178 results found
Ademovic Tahirovic A, Angeli D, Strbac G, 2022, Heterogeneous network flow and Petri nets characterize multilayer complex networks, Scientific Reports, Vol: 12, ISSN: 2045-2322
Interacting subsystems are commonly described by networks, where multimodal behaviour found in most natural or engineered systems found recent extension in form of multilayer networks. Since multimodal interaction is often not dictated by network topology alone and may manifest in form of cross-layer information exchange, multilayer network flow becomes of relevant further interest. Rationale can be found in most interacting subsystems, where a form of multimodal flow across layers can be observed in e.g., chemical processes, energy networks, logistics, finance, or any other form of conversion process relying on the laws of conservation. To this end, the formal notion of heterogeneous network flow is proposed, as a multilayer flow function aligned with the theory of network flow. Furthermore, dynamic equivalence is established with the framework of Petri nets, as the baseline model of concurrent event systems. Application of the resulting multilayer Laplacian flow and flow centrality is presented, along with graph learning based inference of multilayer relationships over multimodal data. On synthetic data the proposed framework demonstrates benefits of multimodal flow derivation in critical component identification. It also displays applicability in relationship inference (learning based function approximation) on multimodal time series. On real-world data the proposed framework provides, among others, multimodal flow interpretation of U.S. economic activity, uncovering underlying empirical steady state probability distribution, as well as inherent network (economic) robustness.
Della Rossa M, Pasquini M, Angeli D, 2022, Continuous-time switched systems with switching frequency constraints: Path-complete stability criteria, Automatica, Vol: 137, Pages: 1-9, ISSN: 0005-1098
We propose a novel Lyapunov construction for continuous-time switched systems relying on a graph theoretical Lyapunov construction. Starting with a finite family of continuously differentiable functions, suitable inequalities involving these functions and the vector fields defining the switched system are encoded in a direct and labeled graph. We then provide sufficient conditions for (asymptotic) stability subject to constrained switching times, by relying on the path-completeness of the chosen graph. The analysis is first carried out under the hypothesis of constant switching frequency. Then, the results are generalized to dwell time setting. In the case of linear dynamics, the graph formalism allows us to interpret the existing results on dwell time stability in a unified language. Some numerical examples illustrate the usefulness of the conditions.
Ademovic Tahirovic A, Angeli D, Strbac G, 2021, A complex network approach to power system vulnerability analysis based on rebalance based flow centrality, 2021 IEEE PES General Meeting, Publisher: IEEE
The study of networks is an extensively investigated field of research, with networks and network structure often encoding relationships describing certain systems or processes. Critical infrastructure is understood as being a structure whose failure or damage has considerable impact on safety, security and wellbeing of society, with power systems considered a classic example. The work presented in this paper builds on the long-lasting foundations of network and complex network theory, proposing an extension in form of rebalance based flow centrality for structural vulnerability assessment and critical component identification in adaptive network topologies. The proposed measure is applied to power system vulnerability analysis, with performance demonstrated on the IEEE 30-, 57-and 118-bus test system, out performing relevant methods from the state-of-the-art. The proposed framework is deterministic (guaranteed), analytically obtained (interpretable) and generalizes well with changing network parameters, providing a complementary tool to power system vulnerability analysis and planning.
Pasquini M, Angeli D, 2021, On convergence for hybrid models of gene regulatory networks under polytopic uncertainties: a Lyapunov approach, Journal of Mathematical Biology, Vol: 83, Pages: 1-38, ISSN: 0303-6812
Hybrid models of genetic regulatory networks allow for a simpler analysis with respect to fully detailed quantitative models, still maintaining the main dynamical features of interest. In this paper we consider a piecewise affine model of a genetic regulatory network, in which the parameters describing the production function are affected by polytopic uncertainties. In the first part of the paper, after recalling how the problem of finding a Lyapunov function is solved in the nominal case, we present the considered polytopic uncertain system and then, after describing how to deal with sliding mode solutions, we prove a result of existence of a parameter dependent Lyapunov function subject to the solution of a feasibility linear matrix inequalities problem. In the second part of the paper, based on the previously described Lyapunov function, we are able to determine a set of domains where the system is guaranteed to converge, with the exception of a zero measure set of times, independently from the uncertainty realization. Finally a three nodes network example shows the validity of the results.
