Publications
238 results found
Forni P, Angeli D, 2018, Smooth Lyapunov functions for Multistable Hybrid Systems on Manifolds, IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE, ISSN: 0743-1546
For a broad class of complete hybrid systems evolving on Riemannian manifolds and satisfying mild regularity conditions on the data we introduce a notion of multistability based on the existence of a finite number of compact, globally attractive, and weakly invariant sets. Such notion not only generalizes the standard global uniform asymptotic stability requirement, but can also be characterized in terms of equivalent asymptotic properties, existence of smooth Lyapunov functions, and intrinsic robustness to small perturbations.
Angeli D, Athanasopoulos N, Jungers RM, et al., 2018, A Linear Program to Compare Path-Complete Lyapunov Functions, IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE, ISSN: 0743-1546
We provide an algorithmic procedure allowing to compare stability certificates for discrete-time switching systems and in specific Path-Complete Lyapunov functions (PCLFs). These mathematical objects consist of a set of positive definite functions and a set of Lyapunov inequalities, encoded in a directed, labeled graph. Given two such graphs, we formulate necessary and sufficient conditions to decide if the existence of a PCLF for the first graph implies existence of a PCLF for the second graph, where the corresponding set of functions is constructed by conic combinations of the set of functions related to the first PCLF. The conditions depend only on the topologies of the two graphs and can be verified by solving a linear program. It is the first systematic approach to compare the conservativeness of PCLFs.
Manfredi S, Angeli D, 2018, Consensus-based algorithm for distributed estimation of the maximum of a field, IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE, ISSN: 0743-1546
This paper deals with the problem of distributed estimation of the maximum of a continuous scalar field by combining exhaustive ergodic search with multi-agent consensus protocols. In this original set-up, the presence of unilateral interactions and exogenous signals is considered, the latter representing the measures sampled by the agents and an algorithm is devised to estimate the maximum of the field over the domain spanned by the agents. Necessary and sufficient conditions are given to guarantee convergence to the maximum field value. Illustrative examples are presented to show the effectiveness of the proposed framework and conditions.
De Paola A, Papadaskalopoulos D, Angeli D, et al., 2018, A Game-Theoretic Modeling Approach for Merchant Transmission Planning, 15th International Conference on the European Energy Market (EEM), Publisher: IEEE, ISSN: 2165-4077
De Paola A, Angeli D, Strbac G, 2017, Price-Based Schemes for Distributed Coordination of Flexible Demand in the Electricity Market, IEEE TRANSACTIONS ON SMART GRID, Vol: 8, Pages: 3104-3116, ISSN: 1949-3053
De Paola A, Angeli D, Strbac G, 2017, A semi-decentralized scheme for integration of price-responsive appliances in the electricity market, 20th IFAC World Congress, Publisher: Elsevier, Pages: 6729-6736, ISSN: 1474-6670
A novel semi-decentralized control strategy is proposed for the integration in the power system of large populations of flexible loads, such as electric vehicles and “smart” appliances. To characterize the interactions between the single agents and their effects on the grid, a game theory framework is adopted. The price responsive appliances are modelled as competing players, characterizing a stable and efficient solution as a Nash equilibrium (no device has unilateral interest in changing its scheduled power consumption when the final electricity price is considered). We extend previous results on distributed control of flexible demand, proposing a partial centralization of the power scheduling at critical time instants. In this way, it is possible to ensure convergence to a Nash equilibrium for a wider range of scenarios, considering higher penetration levels of flexible demand and a wider range of parameters for the devices. The effectiveness of the proposed scheme is theoretically proved and its performance is evaluated in simulations, considering a future UK grid with high penetration of flexible demand.
Dong Z, Angeli D, 2017, A generalized approach to Economic Model Predictive Control with terminal penalty functions, IFAC-PapersOnLine, Vol: 50, Pages: 518-523, ISSN: 2405-8963
In this paper, we first introduce upper and a lower bounds of the best asymptotic average performance for nonlinear control systems based on the concepts of dissipativity and control storage functions. This allows to extend the formulation and analysis of Economic Model Predictive Control to more general optimal operation regimes, such as periodic solutions. A performance and stability analysis is carried out within this generalized framework. Finally two examples are proposed and discussed to show the merits of the proposed approach.
