Giancarlo Ferrari-Trecate

Loris Di Natale, Muhammad Zakwan, Bratislav Svetozarevic et al.

Machine Learning (ML) and linear System Identification (SI) have been historically developed independently. In this paper, we leverage well-established ML tools - especially the automatic differentiation framework - to introduce SIMBa, a family of discrete linear multi-step-ahead state-space SI methods using backpropagation. SIMBa relies on a novel Linear-Matrix-Inequality-based free parametrization of Schur matrices to ensure the stability of the identified model. We show how SIMBa generally outperforms traditional linear state-space SI methods, and sometimes significantly, although at the price of a higher computational burden. This performance gap is particularly remarkable compared to other SI methods with stability guarantees, where the gain is frequently above 25% in our investigations, hinting at SIMBa's ability to simultaneously achieve state-of-the-art fitting performance and enforce stability. Interestingly, these observations hold for a wide variety of input-output systems and on both simulated and real-world data, showcasing the flexibility of the proposed approach. We postulate that this new SI paradigm presents a great extension potential to identify structured nonlinear models from data, and we hence open-source SIMBa on https://github.com/Cemempamoi/simba.

Stefano Riverso, Marcello Farina, Giancarlo Ferrari-Trecate

In this paper we consider a linear system represented by a coupling graph between subsystems and propose a distributed control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. Most importantly, as in Riverso et al., 2012 our design procedure enables plug-and-play (PnP) operations, meaning that (i) the addition or removal of subsystems triggers the design of local controllers associated to successors to the subsystem only and (ii) the synthesis of a local controller for a subsystem requires information only from predecessors of the subsystem and it can be performed using only local computational resources. Our method hinges on local tube MPC controllers based on robust control invariant sets and it advances the PnP design procedure proposed in Riverso et al., 2012 in several directions. Quite notably, using recent results in the computation of robust control invariant sets, we show how critical steps in the design of a local controller can be solved through linear programming. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.

Michele Tucci, Lexuan Meng, Josep M. Guerrero et al.

In this paper, we propose a secondary consensus-based control layer for current sharing and voltage balancing in DC microGrids (mGs). To this purpose, we assume that Distributed Generation Units (DGUs) are equipped with decentralized primary controllers guaranteeing voltage stability. This goal can be achieved using, for instance, Plug-and-Play (PnP) regulators. We analyze the behavior of the closed-loop mG by approximating local primary control loops with either unitary gains or first-order transfer functions. Besides proving exponential stability, current sharing, and voltage balancing, we describe how to design secondary controllers in a PnP fashion when DGUs are added or removed. Theoretical results are complemented by simulations, using a 7-DGUs mG implemented in Simulink/PLECS, and experiments on a 3-DGUs mG.

Alexander J. Gallo, Mustafa S. Turan, Francesca Boem et al.

The problem of replay attacks in the communication network between Distributed Generation Units (DGUs) of a DC microgrid is examined. The DGUs are regulated through a hierarchical control architecture, and are networked to achieve secondary control objectives. Following analysis of the detectability of replay attacks by a distributed monitoring scheme previously proposed, the need for a watermarking signal is identified. Hence, conditions are given on the watermark in order to guarantee detection of replay attacks, and such a signal is designed. Simulations are then presented to demonstrate the effectiveness of the technique.

Stefano Riverso, Michele Tucci, Juan C. Vasquez et al.

This paper presents a distributed control architecture for voltage and frequency stabilization in AC islanded microgrids. In the primary control layer, each generation unit is equipped with a local controller acting on the corresponding voltage-source converter. Following the plug-and-play design approach previously proposed by some of the authors, whenever the addition/removal of a distributed generation unit is required, feasibility of the operation is automatically checked by designing local controllers through convex optimization. The update of the voltage-control layer, when units plug -in/-out, is therefore automatized and stability of the microgrid is always preserved. Moreover, local control design is based only on the knowledge of parameters of power lines and it does not require to store a global microgrid model. In this work, we focus on bus-connected microgrid topologies and enhance the primary plug-and-play layer with local virtual impedance loops and secondary coordinated controllers ensuring bus voltage tracking and reactive power sharing. In particular, the secondary control architecture is distributed, hence mirroring the modularity of the primary control layer. We validate primary and secondary controllers by performing experiments with balanced, unbalanced and nonlinear loads, on a setup composed of three bus-connected distributed generation units. Most importantly, the stability of the microgrid after the addition/removal of distributed generation units is assessed. Overall, the experimental results show the feasibility of the proposed modular control design framework, where generation units can be added/removed on the fly, thus enabling the deployment of virtual power plants that can be resized over time.