Zachary S, Tindemans SH, Evans MP, et al., 2021, Scheduling of energy storage., Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol: 379, Pages: 1-16, ISSN: 1364-503X
The increasing reliance on renewable energy generation means that storage may well play a much greater role in the balancing of future electricity systems. We show how heterogeneous stores, differing in capacity and rate constraints, may be optimally, or nearly optimally, scheduled to assist in such balancing, with the aim of minimizing the total imbalance (unserved energy) over any given period of time. It further turns out that in many cases the optimal policies are such that the optimal decision at each point in time is independent of the future evolution of the supply-demand balance in the system, so that these policies remain optimal in a stochastic environment. This article is part of the theme issue 'The mathematics of energy systems'.
Angeli D, Manfredi S, 2021, A resilient consensus protocol for networks with heterogeneous confidence and Byzantine adversaries, IEEE Control Systems Letters, Vol: 6, Pages: 494-499, ISSN: 2475-1456
A class of Adversary Robust Consensus protocols is proposed and analyzed. These are inherently nonlinear, distributed, continuous-time algorithms for multi-agents systems seeking to agree on a common value of a shared variable, in the presence of faulty or malicious Byzantine agents, disregarding protocol rules and communicating arbitrary possibly differing values to neighboring agents. We adopt monotone joint-agent interactions, a general mechanism for processing locally available information and allowing cross-comparisons between state-values of multiple agents simultaneously. The topological features of the network are abstracted as a Petri Net and convergence criteria for the resulting time evolutions formulated in terms of suitable structural properties of its invariants (so called siphons). Finally, simulation results and examples/counterexamples are discussed.
Angeli D, Manfredi S, 2021, On Adversary Robust Consensus Protocols Through Joint-Agent Interactions, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 66, Pages: 1646-1657, ISSN: 0018-9286
Dong Z, Angeli D, 2021, Homothetic Tube-Based Robust Economic MPC With Integrated Moving Horizon Estimation, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 66, Pages: 64-75, ISSN: 0018-9286
Albalawi F, Dong Z, Angeli D, 2021, Regret-based Robust Economic Model Predictive Control for Nonlinear Dissipative Systems, European Control Conference (ECC), Publisher: IEEE, Pages: 1105-1111
Angeli D, Alial-Radhawi M, Sontag E, 2021, A robust Lyapunov criterion for non-oscillatory behaviors in biological interaction networks, IEEE Transactions on Automatic Control, ISSN: 0018-9286
We introduce the notion of non-oscillation, propose a constructive method for its robust verification, and study its application to biological interaction networks (also known as, chemical reaction networks). We begin by revisiting Muldowney's result on the non-existence of periodic solutions based on the study of the variational system of the second additive compound of the Jacobian of a nonlinear system. We show that exponential stability of the latter rules out limit cycles, quasi-periodic solutions, and broad classes of oscillatory behavior. We focus then on nonlinear equations arising in biological interaction networks with general kinetics, and we show that the dynamics of the aforementioned variational system can be embedded in a linear differential inclusion. We then propose algorithms for constructing piecewise linear Lyapunov functions to certify global robust non-oscillatory behavior. Finally, we apply our techniques to study several regulated enzymatic cycles where available methods are not able to provide any information about their qualitative global behavior.
Evans MP, Tindemans SH, Angeli D, 2020, Minimizing unserved energy using heterogeneous energy storage unit (vol 34, pg 3647, 2019), IEEE Transactions on Power Systems, Vol: 35, Pages: 4144-4144, ISSN: 0885-8950
Dong Z, Angeli D, 2020, Homothetic tube-based robust offset-free economic Model Predictive Control, Automatica, Vol: 119, Pages: 1-6, ISSN: 0005-1098
This paper proposes a novel economic Model Predictive Control algorithm aiming at achieving optimal steady-state performance despite the presence of plant-model mismatch or unmeasured nonzero mean disturbances. According to the offset-free formulation, the system’s state is augmented with disturbances and transformed into a new coordinate framework. Based on the new variables, the proposed controller integrates a moving horizon estimator to determine a solution of the nominal system surrounded by a set of potential states compatible with past input and output measurements. The worst cost within a single homothetic tube around the nominal solution is chosen as the economic objective function which is minimized to provide a tightened upper bound for the accumulated real cost within the prediction horizon window. Thanks to the combined use of the nominal system and homothetic tube, the designed optimization problem is recursively feasible and less conservative economic performance bounds are achieved. The proposed controller is demonstrated on a two-tanks system.
