publications

2024

1. Conference

   Learning state observers for recurrent neural network models

   Fabio Bonassi, Carl Andersson, Per Mattsson, and Thomas B Schön

   In 2024 IEEE 63rd Conference on Decision and Control (CDC), 2024

   Abs DOI Bib HTML

   In this paper, we discuss the problem of learning state observers for Recurrent Neural Network (RNN) black-box models of dynamical systems. State observers are indeed key to designing state-feedback control laws, such as nonlinear Model Predictive Control, with satisfactory closed-loop performance. Besides, they can also improve the training procedure of RNN models themselves. Then, we summarize recent developments aimed at jointly learning RNN models and neural network-based state observers, and we propose a new structure based on the recent S5 architecture. We finally test various observer structures on a pH neutralization process benchmark system, showing the advantages and shortcomings of each architecture.

   @inproceedings{bonassi2024learning,
     title = {Learning state observers for recurrent neural network models},
     author = {Bonassi, Fabio and Andersson, Carl and Mattsson, Per and Sch{\"o}n, Thomas B},
     booktitle = {2024 IEEE 63rd Conference on Decision and Control (CDC)},
     year = {2024},
     pages = {7871-7878},
     doi = {10.1109/CDC56724.2024.10886550},
   }

2. Conference

   Estimation and MPC control based on gated recurrent unit neural networks with unknown disturbances

   Eva Masero, Fabio Bonassi, Alessio La Bella, and Riccardo Scattolini

   In 2024 IEEE 63rd Conference on Decision and Control (CDC), 2024

   Abs DOI Bib HTML

   This paper proposes a nonlinear model predictive control (NMPC) approach for incrementally input-to-state stable gated recurrent units (GRU) neural networks affected by state and output disturbances. In particular, a Luenberger-like observer is designed for state and disturbance estimation with guaranteed convergence properties. This paves the way for the design of an NMPC regulator capable of rejecting unknown piecewise-constant disturbances. The method is tested in simulation on a nonlinear benchmark system, i.e., a chemical reaction process, showing promising results.

   @inproceedings{masero2024estimation,
     title = {Estimation and {MPC} control based on gated recurrent unit neural networks with unknown disturbances},
     author = {Masero, Eva and Bonassi, Fabio and La Bella, Alessio and Scattolini, Riccardo},
     booktitle = {2024 IEEE 63rd Conference on Decision and Control (CDC)},
     year = {2024},
     pages = {120-125},
     doi = {10.1109/CDC56724.2024.10886020},
   }

3. Journal

   Learning Control Affine Neural NARX Models for Internal Model Control Design

   Jing Xie, Fabio Bonassi, and Riccardo Scattolini

   IEEE Transactions on Automation Science and Engineering, 2024

   Abs DOI arXiv Bib HTML

   This paper explores the use of Control Affine Neural Nonlinear AutoRegressive eXogenous (CA-NNARX) models for nonlinear system identification and model-based control design. The idea behind this architecture is to match the known control-affine structure of the system to achieve improved performance. Coherently with recent literature of neural networks for data-driven control, we first analyze the stability properties of CA-NNARX models, devising sufficient conditions for their incremental Input-to-State Stability (δISS) that can be enforced at the model training stage. The model’s stability property is then leveraged to design a stable Internal Model Control (IMC) architecture. The proposed control scheme is tested on a real Quadruple Tank benchmark system to address the output reference tracking problem. The results achieved show that (i) the modeling accuracy of CA-NNARX is superior to the one of a standard NNARX model for given weight size and training epochs, (ii) the proposed IMC law provides performance comparable to the ones of a standard Model Predictive Controller (MPC) at a significantly lower computational burden, and (iii) the δISS of the model is beneficial to the closed-loop performance. Note to Practitioners —Many engineering systems, such as robotic manipulators and chemical reactors, are described by Control Affine (CA) models, characterized by onlinear dynamics where the control variable enters in a linear way. If only this structural information is available without any additional knowledge, for instance on the order of the system or on the value of its parameters, a black-box identification approach can be followed to estimate the model from data. For these reasons, in this paper we propose a modeling and control design method suited for this class of systems. Specifically, we assume that the system is described by a CA-Neural Nonlinear AutoRegressive eXogenous (CA-NNARX) model. Then, the estimated model is used to design a stable Internal Model Control (IMC) scheme for the solution of output reference tracking problems. The stability, performance, and robustness properties of the proposed approach are studied and tested in the control of a laboratory system. In addition, a simulation analysis shows how IMC represents a valid alternative to the popular Model Predictive Control (MPC) approach, in particular for embedded systems, where the computation power required by MPC can be too high.