Andrea Martin, Luca Furieri, Florian Dörfler et al.

We consider control of dynamical systems through the lens of competitive analysis. Most prior work in this area focuses on minimizing regret, that is, the loss relative to an ideal clairvoyant policy that has noncausal access to past, present, and future disturbances. Motivated by the observation that the optimal cost only provides coarse information about the ideal closed-loop behavior, we instead propose directly minimizing the tracking error relative to the optimal trajectories in hindsight, i.e., imitating the clairvoyant policy. By embracing a system level perspective, we present an efficient optimization-based approach for computing follow-the-clairvoyant (FTC) safe controllers. We prove that these attain minimal regret if no constraints are imposed on the noncausal benchmark. In addition, we present numerical experiments to show that our policy retains the hallmark of competitive algorithms of interpolating between classical $\mathcal{H}_2$ and $\mathcal{H}_\infty$ control laws - while consistently outperforming regret minimization methods in constrained scenarios thanks to the superior ability to chase the clairvoyant.

Muhammad Zakwan, Liang Xu, Giancarlo Ferrari-Trecate

Deep neural networks can be fragile and sensitive to small input perturbations that might cause a significant change in the output. In this paper, we employ contraction theory to improve the robustness of neural ODEs (NODEs). A dynamical system is contractive if all solutions with different initial conditions converge to each other exponentially fast. As a consequence, perturbations in initial conditions become less and less relevant over time. Since in NODEs the input data corresponds to the initial condition of dynamical systems, we show contractivity can mitigate the effect of input perturbations. More precisely, inspired by NODEs with Hamiltonian dynamics, we propose a class of contractive Hamiltonian NODEs (CH-NODEs). By properly tuning a scalar parameter, CH-NODEs ensure contractivity by design and can be trained using standard backpropagation. Moreover, CH-NODEs enjoy built-in guarantees of non-exploding gradients, which ensure a well-posed training process. Finally, we demonstrate the robustness of CH-NODEs on the MNIST image classification problem with noisy test data.

Stefano Riverso, Marcello Farina, Giancarlo Ferrari-Trecate

In this paper we consider a linear system structured into physically coupled subsystems and propose a decentralized control scheme capable to guarantee asymptotic stability and satisfaction of constraints on system inputs and states. The design procedure is totally decentralized, since the synthesis of a local controller uses only information on a subsystem and its neighbors, i.e. subsystems coupled to it. We first derive tests for checking if a subsystem can be plugged into (or unplugged from) an existing plant without spoiling overall stability and constraint satisfaction. When this is possible, we show how to automatize the design of local controllers so that it can be carried out in parallel by smart actuators equipped with computational resources and capable to exchange information with neighboring subsystems. In particular, local controllers exploit tube-based Model Predictive Control (MPC) in order to guarantee robustness with respect to physical coupling among subsystems. Finally, an application of the proposed control design procedure to frequency control in power networks is presented.

Luca Furieri, Clara Lucía Galimberti, Giancarlo Ferrari-Trecate

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS) approach offers an effective solution based on convex programming. Beyond this case, a globally optimal solution cannot be found in a tractable way, in general. In this paper, we develop a parametrization of all and only the control policies stabilizing a given time-varying nonlinear system in terms of the combined effect of 1) a strongly stabilizing base controller and 2) a stable SLS operator to be freely designed. Based on this result, we propose a Neural SLS (Neur-SLS) approach guaranteeing closed-loop stability during and after parameter optimization, without requiring any constraints to be satisfied. We exploit recent Deep Neural Network (DNN) models based on Recurrent Equilibrium Networks (RENs) to learn over a rich class of nonlinear stable operators, and demonstrate the effectiveness of the proposed approach in numerical examples.

