arXiv subjects

David Angeli

Publications and source records attributed to David Angeli.

At least 19 recordsLinked to original sources

arXiv2026

Decentralized Control Synthesis in IBR-Dominated Power Systems: A Block Diagonal Dominance Based Approach

Integrating inverter-based resources (IBRs) from multiple vendors into power systems is challenging because their controllers are typically designed independently, with little coordination. To address this problem, this paper proposes a decentralized control synthesis framework for IBRs based on block-diagonal dominance (BDD) theory, which ensures the small-signal stability of multi-IBR power systems. By leveraging the grid frequency response, this approach enables a decentralized multi-input multi-output (MIMO) control design. Furthermore, the BDD-constrained design integrates a guaranteed minimum decay rate and defines a novel numerical metric to quantify the conservatism inherent in the decentralized stability certificate. The proposed control design with BDD constraints and minimum decay rate implementation is validated through a case study of the IEEE 9-bus test system.

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arXiv2026

Decentralized Stability of IBR-dominated Power Grids Using Block Diagonal Dominance

The growing penetration of inverter-based resources (IBRs) necessitates stability assessment methods that are scalable, decentralized, and model-agnostic. This paper develops a block diagonal dominance (BDD) criterion for decentralized small-signal stability of IBR-dominated power grids. The proposed approach forms the basis for an enhanced IBR connection compliance condition from a small-signal stability perspective that can be evaluated locally for IBRs to be connected to the grid. The proposed approach is shown to be much less conservative than strict diagonal dominance (SDD). Beyond mere stability, we ensure a minimum decay rate or maximum settling time for IBR-induced oscillation. Crucially, these are achieved without imposing restrictive assumptions on network or IBR models. The framework therefore, offers a practical and theoretically grounded basis for decentralized stability certificate of IBR-dominated power grids.

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arXiv2026

Tube-Based Robust Data-Driven Predictive Control

This paper presents a tractable tube-based robust data-driven predictive control scheme that uses only a single finite noisy input-state trajectory of an unknown discrete-time linear time-invariant (LTI) system. A simplex constraint is imposed on the Hankel coefficient vector, yielding explicit polyhedral bounds on the prediction mismatch induced by bounded measurement noise. Using certified initial and terminal robust positively invariant (RPI) sets, we derive a tube-tightened formulation whose online optimization problem is a strictly convex quadratic program (QP). The resulting controller guarantees recursive feasibility, robust satisfaction of input and state constraints, and practical input-to-state stability of the closed loop with respect to measurement noise. Numerical examples illustrate the effectiveness, robustness, and closed-loop performance of the proposed method.

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arXiv2026

Data-Driven Synthesis of Robust Positively Invariant Sets from Noisy Data

This paper develops a method to construct robust positively invariant (RPI) tube sets from finite noisy input-state data of an unknown linear time-invariant (LTI) system, yielding tubes that can be directly embedded in tube-based robust data-driven predictive control. Data-consistency uncertainty sets are constructed under process/measurement noise with polytopic/ellipsoidal bounds. In the measurement-noise case, we provide a deterministic and data-consistent procedure to certify the induced residual bound from data. Based on these sets, a robustly stabilizing state-feedback gain is certified via a common quadratic contraction, which in turn enables constructive polyhedral/ellipsoidal RPI tube computation. Numerical examples quantify the conservatism induced by noisy data and the employed certification step.

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arXiv2025

From Dissipativity Property to Data-Driven GAS Certificate of Degree-One Homogeneous Networks with Unknown Topology

In this work, we propose a data-driven divide and conquer strategy for the stability analysis of interconnected homogeneous nonlinear networks of degree one with unknown models and a fully unknown topology. The proposed scheme leverages joint dissipativity-type properties of subsystems described by storage functions, while providing a stability certificate over unknown interconnected networks. In our data-driven framework, we begin by formulating the required conditions for constructing storage functions as a robust convex program (RCP). Given that unknown models of subsystems are integrated into one of the constraints of the RCP, we collect data from trajectories of each unknown subsystem and provide a scenario convex program (SCP) that aligns with the original RCP. We solve the SCP as a linear program and construct a storage function for each subsystem with unknown dynamics. Under some newly developed data-driven compositionality conditions, we then construct a Lyapunov function for the fully unknown interconnected network utilizing storage functions derived from data of individual subsystems. We show that our data-driven {divide and conquer strategy} provides correctness guarantees (as opposed to probabilistic confidence) while significantly mitigating the sample complexity problem existing in data-driven approaches. To illustrate the effectiveness of our proposed results, we apply our approaches to three different case studies involving interconnected homogeneous (nonlinear) networks with unknown models. We collect data from trajectories of unknown subsystems and verify the global asymptotic stability (GAS) of the interconnected system with a guaranteed confidence.

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arXiv2025

A Truthful Mechanism Design for Distributed Optimisation Algorithms in Networks with Self-interested Agents

Enhancing resilience in multi-agent systems in the face of selfish agents is an important problem that requires further characterisation. This work develops a truthful mechanism that avoids self-interested and strategic agents maliciously manipulating the algorithm. We prove theoretically that the proposed mechanism incentivises self-interested agents to participate and follow the provided algorithm faithfully. Additionally, the mechanism is compatible with any distributed optimisation algorithm that can calculate at least one subgradient at a given point. Finally, we present an illustrative example that shows the effectiveness of the mechanism.

