Publications
238 results found
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
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- Citations: 1
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.
Angeli D, Manfredi S, 2019, On consensus protocols allowing joint-agent interactions, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 3660-3665, ISSN: 0743-1546
In this note we consider consensus protocols where an agent would not be influenced by any of his neighbours singularly taken, but might be sensitive to the simultaneous and coherent influence of two or more of them. This may resemble several common behaviours in social, economic and opinion networks (i.e. conformity, risk aversion, social inertia, herding). We derive novel graph-theoretical concepts to describe and analyze the ability of general networks with joint-agent interactions to converge towards consensus. Interestingly, and for the first time, we borrow to this end the language of Petri Nets as a convenient way to describe bipartite directed graphs, showing how the notion of siphon is helpful in characterizing the flow of information across the network and its ability to induce attainment of consensus among agents in the considered set-up.
Dong Z, Angeli D, 2019, Tube-based robust Economic Model Predictive Control on dissipative systems with generalized optimal regimes of operation, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 4309-4314, ISSN: 0743-1546
This paper presents a tube-based robust economic MPC controller for discrete-time nonlinear systems that are perturbed by disturbance inputs. The proposed algorithm minimizes a modified economic objective function which considers the worst cost within a tube around the solution of the associated nominal system. Recursive feasibility and an a-priori upper bound to the closed-loop asymptotic average performance are ensured. Thanks to the use of dissipativity of the nominal system with a suitable supply rate, the closed-loop system under the proposed controller is shown to be asymptotically stable, in the sense that it is driven to an optimal robust invariant set. Finally, some illustrative examples, optimally operated at qualitatively different regimes, are addressed and the performances by using our new controller and those in the literature are compared.
De Paola A, Fele F, Angeli D, et al., 2019, Distributed coordination of price-responsive electric loads: a receding horizon approach, 57th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 6033-6040, ISSN: 0743-1546
This paper presents a novel receding horizon framework for the power scheduling of flexible electric loads performing heterogeneous periodic tasks. The loads are characterized as price-responsive agents and their interactions are modelled through an infinite-time horizon aggregative game. A distributed control strategy based on iterative better-response updates is proposed to coordinate the loads, proving its convergence and global optimality with Lyapunov stability tools. Robustness with respect to variations in the number and tasks of players is also ensured. Finally, the performance of the control scheme is evaluated in simulation, coordinating the daily battery charging of a large fleet of electric vehicles.
Evans MP, Angeli D, Strbac G, et al., 2019, Chance-Constrained Ancillary Service Specification for Heterogeneous Storage Devices, Publisher: IEEE
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- Citations: 3
De Paola A, Trovato V, Angeli D, et al., 2019, Value of Thermostatic Loads in Energy/Frequency Response Markets: a Mean Field Game Approach, IEEE Milan PowerTech Conference, Publisher: IEEE
Pirkelmann S, Angeli D, Gruene L, 2019, Approximate computation of storage functions for discrete-time systems using sum-of-squares techniques, 8th International-Federation-of-Automatic-Control (IFAC) Symposium on Mechatronic Systems (MECHATRONICS) / 11th International-Federation-of-Automatic-Control (IFAC) Symposium on Nonlinear Control Systems (NOLCOS), Publisher: ELSEVIER, Pages: 508-513, ISSN: 2405-8963
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- Citations: 6
Gong X, De Paola A, Angeli D, et al., 2018, A distributed price-based strategy for flexible demand coordination in multi-area, IEEE PES Innovative Smart Grid Technologies Conference Europe (ISGT-Europe), Publisher: IEEE, ISSN: 2165-4816
This paper presents a novel distributed control strategy for large-scale deployment of price-responsive flexible demand. Differently from previous theoretical studies on the subject, the proposed analysis explicitly models multi-area systems, accounting for transmission lines of limited capacity and different locational marginal prices (LMP) throughout the network. A game-theoretic framework is adopted, designing a demand coordination scheme that converges to a stable market configuration (characterized as an aggregative equilibrium) through iterative price broadcasts. The performance of the proposed control strategy, that also ensures flattened generation profiles and reduced generation costs, is evaluated in simulation on a five-bus power system.