Daniele Martinelli, Clara Lucía Galimberti, Ian R. Manchester et al.

In this work, we introduce and study a class of Deep Neural Networks (DNNs) in continuous-time. The proposed architecture stems from the combination of Neural Ordinary Differential Equations (Neural ODEs) with the model structure of recently introduced Recurrent Equilibrium Networks (RENs). We show how to endow our proposed NodeRENs with contractivity and dissipativity -- crucial properties for robust learning and control. Most importantly, as for RENs, we derive parametrizations of contractive and dissipative NodeRENs which are unconstrained, hence enabling their learning for a large number of parameters. We validate the properties of NodeRENs, including the possibility of handling irregularly sampled data, in a case study in nonlinear system identification.

Michele Tucci, Alessandro Floriduz, Stefano Riverso et al.

In this paper, we provide an extension of the scalable algorithm proposed in (Riverso et al., 2015) for the design of Plug-and-Play (PnP) controllers for AC Islanded microGrids (ImGs). The method in (Riverso et al., 2015) assumes DGUs are arranged in a load-connected topology, i.e. loads can appear only at the output terminals of inverters. For handling totally general interconnections of DGUs and loads, we describe an approach based on Kron Reduction (KR), a network reduction method giving an equivalent load-connected model of the original ImG. However, existing KR approaches can fail in preserving the structure of transfer functions representing transmission lines. To avoid this drawback, we introduce an approximate KR algorithm, still capable to represent exactly the asymptotic periodic behavior of electric signals even if they are unbalanced. Our results are backed up with simulations illustrating features of the new KR approach as well as its use for designing PnP controllers in a 21-bus ImG derived from an IEEE test feeder.

Michele Tucci, Stefano Riverso, Giancarlo Ferrari-Trecate

We consider the problem of stabilizing voltages in DC microGrids (mGs) given by the interconnection of Distributed Generation Units (DGUs), power lines and loads. We propose a decentralized control architecture where the primary controller of each DGU can be designed in a Plug-and-Play (PnP) fashion, allowing the seamless addition of new DGUs. Differently from several other approaches to primary control, local design is independent of the parameters of power lines. Moreover, differently from the PnP control scheme in [1], the plug-in of a DGU does not require to update controllers of neighboring DGUs. Local control design is cast into a Linear Matrix Inequality (LMI) problem that, if unfeasible, allows one to deny plug-in requests that might be dangerous for mG stability. The proof of closed-loop stability of voltages exploits structured Lyapunov functions, the LaSalle invariance theorem and properties of graph Laplacians. Theoretical results are backed up by simulations in PSCAD.

Muhammad Zakwan, Massimiliano d'Angelo, Giancarlo Ferrari-Trecate

This paper investigates the universal approximation capabilities of Hamiltonian Deep Neural Networks (HDNNs) that arise from the discretization of Hamiltonian Neural Ordinary Differential Equations. Recently, it has been shown that HDNNs enjoy, by design, non-vanishing gradients, which provide numerical stability during training. However, although HDNNs have demonstrated state-of-the-art performance in several applications, a comprehensive study to quantify their expressivity is missing. In this regard, we provide a universal approximation theorem for HDNNs and prove that a portion of the flow of HDNNs can approximate arbitrary well any continuous function over a compact domain. This result provides a solid theoretical foundation for the practical use of HDNNs.

Danilo Saccani, Luca Furieri, Giancarlo Ferrari-Trecate

The growing complexity of modern control tasks calls for controllers that can react online as objectives and disturbances change, while preserving closed-loop stability. Recent approaches for improving the performance of nonlinear systems while preserving closed-loop stability rely on time-invariant recurrent neural-network controllers, but offer no principled way to update the controller during operation. Most importantly, switching from one stabilizing policy to another can itself destabilize the closed-loop. We address this problem by introducing a stability-preserving update mechanism for nonlinear, neural-network-based controllers. Each controller is modeled as a causal operator with bounded $\ell_p$-gain, and we derive gain-based conditions under which the controller may be updated online. These conditions yield two practical update schemes, time-scheduled and state-triggered, that guarantee the closed-loop remains $\ell_p$-stable after any number of updates. Our analysis further shows that stability is decoupled from controller optimality, allowing approximate or early-stopped controller synthesis. We demonstrate the approach on nonlinear systems with time-varying objectives and disturbances, and show consistent performance improvements over static and naive online baselines while guaranteeing stability.