Forni P, Angeli D, 2017, Smooth Lyapunov Functions for Multistable Differential Inclusions, IFAC PAPERSONLINE, Vol: 50, Pages: 1661-1666, ISSN: 2405-8963
We provide a converse Lyapunov theorem for differential inclusions with upper semicontinuous right-hand side, admitting a finite number of compact, globally attractive, weakly invariant sets, and evolving on Riemannian manifolds. Such properties entail multistable behavior in differential inclusions and may gather interest in a number of applications where uncertainty and discontinuities of the vector field play a major role.
Forni P, Angeli D, 2017, Characterizations of integral input-to-state stability for systems with multiple invariant sets, IEEE Transactions on Automatic Control, Vol: 62, Pages: 3729-3743, ISSN: 0018-9286
We extend the classical integral Input-to-State Stability (iISS) theory to systems evolving on complete Riemannian manifolds and admitting multiple disjoint invariant sets, so as to allow a much broader variety of dynamical behaviors of interest. Building upon a recent extension of the Input-to-State (ISS) theory for this same class of systems, we provide characterizations of the iISS concept in terms of dissipation inequalities and integral estimates as well as connections with the Strong iISS notion. Finally, we discuss some examples within the domain of mechanical systems.
Angeli D, Athanasopoulos N, Jungers RM, et al., 2017, Path-complete graphs and common Lyapunov functions, HSCC '17, Publisher: ACM, Pages: 81-90
A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time arbitrary switching systems. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. the converse however is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding Path-Complete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path- Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another.
Manfredi S, Angeli D, 2017, Necessary and sufficient conditions for consensus in nonlinear monotone networks with unilateral interactions, Automatica, Vol: 77, Pages: 51-60, ISSN: 0005-1098
This paper deals with an extended framework of the distributed asymptotic agreement problem by allowing the presence of unilateral interactions (optimistic or pessimistic) in place of bilateral ones, for a large class of nonlinear monotone time-varying networks. In this original setup we firstly introduce notions of unilateral optimistic and/or pessimistic interaction, of associated bicolored edge in the interaction graph and a suitable graph-theoretical connectedness property. Secondly, we formulate a new assumption of integral connectivity and show that it is sufficient to guarantee exponential convergence towards the agreement subspace. Finally, we show that the proposed conditions are also necessary for consensuability and discuss how the new notions of bicolored graph and related connectivity concepts encompass the usual criteria in the standard case of bilateral interactions. Theoretical advances are emphasized through illustrative examples given both to support the discussion and to highlight how the proposed framework extends all existing conditions for consensus of monotone networks.
Al-Radhawi MA, Angeli D, 2017, Construction of robust Lyapunov functions for reaction networks, European Control Conference (ECC), Publisher: IEEE, Pages: 928-935
Although Chemical Reaction Networks (CRNs) form a rich class of nonlinear systems that can exhibit wide range of nonlinear behaviours, many common examples are observed to be asymptotically stable regardless of the kinetics. This paper presents the recently uncovered class of Graphically Stable Networks (GSNs) which is characterized by the existence of a robust Lyapunov function defined in the reaction coordinates. Subject to mild conditions, the existence of these functions guarantees asymptotic stability of a network regardless of the specific form of kinetics. Construction methods for these functions are provided and illustrated by examples.
De Paola A, Angeli D, Strbac G, 2016, Decentralized coordination of large populations of flexible electrical appliances through demand saturation, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Publisher: Institute of Electrical and Electronics Engineers (IEEE), Pages: 4937-4943
This paper presents a novel decentralized control strategy for integration of price-responsive loads in the electricity market. Previous work has shown that, by approximating the devices population 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 by introducing a time varying proportional constraint on the maximum power consumption of the appliances. This allows to saturate the flexible demand and obtain a Nash equilibrium for a much wider range of scenarios. The performance of the proposed control technique, which also minimizes the task time of all appliances, is tested in simulation.