   @article{xie2022robust,
     title = {Learning Control Affine Neural NARX Models for Internal Model Control Design},
     author = {Xie, Jing and Bonassi, Fabio and Scattolini, Riccardo},
     journal = {IEEE Transactions on Automation Science and Engineering},
     doi = {10.1109/TASE.2024.3479321},
     year = {2024},
   }

4. Preprint

   Accounts of using the Tustin-Net architecture on a rotary inverted pendulum

   Stijn Esch, Fabio Bonassi, and Thomas B Schön

   arXiv preprint arXiv:2408.12266, 2024

   Abs arXiv Bib

   In this report we investigate the use of the Tustin neural network architecture (Tustin-Net) for the identification of a physical rotary inverse pendulum. This physics-based architecture is of particular interest as it builds on the known relationship between velocities and positions. We here aim at discussing the advantages, limitations and performance of Tustin-Nets compared to first-principles grey-box models on a real physical apparatus, showing how, with a standard training procedure, the former can hardly achieve the same accuracy as the latter. To address this limitation, we present a training strategy based on transfer learning that yields Tustin-Nets that are competitive with the first-principles model, without requiring extensive knowledge of the setup as the latter.

   @article{van2024accounts,
     title = {Accounts of using the Tustin-Net architecture on a rotary inverted pendulum},
     author = {van Esch, Stijn and Bonassi, Fabio and Sch{\"o}n, Thomas B},
     journal = {arXiv preprint arXiv:2408.12266},
     year = {2024},
   }

5. Journal

   On the equivalence of direct and indirect data-driven predictive control approaches

   Per Mattsson, Fabio Bonassi, Valentina Breschi, and Thomas B Schön

   IEEE Control System Letters, 2024

   Abs arXiv Bib

   Recently, several direct Data-Driven Predictive Control (DDPC) methods have been proposed, advocating the possibility of designing predictive controllers from historical input-output trajectories without the need to identify a model. In this work, we show their equivalence to a (relaxed) indirect approach, allowing us to reformulate direct methods in terms of estimated parameters and covariance matrices. This allows us to provide further insights into how these direct predictive control methods work, showing that, for unconstrained problems, the direct methods are equivalent to subspace predictive control with a reduced weight on the tracking cost, and analyzing the impact of the data length on tuning strategies. Via a numerical experiment, we also illustrate why the performance of direct DDPC methods with fixed regularization tends to degrade as the number of training samples increases.

   @article{mattsson2024equivalence,
     title = {On the equivalence of direct and indirect data-driven predictive control approaches},
     author = {Mattsson, Per and Bonassi, Fabio and Breschi, Valentina and Sch{\"o}n, Thomas B},
     journal = {IEEE Control System Letters},
     year = {2024},
     volume = {8},
     pages = {796-801},
   }

6. Conference

   Structured state-space models are deep Wiener models

   Fabio Bonassi, Carl Andersson, Per Mattsson, and Thomas B Schön

   In 20th IFAC Symposium on System Identification (SYSID), 2024

   Abs DOI arXiv Bib HTML

   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.