Danilo Saccani, Haoming Shen, Luca Furieri et al.

We study a control architecture for nonlinear constrained systems that integrates a performance-boosting (PB) controller with a scheduled Predictive Safety Filter (PSF). The PSF acts as a pre-stabilizing base controller that enforces state and input constraints. The PB controller, parameterized as a causal operator, influences the PSF in two ways: it proposes a performance input to be filtered, and it provides a scheduling signal to adjust the filter's Lyapunov-decrease rate. We prove two main results: (i) Stability by design: any controller adhering to this parametrization maintains closed-loop stability of the pre-stabilized system and inherits PSF safety. (ii) Trajectory-set expansion: the architecture strictly expands the set of safe, stable trajectories achievable by controllers combined with conventional PSFs, which rely on a pre-defined Lyapunov decrease rate to ensure stability. This scheduling allows the PB controller to safely execute complex behaviors, such as transient detours, that are provably unattainable by standard PSF formulations. We demonstrate this expanded capability on a constrained inverted pendulum task with a moving obstacle.

Riccardo Cescon, Andrea Martin, Giancarlo Ferrari-Trecate

The Linear Quadratic Gaussian (LQG) regulator is a cornerstone of optimal control theory, yet its performance can degrade significantly when the noise distributions deviate from the assumed Gaussian model. To address this limitation, this work proposes a distributionally robust generalization of the finite-horizon LQG control problem. Specifically, we assume that the noise distributions are unknown and belong to ambiguity sets defined in terms of an entropy-regularized Wasserstein distance centered at a nominal Gaussian distribution. By deriving novel bounds on this Sinkhorn discrepancy and proving structural and topological properties of the resulting ambiguity sets, we establish global optimality of linear policies. Numerical experiments showcase improved distributional robustness of our control policy.

Jean-Sébastien Brouillon, Florian Dörfler, Giancarlo Ferrari-Trecate

Maximum Likelihood Estimation of continuous variable models can be very challenging in high dimensions, due to potentially complex probability distributions. The existence of multiple interdependencies among variables can make it very difficult to establish convergence guarantees. This leads to a wide use of brute-force methods, such as grid searching and Monte-Carlo sampling and, when applicable, complex and problem-specific algorithms. In this paper, we consider inference problems where the variables are related by multiaffine expressions. We propose a novel Alternating and Iteratively-Reweighted Least Squares (AIRLS) algorithm, and prove its convergence for problems with Generalized Normal Distributions. We also provide an efficient method to compute the variance of the estimates obtained using AIRLS. Finally, we show how the method can be applied to graphical statistical models. We perform numerical experiments on several inference problems, showing significantly better performance than state-of-the-art approaches in terms of scalability, robustness to noise, and convergence speed due to an empirically observed super-linear convergence rate.

Daniele Ravasio, Danilo Saccani, Marcello Farina et al.

This work proposes a two-layered control scheme for constrained nonlinear systems represented by a class of recurrent neural networks and affected by additive disturbances. In particular, a base controller ensures global or regional closed-loop l_p-stability of the error in tracking a desired equilibrium and the satisfaction of input and output constraints within a robustly positive invariant set. An additional control contribution, derived by combining the internal model control principle with a stable operator, is introduced to improve system performance. This operator, implemented as a stable neural network, can be trained via unconstrained optimisation on a chosen performance metric, without compromising closed-loop equilibrium tracking or constraint satisfaction, even if the optimisation is stopped prematurely. In addition, we characterise the class of closed-loop stable behaviours that can be achieved with the proposed architecture. Simulation results on a pH-neutralisation benchmark demonstrate the effectiveness of the proposed approach.

