133 results on '"Network analysis and control"'
Search Results
2. Cluster Synchronization as a Mechanism of Free Recall in Working Memory Networks
- Author
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Matin Jafarian, David Chavez Huerta, Gianluca Villani, Anders Lansner, and Karl H. Johansson
- Subjects
Network analysis and control ,stability of nonlinear systems ,systems neuroscience ,Control engineering systems. Automatic machinery (General) ,TJ212-225 ,Technology - Abstract
This article studies free recall, i.e., the reactivation of stored memory items, namely patterns, in any order, of a model of working memory. Our free recall model is based on a biologically plausible modular neural network composed of $H$ modules, namely hypercolumns, each of which is a bundle of $M$ minicolumns. The coupling weights and constant bias values of the network are determined by a Hebbian plasticity rule. Using techniques from nonlinear stability theory, we show that cluster synchronization is the central mechanism governing free recall of orthogonally encoded patterns. Particularly, we show that free recall's cluster synchronization is the combination of two main mechanisms: simultaneous activities of minicolumns representing an encoded pattern, i.e., within-pattern synchronization, together with time-divided activities of minicolumns representing different patterns. We characterize the coupling and bias value conditions under which cluster synchronization emerges. We also discuss the role of heterogeneous coupling weights and bias values of minicolumns' dynamics in free recall. Specifically, we compare the behaviour of two $H \times 2$ networks with identical and non-identical coupling weights and bias values. For these two networks, we obtain bounds on couplings and bias values under which both encoded patterns are recalled. Our analysis shows that having non-identical couplings and bias values for different patterns increases the possibility of their free recall. Numerical simulations are given to validate the theoretical analysis.
- Published
- 2023
- Full Text
- View/download PDF
3. Distributed Data-Driven Control of Network Systems
- Author
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Federico Celi, Giacomo Baggio, and Fabio Pasqualetti
- Subjects
Distributed control and optimization ,learning for control ,network analysis and control ,optimal control ,Control engineering systems. Automatic machinery (General) ,TJ212-225 ,Technology - Abstract
Imperfect models lead to imperfect controllers and deriving accurate models from first principles or system identification is especially challenging in networked systems. Instead, data can be used to directly compute controllers, without requiring any system identification or modeling. In this paper we propose a strategy to directly learn control actions when data from past system trajectories is distributed among multiple agents in a network. The approach we develop provably converges to a suboptimal solution in a finite number of steps, bounded by the diameter of the network, and with a sub-optimality gap that can be characterized as a function of data, and that can be made arbitrarily small. We further characterize the robustness properties of our approach and give provable guarantees on its performance when data are affected by noise or by a class of attacks.
- Published
- 2023
- Full Text
- View/download PDF
4. Optimal time-invariant distributed formation tracking for second-order multi-agent systems.
- Author
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Fabris, Marco, Fattore, Giulio, and Cenedese, Angelo
- Subjects
MULTIAGENT systems ,NEWTON-Raphson method ,TRAJECTORY optimization ,POTENTIAL functions ,PSYCHOLOGICAL feedback ,SYSTEMS integrators - Abstract
This paper addresses the optimal time-invariant formation tracking problem with the aim of providing a distributed solution for multi-agent systems with second-order integrator dynamics. In the literature, most of the results related to multi-agent formation tracking do not consider energy issues while investigating distributed feedback control laws. In order to account for this crucial design aspect, we contribute by formalizing and proposing a solution to an optimization problem that encapsulates trajectory tracking, distance-based formation control and input energy minimization, through a specific and key choice of potential functions in the optimization cost. To this end, we show how to compute the inverse dynamics in a centralized fashion by means of the Projector-Operator-based Newton's method for Trajectory Optimization (PRONTO) and, more importantly, we exploit such an offline solution as a general reference to devise a stabilizing online distributed control law. Finally, numerical examples involving a cubic formation following a chicane-like path in the 3D space are provided to validate the proposed control strategies. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
5. A Necessary and Sufficient Condition of an Interfering Reverse Edge for a Directed Acyclic Graph.
- Author
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Zhang, Hai-Tao, Cao, Haosen, and Chen, Zhiyong
- Subjects
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DIRECTED acyclic graphs , *COLLECTIVE behavior , *MULTIAGENT systems , *DYNAMICAL systems , *DISTRIBUTED algorithms , *SOCIAL networks , *DIRECTED graphs - Abstract
A directed acyclic graph (DAG) is a common topology in biological, engineering, and social networks. A network topology is critical in determining a collective behavior of a network dynamic system. For example, the convergence rate of a consensus behavior in a multiagent system relies on the eigenvalues of the Laplacian associated with the network topology. This article aims to analyze the influence of adding a reverse edge into a DAG on convergence rate. It reveals the existence of the so-called interfering reverse edges; adding one single edge in this category can reduce the so-called dominant convergence rate even for a large network. More specifically, a necessary and sufficient condition of an interfering reverse edge is explicitly constructed. According to the condition, a computationally efficient method is proposed to assess an interfering reverse edge. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. A Lyapunov Framework for Nested Dynamical Systems on Multiple Time Scales With Application to Converter-Based Power Systems.
- Author
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Subotic, Irina, Gros, Dominic, Colombino, Marcello, and Dorfler, Florian
- Subjects
- *
DYNAMICAL systems , *GLOBAL asymptotic stability , *NONLINEAR dynamical systems , *AD hoc computer networks , *ELECTRICAL load - Abstract
In this article, we present a Lyapunov framework for establishing stability with respect to a compact set for a nested interconnection of nonlinear dynamical systems ordered from slow to fast according to their convergence rates, where each of the dynamics is influenced only by the slower dynamics and the successive fastest one. The proposed approach explicitly considers more than two time scales, it does not require modeling multiple time scales via scalar time constants, and provides analytic bounds that make ad-hoc time-scale separation arguments rigorous. Motivated by the technical results, we develop a novel control strategy for a grid-forming power converter that consists of an inner cascaded two-degree-of-freedom controller and dispatchable virtual oscillator control as a reference model. The resulting closed-loop converter-based ac power system is in the form of a nested system with multiple time scales. We apply our technical results to obtain explicit bounds on the controller set points, branch powers, and control gains that guarantee almost global asymptotic stability of the multiconverter ac power system with respect to a prespecified solution of the ac power flow equations. Finally, we validate the performance of the proposed control structure in a case study using a high-fidelity simulation with detailed hardware validated converter models. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
7. The Impact of Deniers on Epidemics: A Temporal Network Model
- Author
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Lorenzo Zino, Alessandro Rizzo, and Maurizio Porfiri
- Subjects
Control and Optimization ,Network analysis and control ,control of networks ,Control and Systems Engineering - Published