   @inproceedings{bonassi2024structured,
     title = {Structured state-space models are deep Wiener models},
     year = {2024},
     booktitle = {20th IFAC Symposium on System Identification (SYSID)},
     author = {Bonassi, Fabio and Andersson, Carl and Mattsson, Per and Sch{\"o}n, Thomas B},
     url = {https://www.sciencedirect.com/science/article/pii/S2405896324013168},
     doi = {10.1016/j.ifacol.2024.08.536},
   }

7. Book

   Reconciling Deep Learning and Control Theory: Recurrent Neural Networks for Indirect Data-Driven Control

   Fabio Bonassi

   In Special Topics in Information Technology, 2024

   Abs DOI Bib HTML

   This Brief aims to discuss the potential of Recurrent Neural Networks (RNNs) for indirect data-driven control. Indeed, while RNNs have long been known to be universal approximators of dynamical systems, their adoption for system identification and control has been limited by the lack of solid theoretical foundations. We here intend to summarize a novel approach to address this gap, which is structured in two contributions. First, a framework for learning safe and robust RNN models is devised, relying on the Incremental Input-to-State Stability (}}\backslashdelta }}\deltaISS) notion. Then, after a }}\backslashdelta }}\deltaISS black-box model of the plant is identified, its use for the design of model-based control laws (such as Nonlinear MPC) with closed-loop performance guarantees is illustrated. Finally, the main open problems and future research directions are outlined.

   @incollection{bonassi2024reconciling,
     title = {Reconciling Deep Learning and Control Theory: Recurrent Neural Networks for Indirect Data-Driven Control},
     author = {Bonassi, Fabio},
     booktitle = {Special Topics in Information Technology},
     pages = {77--87},
     year = {2024},
     publisher = {Springer},
     doi = {10.1007/978-3-031-51500-2_7},
     url = {https://link.springer.com/chapter/10.1007/978-3-031-51500-2_7},
   }

8. Journal

   Nonlinear MPC design for incrementally ISS systems with application to GRU networks

   Fabio Bonassi, Alessio La Bella, Marcello Farina, and Riccardo Scattolini

   Automatica, 2024

   Abs DOI arXiv Bib HTML

   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.

   @article{bonassi2024nonlinear,
     title = {Nonlinear MPC design for incrementally ISS systems with application to GRU networks},
     author = {Bonassi, Fabio and {La Bella}, Alessio and Farina, Marcello and Scattolini, Riccardo},
     journal = {Automatica},
     publisher = {Elsevier},
     volume = {159},
     pages = {111381},
     year = {2024},
     issn = {0005-1098},
     doi = {10.1016/j.automatica.2023.111381},
     url = {https://www.sciencedirect.com/science/article/pii/S0005109823005484}
   }

2023

1. Conference

   Deep Long-Short Term Memory networks: Stability properties and Experimental validation

   Fabio Bonassi, Alessio La Bella, Giulio Panzani, Marcello Farina, and Riccardo Scattolini

   In 2023 European Control Conference (ECC), 2023

   Abs arXiv Bib HTML

   The aim of this work is to investigate the use of Incrementally Input-to-State Stable (𝛿ISS) deep Long Short Term Memory networks (LSTMs) for the identification of nonlinear dynamical systems. We show that suitable sufficient conditions on the weights of the network can be leveraged to setup a training procedure able to learn provenly-𝛿ISS LSTM models from data. The proposed approach is tested on a real brake-by-wire apparatus to identify a model of the system from input-output experimentally collected data. Results show satisfactory modeling performances.

   @inproceedings{bonassi2023deep,
     title = {Deep Long-Short Term Memory networks: Stability properties and Experimental validation},
     author = {Bonassi, Fabio and La Bella, Alessio and Panzani, Giulio and Farina, Marcello and Scattolini, Riccardo},
     booktitle = {2023 European Control Conference (ECC)},
     year = {2023},
     pages = {1-6},
   }

2. Journal

   Robust offset-free nonlinear model predictive control for systems learned by neural nonlinear autoregressive exogenous models