de Paola A, Angeli D, Strbac G, 2018, On distributed scheduling of flexible demand and Nash equilibria in the electricity market, Dynamic Games and Applications, Vol: 8, Pages: 761-798, ISSN: 2153-0785
This paper presents a novel game theory approach for large-scale deployment of price-responsive electrical appliances. In the proposed distributed control scheme, each appliance independently schedules its power consumption on the basis of a broadcast demand/price signal, aiming to complete its task at minimum cost. The conflicting interactions of the appliances, competing for power consumption at the cheapest hours of the day, are modelled through a differential game with a continuum of players, and efficient deployment of flexible demand is characterized as a Nash equilibrium. A novel approach is adopted to derive necessary and sufficient equilibrium conditions: intrinsic properties of the problem (price monotonicity, unidirectionality of power transfers) are exploited to perform an equilibrium study based on sublevel sets of the considered demand profiles. As a result, it is possible to determine for which penetration levels of flexible demand, types of appliances and inflexible demand profiles it is possible to achieve an equilibrium. Such stable configuration is achieved through the broadcast of a single demand/price signal and does not require iterated exchange of information between devices and coordinator. In addition, the global optimality of the equilibrium is proved, necessary conditions for Pareto optimality are derived, and a preliminary analysis of devices with partial time availability is carried out. The performance of the proposed control strategy is evaluated in simulation, considering realistic future scenarios of the UK power system with large penetration of flexible demand.
Dong Z, Angeli D, 2018, Analysis of economic model predictive control with terminal penalty functions on generalized optimal regimes of operation, INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Vol: 28, Pages: 4790-4815, ISSN: 1049-8923
De Paola A, Gong X, Angeli D, et al., 2018, Coordination of micro-storage devices in power grids: a multi-agent system approach for energy arbitrage, IEEE Conference on Control Technology and Applications (CCTA), Publisher: IEEE, Pages: 871-878
Angeli D, Muller M, 2018, Economic model predictive control: Some design tools and analysis techniques, Handbook of Model Predictive Control, Editors: Rakovic, Levine, Publisher: Springer, Pages: 145-167, ISBN: 9783319774886
In recent years, Economic Model Predictive Control has emerged as a variant of traditional (tracking) MPC which aims at maximizing economic profitability by directly minimizing, over a receding prediction horizon, the costs incurred in system’s operation. Several design alternatives have been proposed in the literature, as well as suitable tools for the analysis of stability and performance of the different design methods. This note provides the authors’ perspective on some of the most relevant results that appeared within this framework as well as, for interested readers, references to the technical papers where such results have first been discussed.
De Paola A, Papadaskalopoulos D, Angeli D, et al., 2018, Investigating the social efficiency of merchant transmission planning through a non-cooperative game-theoretic framework, IEEE Transactions on Power Systems, Vol: 33, Pages: 4831-4841, ISSN: 0885-8950
Merchant transmission planning is considered as a further step towards the full liberalization of the electricity industry. However, previous modeling approaches do not comprehensively explore its social efficiency as they cannot effectively deal with a large number of merchant companies. This paper addresses this fundamental challenge by adopting a novel non-cooperative game-theoretic approach. Specifically, the number of merchant companies is assumed sufficiently large to be approximated as a continuum. This allows the derivation of mathematical conditions for the existence of a Nash Equilibrium solution of the merchant planning game. By analytically and numerically comparing this solution against the one obtained through the traditional centralized planning approach, the paper demonstrates that merchant planning can maximize social welfare only when the following conditions are satisfied: a) fixed investment costs are neglected and b) the network is radial and does not include any loops. Given that these conditions do not generally hold in reality, these findings suggest that even a fully competitive merchant transmission planning framework, involving the participation of a very large number of competing merchant companies, is not generally capable of maximizing social welfare.
Evans M, Tindemans SH, Angeli D, 2018, Robustly maximal utilisation of energy-constrained distributed resources, PSCC 2018 - 20th Power Systems Computation Conference, Publisher: IEEE
We consider the problem of dispatching a fleet of distributed energy reserve devices to collectively meet a sequence of power requests over time. Under the restriction that reserves cannot be replenished, we aim to maximise the survival time of an energy-constrained islanded electrical system; and we discuss realistic scenarios in which this might be the ultimate goal of the grid operator. We present a policy that achieves this optimality, and generalise this into a set-theoretic result that implies there is no better policy available, regardless of the realised energy requirement scenario.
Manfredi S, Angeli D, 2018, Asymptotic consensus on the average of a field for time-varying nonlinear networks under almost periodic connectivity, IEEE Transactions on Automatic Control, Vol: 63, Pages: 2389-2404, ISSN: 0018-9286
The paper presents new results on asymptotic consensus for continuous time nonautonomous nonlinear networks under almost-periodic interactions. We introduce such consensus algorithms in order to estimate the average of a measured field, despite the presence of limited agents' interaction (herein represented by almost periodic connectivity). To this end, a suitable notion of integral connectivity is exploited, frozen in state variables, and of simple verification, thanks to ergodicity of the underlying agents' spatial dynamics. In the considered setup, consensus variables are different than those affecting network's connectivity unlike most of the existing literature on asymptotic agreement. The application of the proposed results is illustrated considering two representative examples in the scenario of autonomous sampling by mobile sensor agents.
