Bonassi Fabio

The goal of this paper is to provide a system identification-friendly introduction to the Structured State-space Models (SSMs). These models have become recently popular in the machine learning community since, owing to their parallelizability, they can be efficiently and scalably trained to tackle extremely-long sequence classification and regression problems. Interestingly, SSMs appear as an effective way to learn deep Wiener models, which allows to reframe SSMs as an extension of a model class commonly used in system identification. In order to stimulate a fruitful exchange of ideas between the machine learning and system identification communities, we deem it useful to summarize the recent contributions on the topic in a structured and accessible form. At last, we highlight future research directions for which this community could provide impactful contributions.

This brief addresses the design of a Nonlinear Model Predictive Control (NMPC) strategy for exponentially incremental Input-to-State Stable (ISS) systems. In particular, a novel formulation is devised, which does not necessitate the onerous computation of terminal ingredients, but rather relies on the explicit definition of a minimum prediction horizon ensuring closed-loop stability. The designed methodology is particularly suited for the control of systems learned by Recurrent Neural Networks (RNNs), which are known for their enhanced modeling capabilities and for which the incremental ISS properties can be studied thanks to simple algebraic conditions. The approach is applied to Gated Recurrent Unit (GRU) networks, providing also a method for the design of a tailored state observer with convergence guarantees. The resulting control architecture is tested on a benchmark system, demonstrating its good control performances and efficient applicability.

This doctoral thesis aims to establish a theoretically-sound framework for the adoption of Recurrent Neural Network (RNN) models in the context of nonlinear system identification and model-based control design. The idea, long advocated by practitioners, of exploiting the remarkable modeling performances of RNNs to learn black-box models of unknown nonlinear systems, and then using such models to synthesize model-based control laws, has already shown considerable potential in many practical applications. On the other hand, the adoption of these architectures by the control systems community has been so far limited, mainly because the generality of these architectures makes it difficult to attain general properties and to build solid theoretical foundations for their safe and profitable use for control design. To address these gaps, we first provide a control engineer-friendly description of the most common RNN architectures, i.e., Neural NARXs (NNARXs), Gated Recurrent Units (GRUs), and Long Short-Term Memory networks (LSTMs), as well as their training procedure. The stability properties of these architectures are then analyzed, using common nonlinear systems’ stability notions such as the Input-to-State Stability (ISS), the Input-to-State Practical Stability (ISPS), and the Incremental Input-to-State Stability (δISS). In particular, sufficient conditions for these properties are devised for the considered RNN architectures, and it is shown how to enforce these conditions during the training procedure, in order to learn provenly stable RNN models. Model-based control strategies are then synthesized for these models. In particular, nonlinear model predictive control schemes are first designed: in this context, the model’s δISS is shown to enable the attainment of nominal closed-loop stability and, under a suitable design of the control scheme, also robust asymptotic zero-error output regulation. Then, an alternative computationally-lightweight control scheme, based on the internal model control strategy, is proposed, and its closed-loop properties are discussed. The performances of these control schemes are tested on several nonlinear benchmark systems, demonstrating the potentiality of the proposed framework. Finally, some fundamental issues for the practical implementation of RNN-based control strategies are mentioned. In particular, we discuss the need for the safety verification of RNN models and their adaptation in front of changes of the plant’s behavior, the definition of RNN structures that exploit qualitative physical knowledge of the system to boost the performances and interpretability of these models, and the problem of designing control schemes that are robust to the unavoidable plant-model mismatch.

This paper aims to discuss and analyze the potentialities of Recurrent Neural Networks (RNN) in control design applications. The main families of RNN are considered, namely Neural Nonlinear AutoRegressive eXogenous, Echo State Networks, Long Short Term Memory, and Gated Recurrent Units. The goal is twofold. Firstly, to survey recent results concerning the training of RNN that enjoy Input-to-State Stability (ISS) and Incremental Input-to-State Stability (𝛿ISS) guarantees. Secondly, to discuss the issues that still hinder the widespread use of RNN for control, namely their robustness, verifiability, and interpretability. The former properties are related to the so-called generalization capabilities of the networks, i.e. their consistency with the underlying real plants, even in presence of unseen or perturbed input trajectories. The latter is instead related to the possibility of providing a clear formal connection between the RNN model and the plant. In this context, we illustrate how ISS and 𝛿ISS represent a significant step towards the robustness and verifiability of the RNN models, while the requirement of interpretability paves the way to the use of physics-based networks. The design of model predictive controllers with RNN as plant’s model is also briefly discussed. Lastly, some of the main topics of the paper are illustrated on a simulated chemical system.

The goal of this paper is to provide sufficient conditions for guaranteeing the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) of Gated Recurrent Units (GRUs) neural networks. These conditions, devised for both single-layer and multi-layer architectures, consist of nonlinear inequalities on network’s weights. They can be employed to check the stability of trained networks, or can be enforced as constraints during the training procedure of a GRU. The resulting training procedure is tested on a Quadruple Tank nonlinear benchmark system, showing satisfactory modeling performances.