   Jing Xie, Fabio Bonassi, Marcello Farina, and Riccardo Scattolini

   International Journal of Robust and Nonlinear Control, 2023

   Abs DOI arXiv Bib HTML

   This paper presents a robust Model Predictive Control (MPC) scheme that provides offset-free setpoint tracking for systems described by Neural Nonlinear AutoRegressive eXogenous (NNARX) models. The NNARX model learns the dynamics of the plant from input-output data, and during the training the Incremental Input-to-State Stability (𝛿ISS) property is forced to guarantee stability. The trained NNARX model is then augmented with an explicit integral action on the output tracking error, which allows the control scheme to enjoy offset-free tracking ability. A tube-based MPC is finally designed, leveraging the unique structure of the model, to ensure robust stability and robust asymptotic zero error regulation for constant reference signals in the presence of model-plant mismatch or unknown disturbances. Numerical simulations on a water heating system show the effectiveness of the proposed control algorithm.

   @article{xie2022robusu,
     title = {Robust offset-free nonlinear model predictive control for systems learned by neural nonlinear autoregressive exogenous models},
     author = {Xie, Jing and Bonassi, Fabio and Farina, Marcello and Scattolini, Riccardo},
     journal = {International Journal of Robust and Nonlinear Control},
     doi = {10.1002/rnc.6883},
     year = {2023},
   }

3. Thesis

   Reconciling deep learning and control theory: recurrent neural networks for model-based control design

   Fabio Bonassi

   Feb 2023

   Chorafas Prize Abs Bib HTML

   Dimitris N. Chorafas Ph.D. Award from the Dimitris N. Chorafas Foundation (Switzerland) to the best Ph.D. theses for their high potential for practical application and the special significance attached to their aftermath

   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.

   @phdthesis{bonassi2023reconciling,
     title = {Reconciling deep learning and control theory: recurrent neural networks for model-based control design},
     author = {Bonassi, Fabio},
     year = {2023},
     month = feb,
     address = {Milan, Italy},
     school = {Politecnico di Milano},
     type = {PhD thesis},
   }

2022

1. Conference

   An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models

   Fabio Bonassi, Jing Xie, Marcello Farina, and Riccardo Scattolini

   In 2022 IEEE 61st Conference on Decision and Control (CDC), Feb 2022

   Abs DOI arXiv Bib HTML

   This paper deals with the design of nonlinear MPC controllers that provide offset-free setpoint tracking for models described by Neural Nonlinear AutoRegressive eXogenous (NNARX) networks. The NNARX model is identified from input-output data collected from the plant, and can be given a state-space representation with known measurable states made by past input and output variables, so that a state observer is not required. In the training phase, the Incremental Input-to-State Stability (δISS) property can be forced when consistent with the behavior of the plant. The δISS property is then leveraged to augment the model with an explicit integral action on the output tracking error, which allows to achieve offset-free tracking capabilities to the designed control scheme. The proposed control architecture is numerically tested on a water heating system and the achieved results are compared to those scored by another popular offset-free MPC method, showing that the proposed scheme attains remarkable performances even in presence of disturbances acting on the plant.

   @inproceedings{bonassi2022offset,
     title = {An Offset-Free Nonlinear MPC scheme for systems learned by Neural NARX models},
     author = {Bonassi, Fabio and Xie, Jing and Farina, Marcello and Scattolini, Riccardo},
     booktitle = {2022 IEEE 61st Conference on Decision and Control (CDC)},
     year = {2022},
     pages = {2123-2128},
     doi = {10.1109/CDC51059.2022.9992362},
   }

2. Conference

   Towards lifelong learning of Recurrent Neural Networks for control design

   Fabio Bonassi, Jing Xie, Marcello Farina, and Riccardo Scattolini

   In 2022 European Control Conference (ECC), Feb 2022

   Abs DOI arXiv Bib HTML

   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.

   @inproceedings{bonassi2022towards,
     title = {Towards lifelong learning of Recurrent Neural Networks for control design},
     author = {Bonassi, Fabio and Xie, Jing and Farina, Marcello and Scattolini, Riccardo},
     booktitle = {2022 European Control Conference (ECC)},
     pages = {2018-2023},
     year = {2022},
     doi = {10.23919/ECC55457.2022.9838393},
   }

3. Journal

   On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments

   Fabio Bonassi, Marcello Farina, Jing Xie, and Riccardo Scattolini

   Journal of Process Control, Feb 2022

   Abs DOI arXiv Bib HTML

   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.