Pasquini M, Angeli D, 2020, On Convergence for Piecewise Affine Models of Gene Regulatory Networks via a Lyapunov Approach, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 65, Pages: 3333-3348, ISSN: 0018-9286
Tesi A, Angeli D, 2020, On second order consensus protocols allowing joint-agent interactions, 58th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3509-3514, ISSN: 0743-1546
In this note, we propose a second order consensus protocol allowing joint-agent interactions. Our analysis is addressed to networks where agents are grouped in interaction triplets. A triplet is a set of three distinct agents, where the interaction dynamics is such that one member is sensitive to the influence brought by the other two only when it receives simultaneous and consistent opinions from them. This allows the network to reach a second order consensus configuration more robustly, even in the presence of exogenous disturbances on the dynamics of one or more agents. The piecewise linear function used to model the robust interaction within a triplet leads to the energy of the interaction being conserved along certain directions, as if some agents were connected by virtual springs. In conclusion, a convergence analysis is performed by means of the recursive detection of such conservation laws.
Manfredi S, Angeli D, 2020, Robust distributed estimation of the maximum of a field, IEEE Transactions on Control of Network Systems, Vol: 7, Pages: 372-383, ISSN: 2325-5870
This paper deals with the problem of robust distributed sampling of a field in the presence of unreliable sensors/agents. An algorithm is devised to estimate the maximum of the field over the domain spanned by the agents where some of the sensors can sample wrong measurements over a finite time, higher than the maximum field value. Necessary and sufficient conditions are given to guarantee convergence to the maximum field value and a robust and redundant algorithm design is presented by combining an exhaustive ergodic search with multiagent consensus protocols. In this original setup, the presence of unilateral interactions and exogenous signals is considered, the latter representing the measures sampled by the agents. Representative examples are presented to illustrate the effectiveness of the proposed framework and conditions.
Al-Radhawi MA, Angeli D, Sontag ED, 2020, A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks, PLoS Computational Biology, Vol: 16, Pages: 1-37, ISSN: 1553-734X
Complex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally. The kinetics can also change with environmental variations. This work addresses the following question: given a set of reactions and without assuming a particular form for the kinetics, what can we say about the asymptotic behavior of the network? Specifically, it introduces a class of networks that are “structurally (mono) attractive” meaning that they are incapable of exhibiting multiple steady states, oscillation, or chaos by virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function called a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks (LEARN), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. Basic motifs, three-body binding, and genetic networks are studied firs
Evans MP, Tindemans SH, Angeli D, 2020, Minimizing Unserved Energy Using Heterogeneous Storage Units, IEEE-Power-and-Energy-Society General Meeting (PESGM), Publisher: IEEE, ISSN: 1944-9925
Papadaskalopoulos D, Fan Y, De Paola A, et al., 2020, Game-theoretic modeling of merchant transmission investments, Lecture Notes in Energy, Pages: 381-414
Merchant transmission investment planning has recently emerged as a promising alternative or complement to the traditional centralized planning paradigm and it is considered as a further step toward the deregulation and liberalization of the electricity industry. However, its widespread application requires addressing two fundamental research questions: which entities are likely to undertake merchant transmission investments and whether this planning paradigm can maximize social welfare as the traditional centralized paradigm. Unfortunately, previously proposed approaches to quantitatively model this new planning paradigm do not comprehensively capture the strategic behavior and decision-making interactions between multiple merchant investors. This Chapter proposes a novel non-cooperative game-theoretic modeling framework to capture these realistic aspects of merchant transmission investments and provide insightful answers to the above research questions. More specifically, two different models, both based on non-cooperative game theory, have been developed. The first model addresses the first research question by adopting an equilibrium programming approach. The decision-making problem of each merchant investing player is formulated as a bi-level optimization problem, accounting for the impacts of its own actions on locational marginal prices (LMP) as well as the actions of all competing players. This problem is solved after converting it to a mathematical program with equilibrium constraints (MPEC). An iterative diagonalization method is employed to search for the likely outcome of the strategic interactions between multiple players, i.e., Nash equilibria (NE) of the game. Case studies on a simple 2-node system demonstrate that merchant networks investments will be mostly undertaken by generation companies in areas with low LMP and demand companies in areas with high LMP, as apart from collecting congestion revenue they also increase their energy surpluses. These
Della Rossa M, Pasquini M, Angeli D, 2020, Path-Complete Lyapunov Functions for Continuous-Time Switching Systems, 59th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3279-3284, ISSN: 0743-1546
Pasquini M, Angeli D, 2020, Study of Piecewise Multi-affine models for Genetic Regulatory Networks via a Lyapunov approach: an LMI framework, 21st IFAC World Congress on Automatic Control - Meeting Societal Challenges, Publisher: ELSEVIER, Pages: 16739-16744, ISSN: 2405-8963
Evans MP, Tindemans SH, Angeli D, 2020, A graphical measure of aggregate flexibility for energy-constrained distributed resources, IEEE Transactions on Smart Grid, Vol: 11, Pages: 106-117, ISSN: 1949-3061
We consider the problem of dispatching a fleet of heterogeneous energy storage units to provide grid support. Under the restriction that recharging is not possible during the time frame of interest, we develop an aggregate measure of fleet flexibility with an intuitive graphical interpretation. This analytical expression summarises the full set of demand traces that the fleet can satisfy, and can be used for immediate and straightforward determination of the feasibility of any service request. This representation therefore facilitates a wide range of capability assessments, such as flexibility comparisons between fleets or the determination of a fleet’s ability to deliver ancillary services. Examples are shown of applications to fleet flexibility comparisons, signal feasibility assessment and the optimisation of ancillary service provision.