- 2023
8. Synchronization on Riemannian Manifolds: Multiply Connected Implies Multistable.
- Subjects
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RIEMANNIAN manifolds , *SYNCHRONIZATION , *MULTIAGENT systems , *GEODESIC distance , *GEODESICS - Abstract
This article concerns the evolution of multiagent systems on networks over Riemannian manifolds. The motion of each agent is governed by the gradient descent flow of a disagreement function that is a sum of (squared) distances between pairs of communicating agents. Two metrics are considered: geodesic distances and chordal distances for manifolds that are embedded in an ambient Euclidean space. We show that networks that, roughly speaking, are dominated by a large cycle yield multistable systems if the manifold is multiply connected or contains a closed geodesic that is of locally minimum length in a space of closed curves. This result summarizes previous results on the stability of splay or twist state equilibria of the Kuramoto model on S1 and its generalization, the quantum sync model on SO(n). It also extends them to the Lohe model on U(n). [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
9. A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications.
- Author
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Rego, Francisco Castro, Pu, Ye, Alessandretti, Andrea, Aguiar, A. Pedro, Pascoal, Antonio M., and Jones, Colin N.
- Subjects
- *
STATE feedback (Feedback control systems) , *LINEAR control systems , *LINEAR systems , *ALGORITHMS , *DATA transmission systems - Abstract
This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transmission. In the set-up adopted, sensors and actuators communicate through a network with a strongly connected topology. Unlike the case of centralized linear systems, for which the separation principle holds, the above practical assumption prevents the separate design of observers, and controller because each of the nodes does not necessarily have access to the control inputs generated at all the other nodes. We derive a linear distributed Luenberger observer, and a set of sufficient conditions that guarantee ultimate boundedness of the estimation error, and system state vectors, with bounds that depend on the $\mathcal {L}_{\infty }$ norm of the noise signals, and the number of bits used in the transmissions. A numerical example illustrates the performance and effectiveness of the proposed algorithm in controlling a network of open-loop unstable systems. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
10. H-Infinity Optimal Control for Systems With a Bottleneck Frequency.
- Author
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Bergeling, Carolina, Pates, Richard, and Rantzer, Anders
- Subjects
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STRUCTURAL dynamics , *IRRIGATION water , *FREQUENCY synthesizers , *SPARSE matrices , *LINEAR systems - Abstract
We characterize a class of systems for which the H-infinity optimal control problem can be simplified in a way that enables sparse solutions and efficient computation. For a subclass of the systems, an optimal controller can be explicitly expressed in terms of the matrices of the system's state-space representation. In many applications, the controller given by this formula, which is static, can be implemented in a decentralized or distributed fashion. Examples are temperature dynamics in buildings, water irrigation, and electrical networks. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
11. A new distributed protocol for consensus of discrete-time systems.
- Author
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Cacace, Filippo, Mattioni, Mattia, Monaco, Salvatore, and Normand-Cyrot, Dorothée
- Subjects
DISCRETE-time systems ,LINEAR systems - Abstract
In this paper, a new distributed protocol is proposed to force consensus in a discrete-time network of scalar agents with an arbitrarily assignable convergence rate. Several simulations validate the performances and the improvements with respect to more standard protocols. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
12. Necessary and Sufficient Topological Conditions for Identifiability of Dynamical Networks.
- Author
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van Waarde, Henk J., Tesi, Pietro, and Camlibel, M. Kanat
- Subjects
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TRANSFER functions , *EIGENFUNCTIONS , *MATHEMATICAL models , *POLYNOMIAL time algorithms - Abstract
This article deals with dynamical networks in which the relations between node signals are described by proper transfer functions and external signals can influence each of the node signals. We are interested in graph-theoretic conditions for identifiability of such dynamical networks, where we assume that only a subset of nodes is measured but the underlying graph structure of the network is known. This problem has recently been investigated from a generic viewpoint. Roughly speaking, generic identifiability means that the transfer functions in the network can be identified for “almost all” network matrices associated with the graph. In this article, we investigate the stronger notion of identifiability for all network matrices. To this end, we introduce a new graph-theoretic concept called the graph simplification process. Based on this process, we provide necessary and sufficient topological conditions for identifiability. Notably, we also show that these conditions can be verified by polynomial time algorithms. Finally, we explain how our results generalize existing sufficient conditions for identifiability. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
13. Excitation Allocation for Generic Identifiability of Linear Dynamic Networks With Fixed Modules
- Author
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H. J. Dreef, Shengling Shi, Xiaodong Cheng, M. C. F. Donkers, Paul M. J. Van den Hof, Dynamic Networks: Data-Driven Modeling and Control, Control Systems, EAISI Mobility, Cyber-Physical Systems Center Eindhoven, and Dynamics and Control for Electrified Automotive Systems
- Subjects
Control and Optimization ,Network topology ,Numerical models ,Resource management ,linear systems ,Dynamic scheduling ,Systems and Control (eess.SY) ,White noise ,Network analysis and control ,Electrical Engineering and Systems Science - Systems and Control ,Topology ,Control and Systems Engineering ,FOS: Electrical engineering, electronic engineering, information engineering ,Heuristic algorithms ,identification - Abstract
Identifiability of linear dynamic networks requires the presence of a sufficient number of external excitation signals. The problem of allocating a minimal number of external signals for guaranteeing generic network identifiability in the full measurement case has been recently addressed in the literature. Here we will extend that work by explicitly incorporating the situation that some network modules are known, and thus are fixed in the parametrized model set. The graphical approach introduced earlier is extended to this situation, showing that the presence of fixed modules reduces the required number of external signals. An algorithm is presented that allocates the external signals in a systematic fashion.