Riccardo Cescon, Andrea Martin, Giancarlo Ferrari-Trecate

Classical stochastic control assumes perfect knowledge of the uncertainty affecting the plant. In practice, however, such information is often incomplete. To address this limitation, we consider a distributionally robust control (DRC) problem with ambiguity sets defined via the Sinkhorn discrepancy. Compared to other discrepancy measures based on optimal transport, such as the popular Wasserstein distance, the Sinkhorn divergence does not constrain the worst-case distribution to be discrete, and allows combining observed data with prior knowledge in the form of a reference distribution, making this choice particularly suitable when only few noise samples are available for control design. We first study the properties of Sinkhorn ambiguity sets, establishing convexity and weak compactness under standard assumptions. We then leverage these results to prove that, the Sinkhorn DR linear quadratic control problem over linear policies can be solved through convex programming-even in the presence of DR safety constraints. Finally, we validate our theoretical findings and demonstrate the effectiveness of the proposed approach on a trajectory planning example.

Vaibhav Gupta, Daniele Martinelli, Giancarlo Ferrari-Trecate et al.

In this paper, we present a novel method for synthesising an optimal distributed spatial regret controller using experimentally obtained frequency-response data. Spatial regret provides a measure of the performance gap between a structured distributed controller and an oracle with enhanced communication topology. We relax assumptions on the communication topology, allowing the oracle to adopt any enhanced structure. While this generalisation requires an iterative solution in place of a single convex program, we provide a tractable algorithm that synthesises optimal controllers from frequency-response data while preserving stability and the desired communication structure. Through numerical examples, we illustrate the better performance of the spatial regret controller compared to classical H2/Hinf designs, underscoring the effectiveness of the proposed methodology.

Luca Furieri, Clara Lucía Galimberti, Giancarlo Ferrari-Trecate

The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while boosting the performance of nonlinear control systems using data-driven and deep-learning approaches stands as an important unsolved challenge. In this paper, we tackle the performance-boosting problem with closed-loop stability guarantees. Specifically, we establish a synergy between the Internal Model Control (IMC) principle for nonlinear systems and state-of-the-art unconstrained optimization approaches for learning stable dynamics. Our methods enable learning over arbitrarily deep neural network classes of performance-boosting controllers for stable nonlinear systems; crucially, we guarantee L_p closed-loop stability even if optimization is halted prematurely, and even when the ground-truth dynamics are unknown, with vanishing conservatism in the class of stabilizing policies as the model uncertainty is reduced to zero. We discuss the implementation details of the proposed control schemes, including distributed ones, along with the corresponding optimization procedures, demonstrating the potential of freely shaping the cost functions through several numerical experiments.

Muhammad Zakwan, Vaibhav Gupta, Alireza Karimi et al.

This paper presents an indirect data-driven output feedback controller synthesis for nonlinear systems, leveraging Structured State-space Models (SSMs) as surrogate models. SSMs have emerged as a compelling alternative in modelling time-series data and dynamical systems. They can capture long-term dependencies while maintaining linear computational complexity with respect to the sequence length, in comparison to the quadratic complexity of Transformer-based architectures. The contributions of this work are threefold. We provide the first analysis of controllability and observability of SSMs, which leads to scalable control design via Linear Matrix Inequalities (LMIs) that leverage contraction theory. Moreover, a separation principle for SSMs is established, enabling the independent design of observers and state-feedback controllers while preserving the exponential stability of the closed-loop system. The effectiveness of the proposed framework is demonstrated through a numerical example, showcasing nonlinear system identification and the synthesis of an output feedback controller.

Muhammad Zakwan, Giancarlo Ferrari-Trecate

The control of large-scale cyber-physical systems requires optimal distributed policies relying solely on limited communication with neighboring agents. However, computing stabilizing controllers for nonlinear systems while optimizing complex costs remains a significant challenge. Neural Networks (NNs), known for their expressivity, can be leveraged to parametrize control policies that yield good performance. However, NNs' sensitivity to small input changes poses a risk of destabilizing the closed-loop system. Many existing approaches enforce constraints on the controllers' parameter space to guarantee closed-loop stability, leading to computationally expensive optimization procedures. To address these problems, we leverage the framework of port-Hamiltonian systems to design continuous-time distributed control policies for nonlinear systems that guarantee closed-loop stability and finite $\mathcal{L}_2$ or incremental $\mathcal{L}_2$ gains, independent of the optimzation parameters of the controllers. This eliminates the need to constrain parameters during optimization, allowing the use of standard techniques such as gradient-based methods. Additionally, we discuss discretization schemes that preserve the dissipation properties of these controllers for implementation on embedded systems. The effectiveness of the proposed distributed controllers is demonstrated through consensus control of non-holonomic mobile robots subject to collision avoidance and averaged voltage regulation with weighted power sharing in DC microgrids.