Angeli D, Manfredi S, 2019, A Petri Net approach to consensus in networks with joint-agent interactions, Automatica, Vol: 110, Pages: 1-10, ISSN: 0005-1098
In this paper we consider consensus protocols where an agent might not be influenced by any of his neighbors singularly taken, but could be sensitive to the simultaneous and coherent influence of two or more of them (joint-agent interaction). By abstracting the set of interactions as a Petri Net we provide a graph-theoretical characterization of the ability of the net to attain asymptotic consensus within the considered set-up.
Gong X, De Paola A, Angeli D, et al., 2019, A game-theoretic approach for price-based coordination of flexible devices operating in integrated energy-reserve markets, Energy, Vol: 189, Pages: 1-12, ISSN: 0360-5442
This paper presents a novel distributed control strategy for large scale deployment of demand response. In the considered framework, large populations of storage devices and electric vehicles (EVs) participate to an integrated energy-reserve market. They react to prices and autonomously schedule their operation in order to optimize their own objective functions. The price signals are obtained through the resolution of an optimal power flow problem that explicitly takes into account the impact of demand response on the optimal power dispatch and reserve procurement of committed generation. Differently from previous approaches, the adopted game-theoretic framework provides rigorous theoretical guarantees of convergence and optimality of the proposed control scheme in a multi-price setup that includes ancillary services. The performance of the coordination scheme is also evaluated in simulation on the PJM 5-bus system, demonstrating its capability to flatten demand profiles and reduce the costs of generators and flexible devices.
De Paola A, Trovato V, Angeli D, et al., 2019, A mean field game approach for distributed control of thermostatic loads acting in simultaneous energy-frequency response markets, IEEE Transactions on Smart Grid, Vol: 10, Pages: 5987-5999, ISSN: 1949-3053
This paper proposes a novel distributed solution for the operation of large populations of thermostatically controlled loads (TCLs) providing frequency support. A game-theory framework is adopted, modeling the TCLs as price-responsive rational agents that schedule their energy consumption and allocate frequency response provision in order to minimize their operational costs. The novelty of this work lies in the use of mean field games to abstract the complex interactions of large numbers of TCLs with the grid and in the introduction of an innovative market structure, envisioning distinct price signals for electricity and response. Differently from previous approaches, such prices are not designed ad hoc but are derived instead from an underlying system scheduling model.
Gong X, De Paola A, Angeli D, et al., 2019, Distributed coordination of flexible loads using locational marginal prices, IEEE Transactions on Control of Network Systems, Vol: 6, Pages: 1097-1110, ISSN: 2325-5870
This paper presents a novel distributed control strategy for large-scale deployment of flexible demand in power systems. A game theoretical setting is adopted, modeling the loads as rational players that aim to complete an assigned task at minimum cost and compete for power consumption at the cheapest hours of the day. The main novelty is the analysis of power systems with congestion: the proposed modeling framework envisages heterogeneous groups of loads that operate at different buses, connected by transmission lines of limited capacity. The locational marginal prices of electricity, different in general for each bus, are calculated through an optimal power flow problem, accounting for the impact of the flexible devices on power demand and generation. A new iterative scheme for flexible demand coordination is analytically characterized as a multivalued mapping. Its convergence to a stable market configuration (i.e., variational Wardrop equilibrium) and global optimality are analytically demonstrated, for any penetration level of flexible demand and any grid topology. Distributed implementations of the proposed control strategy are discussed, evaluating their performance with simulations on the IEEE 24-bus system.
