arXiv subjects

Marco Forgione

Publications and source records attributed to Marco Forgione.

28 records · Page 2Linked to original sources

arXiv2023

In-context learning of state estimators

State estimation has a pivotal role in several applications, including but not limited to advanced control design. Especially when dealing with nonlinear systems state estimation is a nontrivial task, often entailing approximations and challenging fine-tuning phases. In this work, we propose to overcome these challenges by formulating an in-context state-estimation problem, enabling us to learn a state estimator for a class of (nonlinear) systems abstracting from particular instances of the state seen during training. To this end, we extend an in-context learning framework recently proposed for system identification, showing via a benchmark numerical example that this approach allows us to (i) use training data directly for the design of the state estimator, (ii) not requiring extensive fine-tuning procedures, while (iii) achieving superior performance compared to state-of-the-art benchmarks.

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arXiv2023

Neural State-Space Models: Empirical Evaluation of Uncertainty Quantification

Effective quantification of uncertainty is an essential and still missing step towards a greater adoption of deep-learning approaches in different applications, including mission-critical ones. In particular, investigations on the predictive uncertainty of deep-learning models describing non-linear dynamical systems are very limited to date. This paper is aimed at filling this gap and presents preliminary results on uncertainty quantification for system identification with neural state-space models. We frame the learning problem in a Bayesian probabilistic setting and obtain posterior distributions for the neural network's weights and outputs through approximate inference techniques. Based on the posterior, we construct credible intervals on the outputs and define a surprise index which can effectively diagnose usage of the model in a potentially dangerous out-of-distribution regime, where predictions cannot be trusted.

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arXiv2022

Learning neural state-space models: do we need a state estimator?

In recent years, several algorithms for system identification with neural state-space models have been introduced. Most of the proposed approaches are aimed at reducing the computational complexity of the learning problem, by splitting the optimization over short sub-sequences extracted from a longer training dataset. Different sequences are then processed simultaneously within a minibatch, taking advantage of modern parallel hardware for deep learning. An issue arising in these methods is the need to assign an initial state for each of the sub-sequences, which is required to run simulations and thus to evaluate the fitting loss. In this paper, we provide insights for calibration of neural state-space training algorithms based on extensive experimentation and analyses performed on two recognized system identification benchmarks. Particular focus is given to the choice and the role of the initial state estimation. We demonstrate that advanced initial state estimation techniques are really required to achieve high performance on certain classes of dynamical systems, while for asymptotically stable ones basic procedures such as zero or random initialization already yield competitive performance.

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arXiv2022

On the adaptation of recurrent neural networks for system identification

This paper presents a transfer learning approach which enables fast and efficient adaptation of Recurrent Neural Network (RNN) models of dynamical systems. A nominal RNN model is first identified using available measurements. The system dynamics are then assumed to change, leading to an unacceptable degradation of the nominal model performance on the perturbed system. To cope with the mismatch, the model is augmented with an additive correction term trained on fresh data from the new dynamic regime. The correction term is learned through a Jacobian Feature Regression (JFR) method defined in terms of the features spanned by the model's Jacobian with respect to its nominal parameters. A non-parametric view of the approach is also proposed, which extends recent work on Gaussian Process (GP) with Neural Tangent Kernel (NTK-GP) to the RNN case (RNTK-GP). This can be more efficient for very large networks or when only few data points are available. Implementation aspects for fast and efficient computation of the correction term, as well as the initial state estimation for the RNN model are described. Numerical examples show the effectiveness of the proposed methodology in presence of significant system variations.

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arXiv2021

Model structures and fitting criteria for system identification with neural networks

This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are fitted to measured data using different criteria including a computationally efficient approach minimizing a regularized multi-step ahead simulation error. In this approach, the neural network parameters are estimated along with the initial conditions used to simulate the output signal in small-size subsequences. A regularization term is included in the fitting cost in order to enforce these initial conditions to be consistent with the estimated system dynamics. Pitfalls and limitations of naive one-step prediction and simulation error minimization are also discussed.

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arXiv2021

Continuous-time system identification with neural networks: Model structures and fitting criteria

This paper presents tailor-made neural model structures and two custom fitting criteria for learning dynamical systems. The proposed framework is based on a representation of the system behavior in terms of continuous-time state-space models. The sequence of hidden states is optimized along with the neural network parameters in order to minimize the difference between measured and estimated outputs, and at the same time to guarantee that the optimized state sequence is consistent with the estimated system dynamics. The effectiveness of the approach is demonstrated through three case studies, including two public system identification benchmarks based on experimental data.

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arXiv2021

dynoNet: a neural network architecture for learning dynamical systems

This paper introduces a network architecture, called dynoNet, utilizing linear dynamical operators as elementary building blocks. Owing to the dynamical nature of these blocks, dynoNet networks are tailored for sequence modeling and system identification purposes. The back-propagation behavior of the linear dynamical operator with respect to both its parameters and its input sequence is defined. This enables end-to-end training of structured networks containing linear dynamical operators and other differentiable units, exploiting existing deep learning software. Examples show the effectiveness of the proposed approach on well-known system identification benchmarks. Examples show the effectiveness of the proposed approach against well-known system identification benchmarks.

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arXiv2021

Deep learning with transfer functions: new applications in system identification

This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end training of structured networks containing linear transfer functions and other differentiable units {by} exploiting standard deep learning software. Two relevant applications of the operator in system identification are presented. The first one consists in the integration of {prediction error methods} in deep learning. The dynamical operator is included as {the} last layer of a neural network in order to obtain the optimal one-step-ahead prediction error. The second one considers identification of general block-oriented models from quantized data. These block-oriented models are constructed by combining linear dynamical operators with static nonlinearities described as standard feed-forward neural networks. A custom loss function corresponding to the log-likelihood of quantized output observations is defined. For gradient-based optimization, the derivatives of the log-likelihood are computed by applying the back-propagation algorithm through the whole network. Two system identification benchmarks are used to show the effectiveness of the proposed methodologies.

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arXiv2021

Efficient Calibration of Embedded MPC

Model Predictive Control (MPC) is a powerful and flexible design tool of high-performance controllers for physical systems in the presence of input and output constraints. A challenge for the practitioner applying MPC is the need of tuning a large number of parameters such as prediction and control horizons, weight matrices of the MPC cost function, and observer gains, according to different trade-offs. The MPC design task is even more involved when the control law has to be deployed to an embedded hardware unit endowed with limited computational resources. In this case, real-time system requirements limit the complexity of the applicable MPC configuration, engendering additional design tradeoffs and requiring to tune further parameters, such as the sampling time and the tolerances used in the on-line numerical solver. To take into account closed-loop performance and real-time requirements, in this paper we tackle the embedded MPC design problem using a global, data-driven, optimization approach We showcase the potential of this approach by tuning an MPC controller on two hardware platforms characterized by largely different computational capabilities.

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arXiv2019

Performance-oriented model learning for data-driven MPC design

Model Predictive Control (MPC) is an enabling technology in applications requiring controlling physical processes in an optimized way under constraints on inputs and outputs. However, in MPC closed-loop performance is pushed to the limits only if the plant under control is accurately modeled; otherwise, robust architectures need to be employed, at the price of reduced performance due to worst-case conservative assumptions. In this paper, instead of adapting the controller to handle uncertainty, we adapt the learning procedure so that the prediction model is selected to provide the best closed-loop performance. More specifically, we apply for the first time the above "identification for control" rationale to hierarchical MPC using data-driven methods and Bayesian optimization.

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