Forni P, Angeli D, 2016, Output-to-State Stability for systems on manifolds with multiple invariant sets, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Publisher: Institute of Electrical and Electronics Engineers (IEEE), Pages: 453-458
Output-to-State Stability (OSS) is a notion of detectability for nonlinear systems that is formulated in the ISS framework. We generalize the notion of OSS for systems evolving on manifolds and having multiple invariant sets. Building upon a recent extension of the Input-to-State Stability (ISS) theory for this very class of systems [1], the paper provides equivalent characterizations of the OSS property in terms of asymptotic estimates of the state trajectories and, in particular, in terms of existence of Lyapunov-like functions.
Manfredi S, Angeli D, 2016, Consensus for nonlinear monotone networks with unilateral interactions, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Publisher: Institute of Electrical and Electronics Engineers (IEEE), Pages: 2609-2614
This paper deals with an extended framework of the distributed asymptotic agreement problem by allowing the presence of unilateral interactions (optimistic or pessimistic) in place of bilateral ones, for a large class of nonlinear monotone time-varying networks. In this original setup we firstly introduce notions of unilateral optimistic and/or pessimistic interaction, of associated bicolored edge in the interaction graph and a suitable graph-theoretical connectedness property. Secondly, we formulate a new assumption of integral connectivity and show that it is sufficient to guarantee exponential convergence towards the agreement subspace. Finally, we remark that the proposed conditions are also necessary for consensuability. Theoretical advances are emphasized through illustrative examples given both to support the discussion and to highlight how the proposed framework extends all existing conditions for consensus of monotone networks.
Forni P, Angeli D, 2016, Cascades of iISS and Strong iISS systems with multiple invariant sets, 2016 IEEE 55th Conference on Decision and Control, CDC 2016, Publisher: Institute of Electrical and Electronics Engineers (IEEE), Pages: 459-464
In recent papers, the notions of Input-to-State Stability (ISS) and Integral ISS (iISS) have been generalized for systems evolving on manifolds and having multiple invariant sets, i.e. multistable systems. The well-known property of conservation of ISS under cascade interconnection has also been proven true for multistable systems in different scenarios [3]. Unfortunately, multistability hampers a straightforward extension of analogous conservation properties for integral ISS systems. By means of counterexamples, this work highlights the necessity of the additional assumptions which yield the conservation of the iISS and Strong iISS properties in cascades of multistable systems. In particular, a characterization of the invariant set of the cascade is provided in terms of its finest possible decomposition.
Forni P, Angeli D, 2016, Input-to-state stability for cascade systems with multiple invariant sets, Systems and Control Letters, Vol: 98, Pages: 97-110, ISSN: 1872-7956
In a recent paper Angeli and Efimov (2015), the notion of Input-to-State Stability (ISS) has been generalized for systems with decomposable invariant sets and evolving on Riemannian manifolds. In this work, we analyze the cascade interconnection of such ISS systems and we characterize the finest possible decomposition of its invariant set for three different scenarios: 1. the driving system exhibits multistability (convergence to fixed points only); 2. the driving system exhibits multi-almost periodicity (convergence to fixed points as well as periodic and almost-periodic orbits) and the driven system is assumed to be incremental ISS; 3. the driving system exhibits multiperiodicity (convergence to fixed points and periodic orbits) whereas the driven system is ISS in the sense of Angeli and Efimov (2015). Furthermore, we provide marginal results on the backward/forward asymptotic behavior of incremental ISS systems and on the response of a contractive system under asymptotically almost-periodic forcing. Three examples illustrate the potentiality of the proposed framework.
Manfredi S, Angeli D, 2016, A Criterion for Exponential Consensus of Time-Varying Non-Monotone Nonlinear Networks, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 62, Pages: 2483-2489, ISSN: 0018-9286
In this technical note, we present new results on exponential consensus for continuous-time nonlinear time varying networks. A key feature in the following is that the monotonicity property is not required, unlike most of existing literature on the subject. Moreover, we give an estimate of the exponential rate of convergence towards the agreement manifold. Finally, representative example and counterexample are given.
Forni P, Angeli D, 2016, The ISS approach to the stability and robustness properties of nonautonomous systems with decomposable invariant sets: an overview, European Journal of Control, Vol: 30, Pages: 50-60, ISSN: 0947-3580
This paper is an overview of recent developments in the Input-to-State Stability framework, dealing in particular with the extension of the classical concept to systems with multiple invariant sets and possibly evolving on Riemannian manifolds. Lyapunov-based characterizations of the properties are discussed as well as applications to the study of cascaded nonlinear systems.