Amin Abyaneh, Mahrokh G. Boroujeni, Hsiu-Chin Lin et al.

Imitation learning is a data-driven approach to learning policies from expert behavior, but it is prone to unreliable outcomes in out-of-sample (OOS) regions. While previous research relying on stable dynamical systems guarantees convergence to a desired state, it often overlooks transient behavior. We propose a framework for learning policies modeled by contractive dynamical systems, ensuring that all policy rollouts converge regardless of perturbations, and in turn, enable efficient OOS recovery. By leveraging recurrent equilibrium networks and coupling layers, the policy structure guarantees contractivity for any parameter choice, which facilitates unconstrained optimization. We also provide theoretical upper bounds for worst-case and expected loss to rigorously establish the reliability of our method in deployment. Empirically, we demonstrate substantial OOS performance improvements for simulated robotic manipulation and navigation tasks.

Luca Furieri, Sucheth Shenoy, Danilo Saccani et al.

We introduce magnitude and direction (MAD) policies, a policy parameterization for reinforcement learning (RL) that preserves Lp closed-loop stability for nonlinear dynamical systems. Despite their completeness in describing all stabilizing controllers, methods based on nonlinear Youla and system-level synthesis are significantly impacted by the difficulty of parametrizing Lp-stable operators. In contrast, MAD policies introduce explicit feedback on state-dependent features - a key element behind the success of reinforcement learning pipelines - without jeopardizing closed-loop stability. This is achieved by letting the magnitude of the control input be described by a disturbance-feedback Lp-stable operator, while selecting its direction based on state-dependent features through a universal function approximator. We further characterize the robust stability properties of MAD policies under model mismatch. Unlike existing disturbance-feedback policy parametrizations, MAD policies introduce state-feedback components compatible with model-free RL pipelines, ensuring closed-loop stability with no model information beyond assuming open-loop stability. Numerical experiments show that MAD policies trained with deep deterministic policy gradient (DDPG) methods generalize to unseen scenarios - matching the performance of standard neural network policies while guaranteeing closed-loop stability by design.

Leonardo Massai, Giancarlo Ferrari-Trecate

Structured state-space models (SSMs) have emerged as a powerful architecture in machine learning and control, featuring stacked layers where each consists of a linear time-invariant (LTI) discrete-time system followed by a nonlinearity. While SSMs offer computational efficiency and excel in long-sequence predictions, their widespread adoption in applications like system identification and optimal control is hindered by the challenge of ensuring their stability and robustness properties. We introduce L2RU, a novel parametrization of SSMs that guarantees input-output stability and robustness by enforcing a prescribed L-bound for all parameter values. This design eliminates the need for complex constraints, allowing unconstrained optimization over L2RUs by using standard methods such as gradient descent. Leveraging tools from system theory and convex optimization, we derive a non-conservative parametrization of square discrete-time LTI systems with a specified L2-bound, forming the foundation of the L2RU architecture. Additionally, we enhance its performance with a bespoke initialization strategy optimized for long input sequences. Through a system identification task, we validate L2RU's superior performance, showcasing its potential in learning and control applications.

Muhammad Zakwan, Liang Xu, Giancarlo Ferrari-Trecate

Neural networks can be fragile to input noise and adversarial attacks. In this work, we consider Convolutional Neural Ordinary Differential Equations (NODEs), a family of continuous-depth neural networks represented by dynamical systems, and propose to use contraction theory to improve their robustness. For a contractive dynamical system two trajectories starting from different initial conditions converge to each other exponentially fast. Contractive Convolutional NODEs can enjoy increased robustness as slight perturbations of the features do not cause a significant change in the output. Contractivity can be induced during training by using a regularization term involving the Jacobian of the system dynamics. To reduce the computational burden, we show that it can also be promoted using carefully selected weight regularization terms for a class of NODEs with slope-restricted activation functions. The performance of the proposed regularizers is illustrated through benchmark image classification tasks on MNIST and FashionMNIST datasets, where images are corrupted by different kinds of noise and attacks.