Pasquini M, Angeli D, 2018, On piecewise quadratic Lyapunov functions for piecewise affine models of gene regulatory networks, Pages: 1071-1076, ISSN: 0743-1546
A piecewise affine (PWA) model of a gene regulatory network is considered. After an introduction to the model, the problem of finding a generally non-smooth function V (x) which is non increasing along the system trajectories is addressed and a way of solving it is given in terms of an LMI's feasibility problem. The presence of sliding modes in the system is explicitly considered and conditions of non-increase of V(x) along these are stated in terms of LMIs. Finally, we present an example which show the resulting V (x) obtained by solving the feasibility problem described.
Fele F, De Paola A, Angeli D, et al., 2018, A framework for receding-horizon control in infinite-horizon aggregative games, Annual Reviews in Control, Vol: 45, Pages: 191-204, ISSN: 1367-5788
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.
Gong X, de Paola A, Angeli D, et al., 2018, Coordination of micro-storage devices in power grids: a multi-agent system approach for energy arbitrage, 2018 IEEE Conference on Control Technology and Applications (CCTA)
De Paola A, Angeli D, Strbac G, 2018, Distributed schemes for efficient deployment of price-responsive demand with partial flexibility, Journal of Control and Decision, Vol: 5, Pages: 164-194, ISSN: 2330-7706
This paper presents novel methodologies for efficient deployment of flexible demand. Large populations of price-responsive loads are coordinated through a price signal and a power constraint broadcast by a central entity. Such quantities are designed in order to minimise a global objective function (e.g. total generation costs) and ensure a one-step convergence to a stable solution, characterised as a Nash equilibrium. Conditions for the sought equilibrium are preliminarily expressed as monotonicity of demand profiles under reordered coordinates and then they are imposed as constraints of a global optimisation, whose solution is calculated numerically. To reduce the computational complexity of the problem in scenarios with high penetration of flexible demand, clustering of the appliances is introduced. The global properties of the final stable solution and its optimality with respect to the task times of the appliances are analysed both theoretically and through simulation results.
De Paola A, Angeli D, Strbac G, 2018, Integration of price-responsive appliances in the energy market through flexible demand saturation, IEEE Transactions on Control of Network Systems, Vol: 5, Pages: 154-166, ISSN: 2325-5870
This paper proposes a novel decentralized technique for efficient integration of flexible demand in the electricity market. The analysis focuses on price-responsive appliances that schedule their power consumption on the basis of a demand/price signal received by a central entity. Previous work has shown that, when the devices population is sufficiently large to be described as a continuum, it is possible to provide necessary and sufficient conditions for the existence of a Nash equilibrium (no device has unilateral interest in changing its scheduling when considering the resulting profile of aggregate demand). These results are now extended in order to achieve an equilibrium also when the mentioned conditions are violated. To this purpose, a time-varying proportional constraint (equal for all devices) is introduced on the power rate of the price-responsive appliances so as to limit the variation of flexible demand that they can introduce at critical time instants. The proposed design technique not only guarantees existence of a Nash equilibrium but it also minimizes the global operation time of the appliances population. Simulation results are provided and it is shown that, under the considered assumptions, each individual appliance completes its task in minimum time.
de Paola A, Angeli D, Strbac G, 2018, Convergence and optimality of a new iterative price-based scheme for distributed coordination of flexible loads in the electricity market, 2017 IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE
This paper proposes a novel distributed control strategy for large-scale deployment of flexible demand. The devices are modelled as competing players that respond to iterative broadcasts of price signals, scheduling their power consumption to operate at minimum cost. By describing their power update at each price broadcast through a multi-valued discrete-time dynamical system and by applying Lyapunov techniques, it is shown that the proposed control strategy always converges to a stable final configuration, characterized as a Wardrop (or aggregative) equilibrium. It is also proved that such equilibrium is socially efficient and optimizes some global performance index of the system (e.g. minimizes total generation costs). These results are achieved under very general assumptions on the electricity price and for any penetration level of flexible demand. Practical implementation of the proposed scheme is discussed and tested in simulation on a future scenario of the UK-grid with large numbers of flexible loads.
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