Angeli D, Casavola A, Tedesco F, 2016, Theoretical advances on Economic Model Predictive Control with time-varying costs, Annual Reviews in Control, Vol: 41, Pages: 218-224, ISSN: 1872-9088
Economic Model Predictive Control is a technique for optimization of economic revenues arising from controlled dynamical processes that has established itself as a variant of standard Tracking Model Predictive Control. It departs from the latter in that arbitrary cost functions are allowed in the formulation of the stage cost. This paper takes a further step in expanding the applicability of Economic Model Predictive Control by illustrating how the paradigm can be adapted in order to accommodate time-varying or parameter-varying costs.
De Paola A, Angeli D, Strbac G, 2016, Frequency support by scheduling of variable-speed wind turbines, 19th IFAC World Congress, Publisher: Elsevier, Pages: 7904-7910, ISSN: 1474-6670
This paper characterizes optimal control policies for wind farms operated as frequency response services in case of a fault of conventional generators. The frequency support is provided through temporary over-production: when frequency drops, the turbines move from the steady-state operating point and extra power is produced by slowing down the turbines and releasing part of their kinetic energy. The control task is formulated and solved as an optimal containment problem: the time during which an extra quantity of power can be produced, within the set speed constraints for each turbine, is maximized. The solutions are calculated and compared for different assumptions on the electric torque of the turbines.
De Paola A, Angeli D, Strbac G, 2016, Analysis of Nash equilibria in energy markets with large populations of price-responsive flexible appliances, 2015 54th IEEE Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 5587-5592, ISSN: 0743-1546
This paper deals with flexible electrical devices that, on the basis of a broadcast price signal, schedule their individual power consumption in order to minimize their energy cost. If 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 in the energy market. This is done by comparing two functions which characterize, respectively, the valley capacity of the inflexible demand and the global properties of the appliances population. The equilibrium conditions, which do not require any iterative procedure to be applied, are finally tested in simulations.
De Paola A, Angeli D, Strbac G, 2016, Scheduling of Wind Farms for Optimal Frequency Response and Energy Recovery, IEEE Transactions on Control Systems Technology, Vol: 24, Pages: 1764-1778, ISSN: 1063-6536
This paper deals with control of variable speed wind turbines, which provide frequency support through temporary overproduction. In particular, it determines the optimal profile of power extraction among multiple generators in order to minimize the total loss of efficiency, while allowing for a prescribed increase in generation. Starting with the simplifying assumption of unconstrained generated/supplied power for the single turbine, the scheduling is characterized as the solution of an optimal control problem. On the basis of this result, a heuristic control strategy is proposed for the case of turbines with limited power output, investigating under which conditions this choice achieves optimality. Using a similar approach, the problem of energy recovery is also considered, calculating the optimal power profiles that bring back the turbines to their working point of maximum efficiency after having provided frequency response.
Sootla A, Oyarzun DA, Angeli D, et al., 2016, Shaping Pulses to Control Bistable Systems: Analysis, Computation and Counterexamples, Automatica, Vol: 63, Pages: 254-264, ISSN: 1873-2836
In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation forpulse-based control comes from applications in synthetic biology, where it is generally difficult to implement real-time feedback controlsystems due to technical limitations in sensors and actuators. We show that for monotone bistable systems, the estimation of the set ofall pulses that switch the system reduces to the computation of one non-increasing curve. We provide an efficient algorithm to computethis curve and illustrate the results with a genetic bistable system commonly used in synthetic biology. We also extend these results tomodels with parametric uncertainty and provide a number of examples and counterexamples that demonstrate the power and limitationsof the current theory. In order to show the full potential of the framework, we consider the problem of inducing oscillations in a monotonebiochemical system using a combination of temporal pulses and event-based control. Our results provide an insight into the dynamics ofbistable systems under external inputs and open up numerous directions for future investigation.