- Published
- 2022
14. Global Analysis of Synchronization Performance for Power Systems: Bridging the Theory-Practice Gap.
- Author
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Paganini, Fernando and Mallada, Enrique
- Subjects
- *
GLOBAL analysis (Mathematics) , *REDUCED-order models , *SYNCHRONIZATION , *ELECTRIC power distribution grids , *IMPACT craters , *DYNAMIC models - Abstract
The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance and calculated under highly simplified assumptions. In this article, we extend this approach to more realistic network scenarios and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a system-wide frequency that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define—and compute in closed form—several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the system frequency, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a synchronization cost that can appropriately quantify interarea oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
15. A Fast Distributed Asynchronous Newton-Based Optimization Algorithm.
- Author
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Mansoori, Fatemeh and Wei, Ermin
- Subjects
- *
MATHEMATICAL optimization , *DISTRIBUTED algorithms , *CONVEX functions , *LINEAR programming , *APPROXIMATION algorithms , *SYMMETRIC matrices - Abstract
One of the most important problems in the field of distributed optimization is the problem of minimizing a sum of local convex objective functions over a networked system. Most of the existing work in this area focuses on developing distributed algorithms in a synchronous setting under the presence of a central clock, where the agents need to wait for the slowest one to finish the update, before proceeding to the next iterate. Asynchronous distributed algorithms remove the need for a central coordinator, reduce the synchronization wait, and allow some agents to compute faster and execute more iterations. In the asynchronous setting, the only known algorithms for solving this problem could achieve an either linear or sublinear rate of convergence. In this paper, we build upon the existing literature to develop and analyze an asynchronous Newton-based method to solve a penalized version of the problem. We show that this algorithm guarantees almost sure convergence with a global linear and local quadratic rate in expectation. Numerical studies confirm the superior performance of our algorithm against other asynchronous methods. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
16. Resilient Leader-Follower Consensus to Arbitrary Reference Values in Time-Varying Graphs.
- Author
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Usevitch, James and Panagou, Dimitra
- Subjects
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REFERENCE values - Abstract
Several algorithms in prior literature have been proposed, which guarantee the consensus of normally behaving agents in a network that may contain adversarially behaving agents. These algorithms guarantee that the consensus value lies within the convex hull of initial normal agents’ states, with the exact consensus value possibly being unknown. In leader-follower consensus problems, however, the objective is for normally behaving agents to track a reference state that may take on values outside of this convex hull. In this paper, we present methods for agents in time-varying graphs with discrete-time dynamics to resiliently track a reference state propagated by a set of leaders, despite a bounded subset of the leaders and followers behaving adversarially. Our results are demonstrated through simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
17. Event-Triggered Control for Semiglobal Robust Consensus of a Class of Nonlinear Uncertain Multiagent Systems.
- Author
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Meng, Haofei, Zhang, Hai-Tao, Wang, Zhen, and Chen, Guanrong
- Subjects
- *
MULTIAGENT systems , *UNCERTAIN systems , *ROBUST control , *DIRECTED graphs - Abstract
In this note, robust consensus for a class of nonlinear second-order multiagent systems with uncertainties is investigated from an event-triggered control approach. An event-triggered distributed control protocol is designed to achieve semiglobal robust leaderless consensus for directed graphs. To guarantee the feasibility of the proposed scheme, the event-based consensus is converted to an event-based stabilization for analysis. Zeno behavior is avoided under the proposed event-triggered mechanism. The effectiveness of the proposed event-triggered scheme is demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
18. Fundamental Limits and Tradeoffs in Autocatalytic Pathways.
- Author
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Siami, Milad, Motee, Nader, Buzi, Gentian, Bamieh, Bassam, Khammash, Mustafa, and Doyle, John C.
- Subjects
- *
AUTOCATALYSIS , *DYNAMICAL systems , *BIOLOGICAL networks , *NONLINEAR analysis , *BIOLOGICAL systems - Abstract
This paper develops some basic principles to study autocatalytic networks and exploit their structural properties in order to characterize their inherent fundamental limits and tradeoffs. In a dynamical system with autocatalytic structure, the system's output is necessary to catalyze its own production. Our study has been motivated by a simplified model of a glycolysis pathway. First, the properties of this class of pathways are investigated through a network model, which consists of a chain of enzymatically catalyzed intermediate reactions coupled with an autocatalytic component. We explicitly derive a hard limit on the minimum achievable $\mathcal L_2$ -gain disturbance attenuation and a hard limit on its minimum required output energy. Then, we show how these resulting hard limits lead to some fundamental tradeoffs between transient and steady-state behavior of the network and its net production. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
19. Self-Triggered Network Coordination Over Noisy Communication Channels.
- Author
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Shi, Mingming, Tesi, Pietro, and De Persis, Claudio
- Subjects
- *
LINEAR operators , *TELECOMMUNICATION systems , *NOISE measurement , *INFORMATION networks , *SENSOR networks , *DIGITAL communications - Abstract
This paper deals with the coordination problems over noisy communication channels. We consider a scenario where the communication between network nodes is corrupted by unknown-but-bounded noise. We introduce a novel coordination scheme which ensures: 1) boundedness of the state trajectories and 2) a linear map from the noise to the nodes disagreement value. The proposed scheme does not require any global information on the network parameters and/or the operating environment (the noise characteristics). Moreover, network nodes can sample at independent rates and in an aperiodic manner. [ABSTRACT FROM AUTHOR]
- Published
- 2020
- Full Text
- View/download PDF
20. The Basic Reproduction Number as a Loop Gain Matrix
- Author
-
Alessandro Colombo
- Subjects
Discrete mathematics ,Eigenvalues and eigenfunctions ,Control and Optimization ,Biological systems ,Coronavirus disease 2019 (COVID-19) ,Spectral radius ,Computation ,Statistics ,Linear system ,COVID-19 ,Computational modeling ,Matrix (mathematics) ,Mathematical model ,Sociology ,Control and Systems Engineering ,Simple (abstract algebra) ,Compartmental and Positive systems ,Epidemics ,Basic reproduction number ,Network analysis and control ,Loop gain - Abstract
The COVID-19 pandemic and the disordered reactions of most governments made the importance of mathematical modelling and model-based predictions evident, even outside the scientific community. The basic reproduction number $\mathcal {R}_{0}$ quickly entered the common jargon, as a concise but effective tool to communicate the spreading power of a disease and estimate, at least roughly, the possible outcomes of the epidemic. However, while $\mathcal {R}_{0}$ is easily defined for simple models, its proper definition is more subtle for larger, state-of-the-art models. Here we show that it is nothing else than the spectral radius of the gain matrix of a linear system, and that this matrix generalizes $\mathcal {R}_{0}$ in the computation of the vector-valued final epidemic size and epidemic threshold, in a large class of finite-dimensional SIR-like models.