   @article{bonassi2022survey,
     title = {On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments},
     author = {Bonassi, Fabio and Farina, Marcello and Xie, Jing and Scattolini, Riccardo},
     journal = {Journal of Process Control},
     volume = {114},
     pages = {92-104},
     year = {2022},
     issn = {0959-1524},
     doi = {10.1016/j.jprocont.2022.04.011},
   }

4. Journal

   Recurrent neural network-based Internal Model Control for stable nonlinear systems

   Fabio Bonassi, and Riccardo Scattolini

   European Journal of Control, Feb 2022

   Abs DOI arXiv Bib HTML

   Owing to their superior modeling capabilities, gated Recurrent Neural Networks (RNNs), such as Gated Recurrent Units (GRUs) and Long Short-Term Memory networks (LSTMs), have become popular tools for learning dynamical systems. This paper aims to discuss how these networks can be adopted for the synthesis of Internal Model Control (IMC) architectures. To this end, a first gated RNN is used to learn a model of the unknown input-output stable plant. Then, another gated RNN approximating the model inverse is trained. The proposed scheme is able to cope with the saturation of the control variables, and it can be deployed on low-power embedded controllers since it does not require any online computation. The approach is then tested on the Quadruple Tank benchmark system, resulting in satisfactory closed-loop performances.

   @article{bonassi2022imc,
     title = {Recurrent neural network-based Internal Model Control for stable nonlinear systems},
     author = {Bonassi, Fabio and Scattolini, Riccardo},
     journal = {European Journal of Control},
     pages = {100632},
     year = {2022},
     issn = {0947-3580},
     doi = {https://doi.org/10.1016/j.ejcon.2022.100632},
     keywords = {Recurrent Neural Network, Internal Model Control, Neurocontrollers},
   }

2021

1. Journal

   On the stability properties of Gated Recurrent Units neural networks

   Fabio Bonassi, Marcello Farina, and Riccardo Scattolini

   System & Control Letters, Feb 2021

   Abs DOI arXiv Bib HTML

   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.

   @article{bonassi2020stability,
     title = {On the stability properties of Gated Recurrent Units neural networks},
     author = {Bonassi, Fabio and Farina, Marcello and Scattolini, Riccardo},
     journal = {System \& Control Letters},
     publisher = {Elsevier},
     volume = {157},
     pages = {105049},
     year = {2021},
     issn = {0167-6911},
     doi = {10.1016/j.sysconle.2021.105049},
     url = {https://www.sciencedirect.com/science/article/pii/S0167691121001791}
   }

2. Conference

   Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks

   Fabio Bonassi, Caio Fabio Oliveira da Silva, and Riccardo Scattolini

   In 3rd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON), Feb 2021

   Abs DOI arXiv Bib HTML

   The use of Recurrent Neural Networks (RNNs) for system identification has recently gathered increasing attention, thanks to their black-box modeling capabilities.Albeit RNNs have been fruitfully adopted in many applications, only few works are devoted to provide rigorous theoretical foundations that justify their use for control purposes. The aim of this paper is to describe how stable Gated Recurrent Units (GRUs), a particular RNN architecture, can be trained and employed in a Nonlinear MPC framework to perform offset-free tracking of constant references with guaranteed closed-loop stability. The proposed approach is tested on a pH neutralization process benchmark, showing remarkable performances.