Evans M, Tindemans S, Angeli D, 2019, Minimising unserved energy using heterogeneous storage units, IEEE Transactions on Power Systems, Vol: 34, Pages: 3647-3656, ISSN: 0885-8950
This paper considers the optimal dispatch of energy constrained heterogeneous storage units to maximise security of supply. A policy, requiring no knowledge of the future, is presented and shown to minimise unserved energy during supply shortfall events, regardless of the supply and demand profiles. It is accompanied by a graphical means to rapidly determine unavoidable energy shortfalls, which can then be used to compare different device fleets. The policy is well-suited for use within the framework of system adequacy assessment; for this purpose, a discrete time optimal policy is conceived, in both analytic and algorithmic forms, such that these results can be applied to discrete time systems and simulation studies. This is exemplified via a generation adequacy study of the British system.
Forni P, Angeli D, 2019, Perturbation theory and singular perturbations for input-to-state multistable systems on manifolds, IEEE Transactions on Automatic Control, Vol: 64, Pages: 3555-3570, ISSN: 0018-9286
We consider the notion of Input-to-State Multistability, which generalizes ISS to nonlinear systems evolving on Riemannian manifolds and possessing a finite number of compact, globally attractive, invariant sets, which in addition satisfy a specific condition of acyclicity. We prove that a parameterized family of dynamical systems whose solutions converge to those of a limiting system inherits such Input-to-State Multistability property from the limiting system in a semi-global practical fashion. A similar result is also established for singular perturbation models whose boundary-layer subsystem is uniformly asymptotically stable and whose reduced subsystem is Input-to-State Multistable. Known results in the theory of perturbations, singular perturbations, averaging, and highly oscillatory control systems, are here generalized to the multistable setting by replacing the classical asymptotic stability requirement of a single invariant set with attractivity and acyclicity of a decomposable invariant one.
Ali Al-Radhawi M, Angeli D, Sontag E, 2019, A computational framework for a Lyapunov-enabled analysis of biochemical reaction networks, Publisher: bioRxiv
Abstract Complex molecular biological processes such as transcription and translation, signal transduction, post-translational modification cascades, and metabolic pathways can be described in principle by biochemical reactions that explicitly take into account the sophisticated network of chemical interactions regulating cell life. The ability to deduce the possible qualitative behaviors of such networks from a set of reactions is a central objective and an ongoing challenge in the field of systems biology. Unfortunately, the construction of complete mathematical models is often hindered by a pervasive problem: despite the wealth of qualitative graphical knowledge about network interactions, the form of the governing nonlinearities and/or the values of kinetic constants are hard to uncover experimentally. The kinetics can also change with environmental variations. This work addresses the following question: given a set of reactions and without assuming a particular form for the kinetics, what can we say about the asymptotic behavior of the network? Specifically, it introduces a class of networks that are “structurally (mono) attractive” meaning that they are incapable of exhibiting multiple steady states, oscillation, or chaos by virtue of their reaction graphs. These networks are characterized by the existence of a universal energy-like function called a Robust Lyapunov function (RLF). To find such functions, a finite set of rank-one linear systems is introduced, which form the extremals of a linear convex cone. The problem is then reduced to that of finding a common Lyapunov function for this set of extremals. Based on this characterization, a computational package, Lyapunov-Enabled Analysis of Reaction Networks ( LEARN ), is provided that constructs such functions or rules out their existence. An extensive study of biochemical networks demonstrates that LEARN offers a new unified framework. Basic motifs, three-body binding, and genetic networks are s
Angeli D, Manfredi S, 2019, Criteria for asymptotic clustering of opinion dynamics towards bimodal consensus, Automatica, Vol: 103, Pages: 230-238, ISSN: 0005-1098
By using the recently introduced framework of unilateral agents interactions, we provide tight graph-theoretical conditions ensuring asymptotic convergence of opinions in finite networks of cooperative agents towards equilibrium configurations where at most 2 distinct opinions persist. Such conditions extend previously known results on asymptotic agreement (or consensus).
Philippe M, Athanasopoulos N, Angeli D, et al., 2019, On path-complete Lyapunov functions: geometry and comparison, IEEE Transactions on Automatic Control, Vol: 64, Pages: 1947-1957, ISSN: 0018-9286
We study optimization-based criteria for the stability of switching systems, known as Path-Complete Lyapunov Functions, and ask the question “can we decide algorithmically when a criterion is less conservative than another'”. Our contribution is twofold. First, we show that a Path-Complete Lyapunov Function, which is a multiple Lyapunov function by nature, can always be expressed as a common Lyapunov function taking the form of a combination of minima and maxima of the elementary functions that compose it. Geometrically, our results provide for each Path-Complete criterion an implied invariant set. Second, we provide a linear programming criterion allowing to compare the conservativeness of two arbitrary given Path-Complete Lyapunov functions.
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