- Published
- 2022
21. A Resilient Consensus Protocol for Networks With Heterogeneous Confidence and Byzantine Adversaries
- Author
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Sabato Manfredi, David Angeli, Angeli, D., and Manfredi, S.
- Subjects
Class (computer programming) ,Control and Optimization ,Theoretical computer science ,fault tolerant system ,Computer science ,cooperative control ,petri nets ,Cyber-physical system ,Network analysis and control ,Petri net ,Computer Science::Multiagent Systems ,Monotone polygon ,distributed control ,Control and Systems Engineering ,Convergence (routing) ,Common value auction ,Protocol (object-oriented programming) ,Counterexample - Abstract
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.
- Published
- 2022
22. Excitation allocation for generic identifiability of linear dynamic networks with fixed modules
- Abstract
Identifiability of linear dynamic networks requires the presence of a sufficient number of external excitation signals. The problem of allocating a minimal number of external signals for guaranteeing generic network identifiability in the full measurement case has been recently addressed in the literature. Here we will extend that work by explicitly incorporating the situation that some network modules are known, and thus are fixed in the parametrized model set. The graphical approach introduced earlier is extended to this situation, showing that the presence of fixed modules reduces the required number of external signals. An algorithm is presented that allocates the external signals in a systematic fashion., Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public., Team Bart De Schutter
- Published
- 2022
- Full Text
- View/download PDF
23. Excitation Allocation for Generic Identifiability of Linear Dynamic Networks With Fixed Modules
- Abstract
Identifiability of linear dynamic networks requires the presence of a sufficient number of external excitation signals. The problem of allocating a minimal number of external signals for guaranteeing generic network identifiability in the full measurement case has been recently addressed in the literature. Here we will extend that work by explicitly incorporating the situation that some network modules are known, and thus are fixed in the parametrized model set. The graphical approach introduced earlier is extended to this situation, showing that the presence of fixed modules reduces the required number of external signals. An algorithm is presented that allocates the external signals in a systematic fashion.
- Published
- 2022
24. Excitation allocation for generic identifiability of linear dynamic networks with fixed modules
- Abstract
Identifiability of linear dynamic networks requires the presence of a sufficient number of external excitation signals. The problem of allocating a minimal number of external signals for guaranteeing generic network identifiability in the full measurement case has been recently addressed in the literature. Here we will extend that work by explicitly incorporating the situation that some network modules are known, and thus are fixed in the parametrized model set. The graphical approach introduced earlier is extended to this situation, showing that the presence of fixed modules reduces the required number of external signals. An algorithm is presented that allocates the external signals in a systematic fashion., Accepted Author Manuscript, Team DeSchutter
- Published
- 2022
- Full Text
- View/download PDF
25. A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications
- Author
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Ye Pu, Francisco F. C. Rego, A. Pedro Aguiar, Andrea Alessandretti, Antonio M. Pascoal, and Colin N. Jones
- Subjects
0209 industrial biotechnology ,Strongly connected component ,quantized consensus ,Computer science ,Linear system ,quantized systems ,average consensus ,network analysis and control ,02 engineering and technology ,State (functional analysis) ,Separation principle ,Computer Science Applications ,Noise ,020901 industrial engineering & automation ,sensor networks ,Control and Systems Engineering ,Control theory ,Norm (mathematics) ,kalman filter ,State observer ,Electrical and Electronic Engineering ,linear system observers - Abstract
This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transmission. In the set-up adopted, sensors and actuators communicate through a network with a strongly connected topology. Unlike the case of centralized linear systems, for which the separation principle holds, the above practical assumption prevents the separate design of observers, and controller because each of the nodes does not necessarily have access to the control inputs generated at all the other nodes. We derive a linear distributed Luenberger observer, and a set of sufficient conditions that guarantee ultimate boundedness of the estimation error, and system state vectors, with bounds that depend on the $\mathcal {L}_{\infty }$ norm of the noise signals, and the number of bits used in the transmissions. A numerical example illustrates the performance and effectiveness of the proposed algorithm in controlling a network of open-loop unstable systems.
- Published
- 2021
26. Distributed Discontinuous Coupling for Convergence in Heterogeneous Networks
- Author
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Pietro DeLellis, Mario di Bernardo, Marco Coraggio, Coraggio, M., De Lellis, P., and Di Bernardo, M.
- Subjects
Coupling ,0209 industrial biotechnology ,Control and Optimization ,Computer science ,02 engineering and technology ,Network analysis and control ,Topology ,Synchronization ,Nonlinear dynamical systems ,020901 industrial engineering & automation ,distributed control ,Control and Systems Engineering ,control of network ,Convergence (routing) ,0202 electrical engineering, electronic engineering, information engineering ,switched systems ,020201 artificial intelligence & image processing ,Vector field ,Protocol (object-oriented programming) ,Heterogeneous network - Abstract
In this letter, we propose the use of a distributed discontinuous coupling protocol to achieve convergence and synchronization in networks of non-identical nonlinear dynamical systems. We show that the synchronous dynamics is a solution to the average of the nodes' vector fields, and derive analytical estimates of the critical coupling gains required to achieve convergence.