   @inproceedings{bonassi2021nonlinear,
     title = {Nonlinear MPC for Offset-Free Tracking of systems learned by GRU Neural Networks},
     volume = {54},
     number = {14},
     pages = {54-59},
     year = {2021},
     issn = {2405-8963},
     booktitle = {3rd IFAC Conference on Modelling, Identification and Control of Nonlinear Systems (MICNON)},
     author = {Bonassi, Fabio and {Oliveira da Silva}, {Caio Fabio} and Scattolini, Riccardo},
     doi = {https://doi.org/10.1016/j.ifacol.2021.10.328},
     url = {https://www.sciencedirect.com/science/article/pii/S240589632101733X},
   }

3. Conference

   Stability of discrete-time feed-forward neural networks in NARX configuration

   Fabio Bonassi, Marcello Farina, and Riccardo Scattolini

   In 19th IFAC Symposium on System Identification (SYSID), Feb 2021

   IFAC Award Abs DOI arXiv Bib HTML

   IFAC Best Student Paper Award at SYSID 2021

   The idea of using Feed-Forward Neural Networks (FFNNs) as regression functions for Nonlinear AutoRegressive eXogenous (NARX) models, leading to models herein named Neural NARXs (NNARXs), has been quite popular in the early days of machine learning applied to nonlinear system identification, owing to their simple structure and ease of application to control design. Nonetheless, few theoretical results are available concerning the stability properties of these models. In this paper we address this problem, providing a sufficient condition under which NNARX models are guaranteed to enjoy the Input-to-State Stability (ISS) and the Incremental Input-to-State Stability (δISS) properties. This condition, which is an inequality on the weights of the underlying FFNN, can be enforced during the training procedure to ensure the stability of the model. The proposed model, along with this stability condition, are tested on the pH neutralization process benchmark, showing satisfactory results.

   @inproceedings{bonassi2021nnarx,
     title = {Stability of discrete-time feed-forward neural networks in NARX configuration},
     volume = {54},
     number = {7},
     pages = {547-552},
     year = {2021},
     booktitle = {19th IFAC Symposium on System Identification (SYSID)},
     issn = {2405-8963},
     doi = {10.1016/j.ifacol.2021.08.417},
     url = {https://www.sciencedirect.com/science/article/pii/S2405896321011915},
     author = {Bonassi, Fabio and Farina, Marcello and Scattolini, Riccardo},
     keywords = {Neural networks, Nonlinear System Identification, Identification for Control, Input-to-State Stability, Incremental Input-to-State Stability},
   }

4. Journal

   Learning model predictive control with long short-term memory networks

   Enrico Terzi, Fabio Bonassi, Marcello Farina, and Riccardo Scattolini

   International Journal of Robust and Nonlinear Control, Feb 2021

   Abs DOI arXiv Bib HTML

   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 (𝛿ISS) 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.

   @article{terzi2021learning,
     title = {Learning model predictive control with long short-term memory networks},
     author = {Terzi, Enrico and Bonassi, Fabio and Farina, Marcello and Scattolini, Riccardo},
     journal = {International Journal of Robust and Nonlinear Control},
     year = {2021},
     publisher = {Wiley Online Library},
     doi = {10.1002/rnc.5519},
     volume = {31},
     number = {18},
     pages = {8877--8896},
     url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rnc.5519},
   }

5. Journal

   Supervised control of hybrid AC-DC grids for power balance restoration

   Fabio Bonassi, Alessio La Bella, Riccardo Lazzari, Carlo Sandroni, and Riccardo Scattolini

   Electric Power Systems Research, Feb 2021

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   In this paper, the flexibility of hybrid AC-DC distribution networks is exploited to coordinate multiple Distributed Energy Resources (DERs) with the aim of promptly restoring unexpected power imbalances caused by intermittent Renewable Energy Sources (RESs) and loads. Given the potential large-scale nature of the problem, the AC distribution network is decomposed into non-overlapping areas named clusters, equipped with MicroGrids (MGs) and non-dispatchable units, and interconnected also by the DC network. Each cluster is endowed with a Model Predictive Controller designed to compensate the local active power variability by requesting balancing services to the local MGs. A supervisory layer is designed and activated to optimally transfer power through the controllable DC links guaranteeing enough operative margins to each cluster. The designed architecture is tested on a benchmark grid composed of the IEEE 37-bus and 13-bus systems, connected by a multi-terminal DC network. The reported numerical results witness the effectiveness of the proposed approach.

