in the design of model predictive controllers (MPC). First, sufficient conditions guaranteeing the Input-to-State stability (ISS) and Incremental Input-to-State stability (delta ISS) of LSTM are derived. These properties are then exploited to design an observer with guaranteed convergence of the state estimate to the true one. Such observer is then embedded in a MPC scheme solving 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, and the reported results confirm the effectiveness of the proposed approach.

Automated summary

This article analyzes the stability properties of long short-term memory (LSTM) networks in the context of designing model predictive controllers (MPC) for plant models. It derives conditions for Input-to-State stability (ISS) and Incremental Input-to-State stability (delta ISS) of LSTM, designs an observer for state estimation convergence, and implements it in a MPC scheme for solving tracking problems. The closed-loop scheme is proven to be asymptotically stable, and numerical tests on a pH reactor simulator confirm the effectiveness of the proposed approach.