- Published
- 2021
27. Performance Improvement in Noisy Linear Consensus Networks With Time-Delay.
- Author
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Ghaedsharaf, Yaser, Siami, Milad, Somarakis, Christoforos, and Motee, Nader
- Subjects
- *
GRAPH theory , *MATHEMATICAL optimization , *MULTIAGENT systems , *TIME delay systems , *LAPLACIAN matrices - Abstract
We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. Performance is measured by network's square of $\mathcal {H}_2$ norm and it is derived in closed form. Moreover, we prove that performance is a convex function of the coupling weights of the underlying graph. We demonstrate that the effect of time-delay reincarnates itself in the form of non-monotonicity, leading to counter-intuitive behaviors of the performance as a function of graph topology. For the network design problem, we propose a tight but simple approximation of the performance measure in order to achieve lower complexity in our problems by eliminating the computationally expensive need for eigendecomposition. More specifically, we discuss three $\mathcal {H}_2$ -based optimal design methods to enhance performance. The proposed algorithms provide near-optimal solutions with improved computational complexity as opposed to existing methods in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
28. Identifiability of Dynamical Networks With Partial Node Measurements.
- Author
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Hendrickx, Julien M., Gevers, Michel, and Bazanella, Alexandre S.
- Subjects
- *
GRAPH theory , *GEOMETRIC vertices , *SENSOR networks , *TRANSFER functions , *WIRELESS sensor networks - Abstract
Much recent research has dealt with the identifiability of a dynamical network in which the node signals are connected by causal linear transfer functions and are excited by known external excitation signals and/or unknown noise signals. A major research question concerns the identifiability of the whole network—topology and all transfer functions—from the measured node signals and external excitation signals. So far all results on the identifiability of the whole network have assumed that all node signals are measured. This paper presents the first results for the situation where not all node signals are measurable, under the assumptions that, first, the topology of the network is known, and, second, each node is excited by a known external excitation. Using graph theoretical properties, we show that the transfer functions that can be identified depend essentially on the topology of the paths linking the corresponding vertices to the measured nodes. A practical outcome is that, under those assumptions, a network can often be identified using only a small subset of node measurements. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
29. Individual Regret Bounds for the Distributed Online Alternating Direction Method of Multipliers.
- Author
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Akbari, Mohammad, Gharesifard, Bahman, and Linder, Tamas
- Subjects
- *
MATHEMATICAL optimization , *NUMERICAL analysis , *CHEMICAL reactions , *MATHEMATICAL analysis , *GRAPH theory - Abstract
We consider a distributed online optimization problem where, at each time, a group of agents choose their individual states, after which an individual cost function is revealed to each of them. The whole network then faces a regret according to the cumulative sum of costs incurred by the agents’ chosen states, and each agent faces an individual regret according to the cumulative sum of costs incurred by the agent's state estimation, perceived as the whole network's chosen state. In order to tackle the minimization of the individual regret using only local information, we assume that the group of agents communicate over a fixed undirected connected graph. We then propose an online version of the alternating direction method of multipliers algorithm, distributed over the communication graph, which allows each agent to drive its individual average regret over time to zero. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
30. Finite-Time Attitude Synchronization With Distributed Discontinuous Protocols.
- Author
-
Wei, Jieqiang, Zhang, Silun, Adaldo, Antonio, Thunberg, Johan, Hu, Xiaoming, and Johansson, Karl H.
- Subjects
- *
FINITE difference time domain method , *SYNCHRONIZATION , *NONLINEAR systems , *NETWORK analysis (Communication) , *MULTIAGENT systems - Abstract
The finite-time attitude synchronization problem is considered in this paper, where the rotation of each rigid body is expressed using the axis-angle representation. Two discontinuous and distributed controllers using the vectorized signum function are proposed, which guarantee almost global and local convergence, respectively. Filippov solutions and nonsmooth analysis techniques are adopted to handle the discontinuities. Sufficient conditions are provided to guarantee finite-time convergence and boundedness of the solutions. Simulation examples are provided to verify the performances of the control protocols designed in this paper. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
31. Network Abstraction With Guaranteed Performance Bounds.
- Author
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Siami, Milad and Motee, Nader
- Subjects
- *
MULTIAGENT systems , *DYNAMICAL systems , *ESTIMATION theory , *OPTIMAL designs (Statistics) , *LINEAR time invariant systems - Abstract
A proper abstraction of a large-scale linear consensus network with a dense coupling graph is one whose number of coupling links is proportional to its number of subsystems and its performance is comparable to the original network. Optimal design problems for an abstracted network are more amenable to efficient optimization algorithms. From the implementation point of view, maintaining such networks are usually more favorable and cost-effective due to their reduced communication requirements across a network. Therefore, approximating a given dense linear consensus network by a suitable abstract network is an important analysis and synthesis problem. In this paper, we develop a framework to compute an abstraction of a given large-scale linear consensus network with guaranteed performance bounds using a nearly linear time algorithm. First, the existence of abstractions of a given network is proven. Then, we present an efficient and fast algorithm for computing a proper abstraction of a given network. Finally, we illustrate the effectiveness of our theoretical findings via several numerical simulations. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
32. H-Infinity Optimal Control for Systems With a Bottleneck Frequency
- Author
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Anders Rantzer, Carolina Bergeling, and Richard Pates
- Subjects
Distributed control ,0209 industrial biotechnology ,Computer science ,Computation ,Linear systems ,02 engineering and technology ,Bottleneck ,H infinity control ,Network analysis and Control ,020901 industrial engineering & automation ,Large-scale systems ,Control theory ,Buildings ,Electrical and Electronic Engineering ,Frequency synthesizers ,Representation (mathematics) ,Computer Science::Databases ,Sparse matrix ,Linear system ,Control Engineering ,Optimal control ,Computer Science Applications ,H-infinity methods in control theory ,Control and Systems Engineering ,Frequency control ,Sparse matrices - Abstract
We characterize a class of systems for which the H-infinity optimal control problem can be simplified in a way that enables sparse solutions and efficient computation. For a subclass of the systems, an optimal controller can be explicitly expressed in terms of the matrices of the system's state-space representation. In many applications, the controller given by this formula, which is static, can be implemented in a decentralized or distributed fashion. Examples are temperature dynamics in buildings, water irrigation and electrical networks.