   @article{bonassi2021supervised,
     title = {Supervised control of hybrid AC-DC grids for power balance restoration},
     author = {Bonassi, Fabio and La Bella, Alessio and Lazzari, Riccardo and Sandroni, Carlo and Scattolini, Riccardo},
     journal = {Electric Power Systems Research},
     volume = {196},
     pages = {107107},
     year = {2021},
     publisher = {Elsevier},
     url = {https://www.sciencedirect.com/science/article/pii/S0378779621000882},
     doi = {10.1016/j.epsr.2021.107107},
   }

2020

1. Conference

   LSTM neural networks: Input to state stability and probabilistic safety verification

   Fabio Bonassi, Enrico Terzi, Marcello Farina, and Riccardo Scattolini

   In Learning for Dynamics and Control (L4DC), Feb 2020

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   The goal of this paper is to analyze Long Short Term Memory (LSTM) neural networks from a dynamical system perspective. The classical recursive equations describing the evolution of LSTM can be recast in state space form, resulting in a time invariant nonlinear dynamical system. In this work, a sufficient condition guaranteeing the Input-to-State (ISS) stability property of this system are provided. Then, a discussion on the verification of LSTM networks is provided; in particular, a dedicated approach based on the scenario algorithm is devised. The proposed method is eventually tested on a pH neutralization process.

   @inproceedings{bonassi2020lstm,
     title = {LSTM neural networks: Input to state stability and probabilistic safety verification},
     author = {Bonassi, Fabio and Terzi, Enrico and Farina, Marcello and Scattolini, Riccardo},
     booktitle = {Learning for Dynamics and Control (L4DC)},
     pages = {85--94},
     year = {2020},
     organization = {PMLR},
     url = {http://proceedings.mlr.press/v120/bonassi20a.html},
   }

2. Conference

   A hierarchical approach for balancing service provision by microgrids aggregators

   Alessio La Bella, Fabio Bonassi, Carlo Sandroni, Lorenzo Fagiano, and Riccardo Scattolini

   In 21st IFAC World Congress, Feb 2020

   Abs DOI Bib HTML

   Volatile renewable energy resources are gaining more and more diffusion throughout the power system, and their intermittent production calls for enhanced balancing efforts. With a recent regulation, the European Union endorsed the participation of aggregated microgrids to the balancing of power system. The resulting assets optimization problem, however, features privacy constraints that prevent a full exchange of information, making fully centralized approaches not suitable. To this purpose, this work proposes a hierarchical approach allowing microgrids’ aggregators to provide balancing services in an efficient and privacy-friendly fashion. This approach is based on a novel method to describe the power exibility that each microgrid can provide, allowing to significantly decrease the computational effort.

   @inproceedings{la2020hierarchical,
     title = {A hierarchical approach for balancing service provision by microgrids aggregators},
     author = {La Bella, Alessio and Bonassi, Fabio and Sandroni, Carlo and Fagiano, Lorenzo and Scattolini, Riccardo},
     booktitle = {21st IFAC World Congress},
     volume = {53},
     number = {2},
     pages = {12930--12935},
     year = {2020},
     publisher = ifac,
     doi = {10.1016/j.ifacol.2020.12.2126},
     url = {https://www.sciencedirect.com/science/article/pii/S2405896320327786},
   }

3. Conference

   A fully distributed control scheme for power balancing in distribution networks

   Alessio La Bella, Fabio Bonassi, Pascal Klaus, and Riccardo Scattolini

   In 21st IFAC World Congress, Feb 2020

   Abs DOI Bib HTML

   The progressive diffusion of generation units based on intermittent renewable energy sources, as well as the increasing volatile power demand, calls for a new framework to compensate the power variability in a local fashion. In this context, the European Union instituted the figure of the Balance Responsible Party, i.e. an entity entitled of internally compensating the power uctuations, exploiting a portfolio of local dispatchable units. Considering a distribution network carrying balance responsibility, this work devises a scalable, fully distributed, multilayer control strategy for internal power balancing. The proposed scheme features multiple local MPC regulators, performing an autonomous power balancing; a supervisory layer based on Distributed Consensus ADMM is introduced to coordinate local regulators when some of them exhausts its local resources. Numerical results eventually show the effectiveness of the approach

