| 1. |
- Altafini, Claudio, 1969-
(författare)
-
A dynamical approach to privacy preserving average consensus
- 2019
-
Ingår i: 2019 IEEE 58th Conference on Decision and Control (CDC). - 9781728113982 - 9781728113999
-
Konferensbidrag (refereegranskat)abstract
- In this paper we propose a novel method for achieving average consensus in a continuous-time multiagent network while avoiding to disclose the initial states of the individual agents. In order to achieve privacy protection of the state variables, we introduce maps, called output masks, which alter the value of the states before transmitting them. These output masks are local (i.e., implemented independently by each agent), deterministic, time-varying and converging asymptotically to the true state. The resulting masked system is also time-varying and has the original (unmasked) system as its limit system. It is shown in the paper that the masked system has the original average consensus value as its only attractor. However, in order to preserve privacy, it cannot share an equilibrium point with the unmasked system, meaning that in the masked system the attractor cannot be also stable.
|
|
| 2. |
- Altafini, Claudio, 1969-
(författare)
-
Investigating stability of Laplacians on signed digraphs via eventual positivity
- 2019
-
Ingår i: 2019 IEEE 58th Conference on Decision and Control (CDC). - : IEEE. - 9781728113982 - 9781728113999
-
Konferensbidrag (refereegranskat)abstract
- Signed Laplacian matrices generally fail to be diagonally dominant and may fail to be stable. For both undirected and directed graphs, in this paper we present conditions guaranteeing the stability of signed Laplacians based on the property of eventual positivity, a Perron-Frobenius type of property for signed matrices. Our conditions are necessary and sufficient for undirected graphs, but only sufficient for digraphs, the gap between necessity and sufficiency being filled by matrices who have this Perron-Frobenius property on the right but not on the left side (i.e., on the transpose). An exception is given by weight balanced signed digraphs, where eventual positivity corresponds to positive semidefinitness of the symmetric part of the Laplacian. Analogous conditions are obtained for signed stochastic matrices.
|
|
| 3. |
- Altafini, Claudio, 1969-
(författare)
-
Minimal eventually positive realizations of externally positive systems
- 2016
-
Ingår i: Automatica. - : Pergamon Press. - 0005-1098 .- 1873-2836. ; 68, s. 140-147
-
Tidskriftsartikel (refereegranskat)abstract
- It is a well-known fact that externally positive linear systems may fail to have a minimal positive realization. In order to investigate these cases, we introduce the notion of minimal eventually positive realization, for which the state update matrix becomes positive after a certain power. Eventually positive realizations capture the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. As a consequence, we show that in discrete-time it is possible to use downsampling to obtain minimal positive realizations matching decimated sequences of Markov coefficients of the impulse response. In continuous-time, instead, if the sampling time is chosen sufficiently long, a minimal eventually positive realization leads always to a sampled realization which is minimal and positive.
|
|
| 4. |
- Altafini, Claudio, 1969-
(författare)
-
Nonintegrable discrete-time driftless control systems: geometric phases beyond the area rule
- 2016
-
Ingår i: 2016 IEEE 55th Conference on Decision and Control (CDC). - : IEEE Press. - 9781509018376 - 9781509018444 - 9781509018383 ; , s. 4692-4697
-
Konferensbidrag (refereegranskat)abstract
- In a continuous-time nonlinear driftless control system, a geometric phase is a consequence of nonintegrability of the vector fields, and it describes how cyclic trajectories in shape space induce non-periodic motion in phase space, according to an area rule. The aim of this paper is to shown that geometric phases exist also for discrete-time driftless nonlinear control systems, but that unlike their continuous-time counterpart, they need not obey any area rule, i.e., even zero-area cycles in shape space can lead to nontrivial geometric phases. When the discrete-time system is obtained through Euler discretization of a continuous-time system, it is shown that the zero-area geometric phase corresponds to the gap between the Euler discretization and an exact discretization of the continuous-time system.
|
|
| 5. |
- Altafini, Claudio, 1969-
(författare)
-
Representing externally positive systems through minimal eventually positive realizations
- 2015
-
Ingår i: Proceedings of the IEEE 54th Annual Conference on Decision and Control (CDC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9781479978861 ; , s. 6385-6390
-
Konferensbidrag (refereegranskat)abstract
- In order to investigate the cases in which an externally positive discrete-time system fails to have a minimal positive realization, in this paper we introduce the notion of minimal eventually positive realization, fr which the state update matrix becomes positive after a certain power. This property captures the idea that in the impulse response of an externally positive system the state of a minimal realization may fail to be positive, but only transiently. It is shown in the paper that whenever a minimal eventually positive realization exists, then the sequence of Markov parameters of the impulse response admits decimated subsequences for which minimal positive realizations exist and can be obtained by downsampling the eventually positive realization.
|
|
| 6. |
- Altafini, Claudio, 1969-, et al.