Al-Radhawi MA, Angeli D, 2016, New approach to the stability of chemical reaction networks: piecewise linear in rates Lyapunov functions, IEEE Transactions on Automatic Control, Vol: 61, Pages: 76-89, ISSN: 1558-2523
Piecewise-linear in rates (PWLR) Lyapunov functions are introduced for a class of chemical reaction networks (CRNs). In addition to their simple structure, these functions are robust with respect to arbitrary monotone reaction rates, of which Mass-Action is a special case. The existence of such functions ensures the convergence of trajectories towards equilibria, and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class. We give the definition of these Lyapunov functions, prove their basic properties, and provide algorithms for constructing them. Examples are provided, relationship with consensus dynamics are discussed, and future directions are elaborated.
Manfredi S, Angeli D, 2015, Frozen state conditions for exponential consensus of time-varying cooperative nonlinear networks, Automatica, Vol: 64, Pages: 182-189, ISSN: 1873-2836
In this paper we present new results on exponential consensus for continuous-time nonlinear time varying cooperative networks. We endow the well known assumption of integral connectivity proposed by Moreau with a remarkable additional feature of being frozen in state variables, making its direct verification more straightforward. Moreover, we give an estimate of the exponential rate of convergence towards the agreement space. Finally, the proposed results are validated for representative examples.
Angeli D, Efimov D, 2015, Characterizations of Input-to-State Stability for systems with multiple invariant sets, IEEE Transactions on Automatic Control, Vol: 60, Pages: 3242-3256, ISSN: 0018-9286
We generalize the theory of Input-to-State Stability (ISS) and of its characterizations by means of Lyapunov dissipation inequalities to the study of systems admitting invariant sets, which are not necessarily stable in the sense of Lyapunov but admit a suitable hierarchical decomposition. It is the latter which allows to greatly extend the class of systems to which ISS theory can be applied, allowing in a unified treatment to deal with oscillators in Euclidean coordinates, almost globally asymptotically stable systems on manifolds, systems with multiple equilibria in Rn just to name a few.
Manfredi S, Angeli D, 2015, On exponential consensus for time-varying non-cooperative nonlinear networks, ECC 2015, Publisher: IEEE, Pages: 557-562
In this paper we present new results on asymptotic consensus for continuous-time nonlinear time varying networks. A key feature in the following is that the monotonicity property (i.e. cooperativity) is not required, unlike most of existing literature on the subject. Additionally, we extend the use of a 'State Frozen' concept [16] and integral connectivity to this non-trivial scenario, and give condition for consensus with the additional merit to be frozen in state variables and therefore of simpler verification. Finally, we give an estimate of the exponential rate of convergence towards the agreement manifold.
Sootla A, Oyarzun DA, Angeli D, et al., 2015, Shaping Pulses to Control Bi-Stable Biological Systems, American Control Conference 2015, Publisher: IEEE, Pages: 3138-3143
In this paper, we present a framework for shaping pulses to control biological systems, and specifically systems in synthetic biology. By shaping we mean computing the magnitude and the length of a pulse, application of which results in reaching the desired control objective. Hence the control signals have only two parameters, which makes these signals amenable to wetlab implementations. We focus on the problem of switching between steady states in a bistable system. We show how to estimate the set of the switching pulses, if the trajectories of the controlled system can be bounded from above and below by the trajectories of monotone systems. We then generalise this result to systems with parametric uncertainty under some mild assumptions on the set of admissible parameters, thus providing some robustness guarantees. We illustrate the results on some example genetic circuits.
Mueller MA, Angeli D, Allgoewer F, 2015, On Necessity and Robustness of Dissipativity in Economic Model Predictive Control, IEEE Transactions on Automatic Control, Vol: 60, Pages: 1671-1676, ISSN: 1558-2523
In this paper, we study a dissipativity property which was recently used in several results on economic model predictive control to ensure optimal operation of a system at steady-state as well as stability. In particular, we first investigate whether this dissipativity property is not only sufficient, but also necessary for optimal steady-state operation. In the most general case, this is not true; nevertheless, under an additional controllability assumption, we show that dissipativity is in fact necessary. Second, we provide a robustness analysis of the dissipativity property with respect to changes in the constraint set, which can result in a change in the considered supply rate.
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.