- Published
- 2021
33. A new connection protocol for multi-consensus of discrete-time systems
- Author
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Mattioni, M., Monaco, S., and Normand-Cyrot, D.
- Subjects
Sampled-data control ,Linear systems ,Network analysis and control - Published
- 2022
34. A mean-field analysis of a network behavioural–epidemic model
- Author
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Mengbin Ye, Alessandro Rizzo, Kathinka Frieswijk, Ming Cao, Lorenzo Zino, and Discrete Technology and Production Automation
- Subjects
Control and Optimization ,Control and Systems Engineering ,stability of nonlinear systems ,FOS: Mathematics ,Quantitative Biology::Populations and Evolution ,Network analysis and control ,Dynamical Systems (math.DS) ,Mathematics - Dynamical Systems ,Quantitative Biology::Other - Abstract
The spread of an epidemic disease and the population's collective behavioural response are deeply intertwined, influencing each other's evolution. Such a co-evolution typically has been overlooked in mathematical models, limiting their real-world applicability. To address this gap, we propose and analyse a behavioural-epidemic model, in which a susceptible-infected-susceptible epidemic model and an evolutionary game-theoretic decision-making mechanism concerning the use of self-protective measures are coupled. Through a mean-field approach, we characterise the asymptotic behaviour of the system, deriving conditions for global convergence to a disease-free equilibrium and characterising the endemic equilibria of the system and their (local) stability. Interestingly, for a certain range of the model parameters, we prove global convergence to a limit cycle, characterised by periodic epidemic outbreaks., Comment: Accepted for publication by IEEE Control Systems Letters (L-CSS)
- Published
- 2022
35. On Assessing Control Actions for Epidemic Models on Temporal Networks
- Author
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Maurizio Porfiri, Alessandro Rizzo, Lorenzo Zino, Faculty of Science and Engineering, and Discrete Technology and Production Automation
- Subjects
Control and Optimization ,Optimization problem ,CONTAINMENT ,Control (management) ,network analysis and control ,01 natural sciences ,epidemics ,010305 fluids & plasmas ,Complement (complexity) ,Network formation ,Control of networks ,predictive model ,Risk analysis (engineering) ,Control and Systems Engineering ,Homogeneous ,Scale (social sciences) ,0103 physical sciences ,epidemiology ,SPREAD ,010306 general physics ,Epidemic model ,Epidemic control - Abstract
In this letter, we propose an epidemic model over temporal networks that explicitly encapsulates two different control actions. We develop our model within the theoretical framework of activity driven networks (ADNs), which have emerged as a valuable tool to capture the complexity of dynamical processes on networks, coevolving at a comparable time scale to the temporal network formation. Specifically, we complement a susceptible-infected-susceptible epidemic model with features that are typical of nonpharmaceutical interventions in public health policies: i) actions to promote awareness, which induce people to adopt self-protective behaviors, and ii) confinement policies to reduce the social activity of infected individuals. In the thermodynamic limit of large-scale populations, we use a mean-field approach to analytically derive the epidemic threshold, which offers viable insight to devise containment actions at the early stages of the outbreak. Through the proposed model, it is possible to devise an optimal epidemic control policy as the combination of the two strategies, arising from the solution of an optimization problem. Finally, the analytical computation of the epidemic prevalence in endemic diseases on homogeneous ADNs is used to optimally calibrate control actions toward mitigating an endemic disease. Simulations are provided to support our theoretical results.
- Published
- 2020
36. Population games on dynamic community networks
- Author
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Alain Govaert, Lorenzo Zino, Emma Tegling, and Discrete Technology and Production Automation
- Subjects
FOS: Computer and information sciences ,TheoryofComputation_MISCELLANEOUS ,Computer Science::Computer Science and Game Theory ,Physics - Physics and Society ,Control and Optimization ,FOS: Physical sciences ,Dynamical Systems (math.DS) ,Physics and Society (physics.soc-ph) ,network analysis and control ,Sociology ,Computer Science - Computer Science and Game Theory ,FOS: Mathematics ,Statistics ,Games ,Mathematical models ,Convergence ,Finite element analysis ,Biological system modeling ,Game theory ,large-scale systems ,Mathematics - Dynamical Systems ,Quantitative Biology - Populations and Evolution ,Social and Information Networks (cs.SI) ,Populations and Evolution (q-bio.PE) ,Computer Science - Social and Information Networks ,Control and Systems Engineering ,FOS: Biological sciences ,Computer Science and Game Theory (cs.GT) - Abstract
In this letter, we deal with evolutionary game theoretic learning processes for population games on networks with dynamically evolving communities. Specifically, we propose a novel mathematical framework in which a deterministic, continuous-time replicator equation on a community network is coupled with a closed dynamic flow process between communities that is governed by an environmental feedback mechanism, resulting in co-evolutionary dynamics. Through a rigorous analysis of the system of differential equations obtained, we characterize the equilibria of the coupled dynamical system. Moreover, for a class of population games with two actions and symmetric rewards a Lyapunov argument is employed to establish an evolutionary folk theorem that guarantees convergence to the evolutionary stable states of the game. Numerical simulations are provided to illustrate and corroborate our findings., 6 pages, 2 figures
- Published
- 2022
37. Leader-Follower Synchronization of a Network of Boundary-Controlled Parabolic Equations with In-Domain Coupling
- Author
-
Abbas Kabalan, Francesco Ferrante, Giacomo Casadei, Andrea Cristofaro, Christophe Prieur, Université Paris sciences et lettres (PSL), GIPSA - Infinite Dimensional Dynamics (GIPSA-INFINITY), GIPSA Pôle Automatique et Diagnostic (GIPSA-PAD), Grenoble Images Parole Signal Automatique (GIPSA-lab), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Grenoble Images Parole Signal Automatique (GIPSA-lab), Université Grenoble Alpes (UGA), University of Perugia, École Centrale de Lyon (ECL), Université de Lyon, Ampère (AMPERE), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Dipartimento di Ingegneria informatica automatica e gestionale (DIAG), Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], ANR-19-P3IA-0003,MIAI,MIAI @ Grenoble Alpes(2019), Ampère, Département Automatique pour l'Ingénierie des Systèmes (AIS), Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-École Centrale de Lyon (ECL), and Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)
- Subjects
Mathematical models ,Control and Optimization ,control of networks ,Distributed parameter systems ,network analysis and control ,Linear matrix inequalities ,Synchronization ,16. Peace & justice ,Electrical Engineering and Systems Science - Systems and Control ,Symmetric matrices ,Control and Systems Engineering ,[INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering ,Couplings ,Space heating ,Control of networks ,Mathematics - Optimization and Control ,Visualization - Abstract
In this letter, we study the leader-synchronization problem for a class of partial differential equations with boundary control and in-domain coupling. We describe the problem in an abstract formulation and we specialize it to a network of parabolic partial differential equations. We consider a setting in which a subset of the followers is connected to the leader through a boundary control, while interconnections among the followers are enforced by distributed in-domain couplings. Sufficient conditions in the form of matrix inequalities for the selection of the control parameters enforcing exponential synchronization are given. Numerical simulations illustrate and corroborate the theoretical findings., Comment: V1 matches published version
- Published
- 2022
38. Partial controllability of network dynamical systems with unilateral inputs
- Author
-
Francesco Lo Iudice, Antonio Coppola, Franco Garofalo, Camilla Ancona, Pietro DE LELLIS, Ancona, Camilla, Lo Iudice, F., Coppola, A., De Lellis, P., and Garofalo, F.