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arXiv2025

Data-Driven Incremental GAS Certificate of Nonlinear Homogeneous Networks: A Scenario Approach with Noisy Data

This work focuses on a compositional data-driven approach to verify incremental global asymptotic stability (delta-GAS) over interconnected homogeneous networks of degree one with unknown mathematical dynamics. Our proposed approach leverages the concept of incremental input-to-state stability (delta-ISS) of subsystems, characterized by delta-ISS Lyapunov functions. To implement our data-driven scheme, we initially reframe the delta-ISS Lyapunov conditions as a robust optimization program (ROP). Due to the presence of unknown subsystem dynamics in the ROP constraints, we develop a scenario optimization program (SOP) by gathering data from trajectories of each unknown subsystem. However, since the measured one-step transition data are corrupted by noise with a known bound on its norm, rendering the proposed SOP intractable, we introduce an auxiliary SOP that explicitly accommodates noisy measurements. We solve the auxiliary SOP and construct a delta-ISS Lyapunov function for each subsystem with unknown dynamics. We then leverage a small-gain compositional condition to facilitate the construction of an incremental Lyapunov function for an unknown interconnected network based on the data-driven delta-ISS Lyapunov functions of its individual subsystems, while providing correctness guarantees, incorporating the bound on the noise norm. We demonstrate that our data-driven compositional approach reduces the sample complexity to the subsystem level. To validate the effectiveness of our approach, we apply it to an unknown controlled physical nonlinear homogeneous network of degree one, comprising 10000 subsystems. By gathering noisy data from each unknown subsystem, we demonstrate that the interconnected network is delta-GAS with a correctness guarantee.

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arXiv2025

On an Abstraction of Lyapunov and Lagrange Stability

This paper studies a set-theoretic generalization of Lyapunov and Lagrange stability for abstract systems described by set-valued maps. Lyapunov stability is characterized as the property of inversely mapping filters to filters, Lagrange stability as that of mapping ideals to ideals. These abstract definitions unveil a deep duality between the two stability notions, enable a definition of global stability for abstract systems, and yield an agile generalization of the stability theorems for basic series, parallel, and feedback interconnections, including a small-gain theorem. Moreover, it is shown that Lagrange stability is abstractly identical to other properties of interest in control theory, such as safety and positivity, whose preservation under interconnections can be thus studied owing to the developed stability results.

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arXiv2024

Certified Learning of Incremental ISS Controllers for Unknown Nonlinear Polynomial Dynamics

Incremental input-to-state stability (delta-ISS) offers a robust framework to ensure that small input variations result in proportionally minor deviations in the state of a nonlinear system. This property is essential in practical applications where input precision cannot be guaranteed. However, analyzing delta-ISS demands precise knowledge of system dynamics to assess the state's incremental response to input changes, posing a challenge in real-world scenarios where mathematical models are unknown. In this work, we develop a data-driven approach to design delta-ISS Lyapunov functions together with their corresponding delta-ISS controllers for continuous-time input-affine nonlinear systems with polynomial dynamics, ensuring the delta-ISS property is achieved without requiring knowledge of the system dynamics. In our data-driven scheme, we collect only two sets of input-state trajectories from sufficiently excited dynamics. By fulfilling a specific rank condition, we design delta-ISS controllers using the collected samples through formulating a sum-of-squares optimization program. The effectiveness of our data-driven approach is evidenced by its application to a physical case study.

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arXiv2024

A small-gain criterion for 2-contraction of large scale interconnected systems

Despite modular conditions to guarantee stability for large-scale systems have been widely studied, few methods are available to tackle the case of networks with multiple equilibria. This paper introduces small-gain like sufficient conditions for 2-contraction of large-scale interconnected systems on the basis of a family of upper-bounds to the $L_2$ gains that arise from the gains computed on individual channels of the second additive variational equation. Such a condition guarantee the 2-additive compound of the system's Jacobian to be exponentially contractive, thus implying convergence towards equilibria of the system's solutions. The gains are obtained by solving suitable Linear Matrix Inequalities. Three interconnected Thomas' systems are considered in order to illustrate the application of the theory and the degree of conservatism.

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arXiv2023

On structural contraction of biological interaction networks

Biological networks are customarily described as structurally robust. This means that they often function extremely well under large forms of perturbations affecting both the concentrations and the kinetic parameters. In order to explain this property, various mathematical notions have been proposed in the literature. In this paper, we propose the notion of structural contractivity, building on the previous work of the authors. That previous work characterized the long-term dynamics of classes of Biological Interaction Networks (BINs), based on "rate-dependent Lyapunov functions". Here, we show that stronger notions of convergence can be established by proving structural contractivity with respect to non-standard polyhedral $\ell_\infty$-norms. In particular, we show that such networks are nonexpansive. With additional verifiable conditions, we show that they are strictly contractive over arbitrary positive compact sets. In addition, we show that such networks entrain to periodic inputs. We illustrate our theory with examples drawn from the modeling of intracellular signaling pathways.