Luca Furieri, Clara Lucía Galimberti, Muhammad Zakwan et al.

Large-scale cyber-physical systems require that control policies are distributed, that is, that they only rely on local real-time measurements and communication with neighboring agents. Optimal Distributed Control (ODC) problems are, however, highly intractable even in seemingly simple cases. Recent work has thus proposed training Neural Network (NN) distributed controllers. A main challenge of NN controllers is that they are not dependable during and after training, that is, the closed-loop system may be unstable, and the training may fail due to vanishing and exploding gradients. In this paper, we address these issues for networks of nonlinear port-Hamiltonian (pH) systems, whose modeling power ranges from energy systems to non-holonomic vehicles and chemical reactions. Specifically, we embrace the compositional properties of pH systems to characterize deep Hamiltonian control policies with built-in closed-loop stability guarantees, irrespective of the interconnection topology and the chosen NN parameters. Furthermore, our setup enables leveraging recent results on well-behaved neural ODEs to prevent the phenomenon of vanishing gradients by design. Numerical experiments corroborate the dependability of the proposed architecture, while matching the performance of general neural network policies.

Jean-Sébastien Brouillon, Emanuele Fabbiani, Pulkit Nahata et al.

The increasing integration of intermittent renewable generation, especially at the distribution level,necessitates advanced planning and optimisation methodologies contingent on the knowledge of thegrid, specifically the admittance matrix capturing the topology and line parameters of an electricnetwork. However, a reliable estimate of the admittance matrix may either be missing or quicklybecome obsolete for temporally varying grids. In this work, we propose a data-driven identificationmethod utilising voltage and current measurements collected from micro-PMUs. More precisely,we first present a maximum likelihood approach and then move towards a Bayesian framework,leveraging the principles of maximum a posteriori estimation. In contrast with most existing con-tributions, our approach not only factors in measurement noise on both voltage and current data,but is also capable of exploiting available a priori information such as sparsity patterns and knownline parameters. Simulations conducted on benchmark cases demonstrate that, compared to otheralgorithms, our method can achieve significantly greater accuracy.

Clara Lucía Galimberti, Luca Furieri, Liang Xu et al.

Deep Neural Networks (DNNs) training can be difficult due to vanishing and exploding gradients during weight optimization through backpropagation. To address this problem, we propose a general class of Hamiltonian DNNs (H-DNNs) that stem from the discretization of continuous-time Hamiltonian systems and include several existing DNN architectures based on ordinary differential equations. Our main result is that a broad set of H-DNNs ensures non-vanishing gradients by design for an arbitrary network depth. This is obtained by proving that, using a semi-implicit Euler discretization scheme, the backward sensitivity matrices involved in gradient computations are symplectic. We also provide an upper-bound to the magnitude of sensitivity matrices and show that exploding gradients can be controlled through regularization. Finally, we enable distributed implementations of backward and forward propagation algorithms in H-DNNs by characterizing appropriate sparsity constraints on the weight matrices. The good performance of H-DNNs is demonstrated on benchmark classification problems, including image classification with the MNIST dataset.

Emanuele Fabbiani, Pulkit Nahata, Giuseppe De Nicolao et al.

The increasing penetration of intermittent distributed energy resources in power networks calls for novel planning and control methodologies which hinge on detailed knowledge of the grid. However, reliable information concerning the system topology and parameters may be missing or outdated for temporally varying electric distribution networks. This paper proposes an online learning procedure to estimate the network admittance matrix capturing topological information and line parameters. We start off by providing a recursive identification algorithm exploiting phasor measurements of voltages and currents. With the goal of accelerating convergence, we subsequently complement our base algorithm with a design-of-experiment procedure which maximizes the information content of data at each step by computing optimal voltage excitations. Our approach improves on existing techniques, and its effectiveness is substantiated by numerical studies on realistic testbeds.