   @inproceedings{la2020fully,
     title = {A fully distributed control scheme for power balancing in distribution networks},
     author = {La Bella, Alessio and Bonassi, Fabio and Klaus, Pascal and Scattolini, Riccardo},
     booktitle = {21st IFAC World Congress},
     volume = {53},
     number = {2},
     pages = {13178--13183},
     year = {2020},
     publisher = ifac,
     doi = {10.1016/j.ifacol.2020.12.141},
     url = {https://www.sciencedirect.com/science/article/pii/S2405896320303992},
   }

4. Conference

   Software-in-the-loop testing of a distributed optimal scheduling strategy for microgrids’ aggregators

   Fabio Bonassi, Alessio La Bella, Lorenzo Fagiano, Riccardo Scattolini, Donato Zarrilli, and 1 more author

   In IEEE PES Innovative Smart Grid Technologies Europe, Feb 2020

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   Recent regulations have explicitly endorsed the provision of ancillary services by Microgrids (MGs). However, the associated technical requirements (e.g. minimum power reserve) still represent an impeding factor for most MGs given their reduced capability. For this reason, approaches to pool MGs into Aggregators, allowing to jointly coordinate MGs to fulfill such requirements, have been proposed but their practical feasibility has been not proved. Therefore, the goal of this paper is to test a previously proposed distributed day-ahead scheduling algorithm on a realistic benchmark with ABB e-mesh(TM) EMS, an industrial-grade MG energy management system. The results show that the approach can deal systematically with different MG units and controllers, maintaining its scalable and optimal performances.

   @inproceedings{bonassi2020software,
     title = {Software-in-the-loop testing of a distributed optimal scheduling strategy for microgrids' aggregators},
     author = {Bonassi, Fabio and La Bella, Alessio and Fagiano, Lorenzo and Scattolini, Riccardo and Zarrilli, Donato and Almaleck, Pablo},
     booktitle = {IEEE PES Innovative Smart Grid Technologies Europe},
     pages = {985--989},
     year = {2020},
     organization = {IEEE},
     publisher = ieee,
     doi = {10.1109/ISGT-Europe47291.2020.9248775},
     url = {https://ieeexplore.ieee.org/abstract/document/9248775},
   }

2019

1. Conference

   Two-layer model predictive control of systems with independent dynamics and shared control resources

   Alessio La Bella, Fabio Bonassi, Marcello Farina, and Riccardo Scattolini

   In 15th IFAC Symposium on Large Scale Complex Systems (LSS), Feb 2019

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   This paper describes an approach to the design of a controller for a system made by dynamically decoupled subsystems. Each subsystem is endowed with local actuators that, in normal operating conditions, are able to compensate for disturbances and to provide the required control action. If, due to too large disturbances, the local control action is not sufficient, the actuators of the neighbouring subsystems can provide the required control contribution. The control scheme is designed according to a hierarchical approach: at the lower layer local Model Predictive Controllers (MPC) are used to compute the required control action. The information about any shortage or excess of control is sent to a supervisor that, if needed, re-balances the local control actions to guarantee global disturbance rejection properties. A simulation example concerning the coordination of small electrical grids is discussed to show the performances of the proposed solution.

   @inproceedings{la2019two,
     publisher = ifac,
     title = {Two-layer model predictive control of systems with independent dynamics and shared control resources},
     author = {La Bella, Alessio and Bonassi, Fabio and Farina, Marcello and Scattolini, Riccardo},
     volume = {52},
     number = {3},
     pages = {96--101},
     year = {2019},
     booktitle = {15th IFAC Symposium on Large Scale Complex Systems (LSS)},
     doi = {10.1016/j.ifacol.2019.06.017},
     url = {https://www.sciencedirect.com/science/article/pii/S2405896319301016},
   }