- Subjects
Controllability ,Control and Optimization ,Network systems ,Dynamic ,FOS: Physical sciences ,Mathematical Physics (math-ph) ,Dynamical system ,Heuristic algorithm ,Constrained control ,Control and Systems Engineering ,Optimization and Control (math.OC) ,Aerospace electronic ,FOS: Mathematics ,Control of network ,Indexe ,Mathematics - Optimization and Control ,Mathematical Physics ,Network analysis and control - Abstract
Our ability to control network dynamical systems is often hindered by constraints on the number and nature of the available control actions, which make controlling the whole network unfeasible. In this manuscript, we focus on the case where unilateral inputs are exerted on a subset of the network nodes. Leveraging the observation that, different from the case of subsystems, unilateral node reachability and controllability are equivalent, we provide conditions for a given node subset to be unilaterally controllable. The theoretical findings are then employed to develop a computationally efficient heuristic to select the nodes where the unilateral inputs should be injected.
- Published
- 2022
39. New spectral bounds on [formula omitted]-norm of linear dynamical networks.
- Author
-
Siami, Milad and Motee, Nader
- Subjects
- *
DYNAMICAL systems , *MATHEMATICAL functions , *MATRICES (Mathematics) , *COMPUTER networks , *COMPUTER simulation , *WHITE noise - Abstract
In this paper, we obtain new lower and upper bounds for the H 2 -norm of a class of linear time-invariant systems subject to exogenous noise inputs. We show that the H 2 -norm, as a performance measure, can be tightly bounded from below and above by some spectral functions of state and output matrices of the system. In order to show the usefulness of our results, we calculate bounds for the H 2 -norm of some network models with specific coupling or graph structures, e.g., systems with normal state matrices, linear consensus networks with directed graphs, and cyclic linear networks. As a specific example, the H 2 -norm of a linear consensus network over a directed cycle graph is computed and shown how its performance scales with the network size. Our proposed spectral bounds reveal the important role and contribution of fast and slow dynamic modes of a system in the best and worst achievable performance bounds under white noise excitation. Finally, we use several numerical simulations to show the superiority of our bounds over the existing bounds in the literature. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
40. Structural Analysis and Optimal Design of Distributed System Throttlers.
- Author
-
Siami, Milad and Skaf, Joelle
- Subjects
- *
DISTRIBUTED computing , *BANDWIDTHS , *LINEAR systems , *SEMIDEFINITE programming , *LAPLACIAN matrices - Abstract
In this paper, we investigate the performance analysis and synthesis of distributed system throttlers (DST). A throttler is a mechanism that limits the flow rate of incoming metrics, e.g., byte per second, network bandwidth usage, capacity, traffic, etc. This can be used to protect a service's backend/clients from getting overloaded, or to reduce the effects of uncertainties in demand for shared services. We study performance deterioration of DSTs subject to demand uncertainty. We then consider network synthesis problems that aim to improve the performance of noisy DSTs via communication link modifications as well as server update cycle modifications. [ABSTRACT FROM PUBLISHER]