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arXiv2023

Dissipativity in infinite horizon optimal control and dynamic programming

In this paper we extend dynamic programming techniques to the study of discrete-time infinite horizon optimal control problems on compact control invariant sets with state-independent best asymptotic average cost. To this end we analyse the interplay of dissipativity and optimal control, and propose novel recursive approaches for the solution of so called shifted Bellman Equations.

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arXiv2023

A small-gain theorem for 2-contraction of nonlinear interconnected systems

This paper introduces small-gain sufficient conditions for $2$-contraction of feedback interconnected systems, on the basis of individual gains of suitable subsystems arising from a modular decomposition of the second additive compound equation. The condition applies even to cases when individual subsystems might fail to be contractive (due to the extra margin of contraction afforded by the second additive compound matrix). Examples of application are provided to illustrate the theory and show its degree of conservatism and scope of applicability.

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arXiv2022

Convergent Economic Model Predictive Control through parameter-varying storage functions for dissipativity

This paper presents a new concept of controlled dissipativity as an extension of the standard dissipativity property to systems with parameter-varying storage functions under the framework of economic model predictive control (EMPC). Based on this concept, two EMPC controllers, integrated with the dissipation inequality constraints rendering the storage function parameters as decision variables, are formulated and the associated recursive feasibility is ensured. Then, the asymptotic convergence to an optimal equilibrium in closed-loop, without requiring the standard dissipativity assumption, is enforced by trading it off with asymptotic performance. The upper bound of asymptotic average closed-loop performance is also evaluated. Finally, an illustrative example by using the EMPC controllers with terminal equilibrium or terminal region conditions is provided to show the effectiveness of our methods.

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arXiv2022

A framework for receding-horizon control in infinite-horizon aggregative games

A novel modelling framework is proposed for the analysis of aggregative games on an infinite-time horizon, assuming that players are subject to heterogeneous periodic constraints. A new aggregative equilibrium notion is presented and the strategic behaviour of the agents is analysed under a receding horizon paradigm. The evolution of the strategies predicted and implemented by the players over time is modelled through a discrete-time multi-valued dynamical system. By considering Lyapunov stability notions and applying limit and invariance results for set-valued correspondences, necessary conditions are derived for convergence of a receding horizon map to a periodic equilibrium of the aggregative game. This result is achieved for any (feasible) initial condition, thus ensuring implicit adaptivity of the proposed control framework to real-time variations in the number and parameters of players. Design and implementation of the proposed control strategy are discussed and an example of distributed control for data routing is presented, evaluating its performance in simulation.

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arXiv2022

On optimal coordinated dispatch for heterogeneous storage fleets with partial availability

This paper addresses the problem of optimal scheduling of an aggregated power profile (during a coordinated discharging or charging operation) by means of a heterogeneous fleet of storage devices subject to availability constraints. Devices have heterogeneous initial levels of energy, power ratings and efficiency; moreover, the fleet operates without cross-charging of the units. An explicit feedback policy is proposed to compute a feasible schedule whenever one exists and scalable design procedures to achieve maximum time to failure or minimal unserved energy in the case of unfeasible aggregated demand profiles. Finally, a time-domain characterization of the set of feasible demand profiles using aggregate constraints is proposed, suitable for optimization problems where the aggregate population behaviour is of interest.

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arXiv2021

Exact aggregate models for optimal management of heterogeneous fleets of storage devices

Future power grids will entail large fleets of storage devices capable of scheduling their charging/discharging profiles so as to achieve lower peak demand and reduce energy bills, by shifting absorption times in sync with the availability of renewable energy sources. Optimal management of such fleets entails large scale optimisation problems which are better dealt with in a hierarchical manner, by clustering together individual devices into fleets. Leveraging on recent results characterizing the set of aggregate demand profiles of a heterogeneous fleet of charging (or, respectively, discharging) devices we propose a way to achieve optimality, in a unit commitment problem, by adopting a simplified formulation with a number of constraints for the fleet that scales linearly in the number of time-slots considered and is independent of the size of the fleet. This is remarkable, as it shows that, under suitable conditions, a heterogeneous fleet of any size can effectively be treated as a single storage unit.

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arXiv2021

Flexibility Framework with Recovery Guarantees for Aggregated Energy Storage Devices

This paper proposes a framework for the procurement of flexibility reserve from aggregated storage fleets. It allows for arbitrary tree structures of aggregation hierarchy, as well as easily implementable disaggregation via broadcast dispatch. By coupling discharge and recovery modes, the proposed framework enables full-cycle capacity to be procured ahead of real time, with guaranteed recovery and exact accounting for losses. The set of feasible discharging requests is exactly encoded, so that there is no reduction in the ability to meet discharging signals, and recovery capabilities are parametrised as a single virtual battery. Included in this paper is a numerical demonstration of the construction of the constituent curves of the framework and the approach is also benchmarked against relevant alternatives.

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