(författare)
-
Signed bounded confidence models for opinion dynamics
- 2018
-
Ingår i: Automatica. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0005-1098 .- 1873-2836. ; 93, s. 114-125
-
Tidskriftsartikel (refereegranskat)abstract
- The aim of this paper is to modify continuous-time bounded confidence opinion dynamics models so that "changes of opinion" (intended as changes of the sign of the initial states) are never induced during the evolution. Such sign invariance can be achieved by letting opinions of different sign localized near the origin interact negatively, or neglect each other, or even repel each other. In all cases, it is possible to obtain sign-preserving bounded confidence models with state-dependent connectivity and with a clustering behavior similar to that of a standard bounded confidence model. (C) 2018 Elsevier Ltd. All rights reserved.
|
|
| 7. |
- Ceragioli, Francesca, et al.
(författare)
-
A bounded confidence model that preserves the signs of the opinions
- 2016
-
Ingår i: Proceedings of the 2016 European Control Conference. - : Institute of Electrical and Electronics Engineers (IEEE). - 9781509025916 - 9781509025909 - 9781509025923 ; , s. 543-548
-
Konferensbidrag (refereegranskat)abstract
- The aim of this paper is to suggest a modification to the usual bounded confidence model of opinion dynamics, so that “changes of opinion” (intended as changes of the sign of the initial state) of an agent are never induced by the dynamics. In order to do so, a bipartite consensus model is used, endowing it with a confidence range. The resulting signed bounded confidence model has a state-dependent connectivity and a behavior similar to its standard counterpart, but in addition it preserves the sign of the opinions by “repelling away” opinions localized near the origin but on different sides with respect to 0.
|
|
| 8. |
- Fontan, Angela, 1991-, et al.
(författare)
-
Investigating mixed-sign equilibria for nonlinear collective decision-making systems
- 2017
-
Ingår i: Proceedings from the 2017 IEEE 56th Annual Conference on Decision and Control (CDC), December 12-15, 2017, Melbourne, Australia. - 9781509028733 - 9781509028726 - 9781509028740 ; , s. 781-786
-
Konferensbidrag (refereegranskat)abstract
- In this paper we provide necessary conditions for the existence of multiple equilibrium points for a class of non-linear cooperative networked systems with saturating interactions which describe models of collective decision-making. The multiple steady states of the dynamics represent the possible outcomes of a decision process, and, except for one positive and one negative, have all mixed signs. The conditions we obtain can be formulated in terms of the algebraic connectivity of the network and are inspired by Perron-Frobenius arguments. It is also shown that the mixed-sign equilibria are contained in a ball of radius given by the norm of the positive equilibrium point and centered in the origin. Numerical examples are given to illustrate the results.
|
|
| 9. |
- Fontan, Angela, 1991-, et al.
(författare)
-
Multiequilibria analysis for a class of collective decision-making networked systems
- 2018
-
Ingår i: IEEE Transactions on Control of Network Systems. - 2325-5870. ; :4, s. 1931-1940
-
Tidskriftsartikel (refereegranskat)abstract
- The models of collective decision-making considered in this paper are nonlinear interconnected cooperative systems with saturating interactions. These systems encode the possible outcomes of a decision process into different steady states of the dynamics. In particular, they are characterized by two main attractors in the positive and negative orthant, representing two choices of agreement among the agents, associated to the Perron-Frobenius eigenvector of the system. In this paper we give conditions for the appearance of other equilibria of mixed sign. The conditions are inspired by Perron-Frobenius theory and are related to the algebraic connectivity of the network. We also show how all these equilibria must be contained in a solid disk of radius given by the norm of the equilibrium point which is located in the positive orthant.
|
|
| 10. |
- Lindmark, Gustav, 1983-, et al.
(författare)
-
Combining centrality measures for control energy reduction in network controllability problems
- 2019
-
Ingår i: Proceedings of the 2019 European Control Conference (ECC). - : Institute of Electrical and Electronics Engineers (IEEE). - 9783907144008 - 9783907144015 - 9781728113142 ; , s. 1518-1523
-
Konferensbidrag (refereegranskat)abstract
- This paper investigates the problem of controlling a complex network with reduced control energy. Two centrality measures are defined, one related to the energy that a control, placed on a node, can exert on the entire network, and the other related to the energy that the network exerts on a node. We show that by combining these two centrality measures conflicting control energy requirements, like minimizing the average energy needed to steer the state in any direction and the energy needed for the worst direction, can be simultaneously taken into account. From an algebraic point of view, the node ranking that we obtain from the combination of our centrality measures is related to the non-normality of the adjacency matrix of the graph.
|
|