- Published
- 2018
- Full Text
- View/download PDF
41. Fekete Points, Formation Control, and the Balancing Problem.
- Author
-
Montenbruck, Jan Maximilian, Zelazo, Daniel, and Allgower, Frank
- Subjects
- *
PAIRED comparisons (Mathematics) , *NETWORK analysis (Communication) , *COOPERATIVE control systems , *AUTONOMOUS robots , *DECENTRALIZED control systems , *MULTIAGENT systems - Abstract
We study formation control problems. Our approach is to let a group of systems maximize their pairwise distances while bringing them all to a given submanifold, determining the shape of the formation. The algorithm we propose allows us to initialize the positions of the individual systems in the ambient space of the given submanifold but brings them to the desired formation asymptotically in a stable fashion. Our control inherently consists of a distributed component, maximizing the pairwise distances, and a decentralized component, asymptotically stabilizing the submanifold. We establish a graph-theoretical interpretation of the equilibria that our control enforces and extends our approach to systems living on the special Euclidean group. Throughout this paper, we illustrate our approach on different examples. [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
42. On the Linear Convergence Rate of the Distributed Block Proximal Method
- Author
-
Giuseppe Notarstefano, Francesco Farina, Farina Francesco, and Notarstefano Giuseppe
- Subjects
0209 industrial biotechnology ,Control and Optimization ,federated learning ,Linear programming ,020206 networking & telecommunications ,network analysis and control ,02 engineering and technology ,Optimization algorithm ,machine learning ,020901 industrial engineering & automation ,Optimization and Control (math.OC) ,Control and Systems Engineering ,Distributed algorithm ,Convergence (routing) ,Convex optimization ,FOS: Mathematics ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Constant (mathematics) ,Convex function ,distributed optimization ,Mathematics - Optimization and Control ,Random variable ,Block (data storage) ,Mathematics - Abstract
The recently developed Distributed Block Proximal Method, for solving stochastic big-data convex optimization problems, is studied in this paper under the assumption of constant stepsizes and strongly convex (possibly non-smooth) local objective functions. This class of problems arises in many learning and classification problems in which, for example, strongly-convex regularizing functions are included in the objective function, the decision variable is extremely high dimensional, and large datasets are employed. The algorithm produces local estimates by means of block-wise updates and communication among the agents. The expected distance from the (global) optimum, in terms of cost value, is shown to decay linearly to a constant value which is proportional to the selected local stepsizes. A numerical example involving a classification problem corroborates the theoretical results., arXiv admin note: text overlap with arXiv:1905.04214
- Published
- 2020
43. Covid-19 and Flattening the Curve: a Feedback Control Perspective
- Abstract
Many of the policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution. This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution of this paper is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno -a small city in Northern Italy that has been among the most harshly hit by the pandemic., Learning & Autonomous Control
- Published
- 2021
- Full Text
- View/download PDF
44. Topology-Independent Robust Stability Conditions for Uncertain MIMO Networks
- Abstract
We give a sufficient and a necessary condition for the topology-independent robust stability of networked systems formed by uncertain MIMO systems. Both conditions involve constants associated with the nominal node dynamics and arc interconnection matrices, the uncertainty bounds, and the maximum connectivity degree of the network; they are scalable (they can be checked locally), independent of the network topology and even of the number of nodes and arcs, and hold for networks of heterogeneous MIMO systems and interconnection matrices, with heterogeneous uncertainties. The dual cases of 1-norm and ∞-norm bounds are considered. In both cases, if the systems at the nodes are diagonal, we get a necessary and sufficient condition. We apply our results to the topology-independent robust stability analysis of a case-study from cancer biology., Accepted Author Manuscript, Team Tamas Keviczky
- Published
- 2021
- Full Text
- View/download PDF
45. H-infinity Optimal Control for Systems with a Bottleneck Frequency
- Abstract
We characterize a class of systems for which the H-infinity optimal control problem can be simplified in a way that enables sparse solutions and efficient computation. For a subclass of the systems, an optimal controller can be explicitly expressed in terms of the matrices of the system's state-space representation. In many applications, the controller given by this formula, which is static, can be implemented in a decentralized or distributed fashion. Examples are temperature dynamics in buildings, water irrigation and electrical networks.
- Published
- 2021
46. Topology-Independent Robust Stability Conditions for Uncertain MIMO Networks
- Abstract
We give a sufficient and a necessary condition for the topology-independent robust stability of networked systems formed by uncertain MIMO systems. Both conditions involve constants associated with the nominal node dynamics and arc interconnection matrices, the uncertainty bounds, and the maximum connectivity degree of the network; they are scalable (they can be checked locally), independent of the network topology and even of the number of nodes and arcs, and hold for networks of heterogeneous MIMO systems and interconnection matrices, with heterogeneous uncertainties. The dual cases of 1-norm and ∞-norm bounds are considered. In both cases, if the systems at the nodes are diagonal, we get a necessary and sufficient condition. We apply our results to the topology-independent robust stability analysis of a case-study from cancer biology., Accepted Author Manuscript, Team Tamas Keviczky
- Published
- 2021
- Full Text
- View/download PDF
47. Covid-19 and Flattening the Curve: a Feedback Control Perspective
- Abstract
Many of the policies that were put into place during the Covid-19 pandemic had a common goal: to flatten the curve of the number of infected people so that its peak remains under a critical threshold. This letter considers the challenge of engineering a strategy that enforces such a goal using control theory. We introduce a simple formulation of the optimal flattening problem, and provide a closed form solution. This is augmented through nonlinear closed loop tracking of the nominal solution, with the aim of ensuring close-to-optimal performance under uncertain conditions. A key contribution of this paper is to provide validation of the method with extensive and realistic simulations in a Covid-19 scenario, with particular focus on the case of Codogno -a small city in Northern Italy that has been among the most harshly hit by the pandemic., Learning & Autonomous Control
- Published
- 2021
- Full Text
- View/download PDF
48. Games on Large Networks: Information and Complexity.
- Author
-
Kordonis, Ioannis and Papavassilopoulos, George P.
- Subjects
- *
GAME theory , *INFORMATION storage & retrieval systems , *COMPUTATIONAL complexity , *APPROXIMATION theory , *MATHEMATICAL simplification - Abstract
In this work, we study Static and Dynamic Games on Large Networks of interacting agents, assuming that the players have some statistical description of the interaction graph, as well as some local information. Inspired by Statistical Physics, we consider statistical ensembles of games and define a Probabilistic Approximate equilibrium notion for such ensembles. A Necessary Information Complexity notion is introduced to quantify the minimum amount of information needed for the existence of a Probabilistic Approximate equilibrium. We then focus on some special classes of games for which it is possible to derive upper and/or lower bounds for the complexity. At first, static and dynamic games on random graphs are studied and their complexity is determined as a function of the graph connectivity. In the low complexity case, we compute Probabilistic Approximate equilibrium strategies. We then consider static games on lattices and derive upper and lower bounds for the complexity, using contraction mapping ideas. A LQ game on a large ring is also studied numerically. Using a reduction technique, approximate equilibrium strategies are computed and it turns out that the complexity is relatively low. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
- Full Text
- View/download PDF
49. Fundamental Limits and Tradeoffs on Disturbance Propagation in Linear Dynamical Networks.
- Author
-
Siami, Milad and Motee, Nader
- Subjects
- *
LINEAR dynamical systems , *STOCHASTIC processes , *PERFORMANCE evaluation , *GRAPH theory , *DISPERSION (Chemistry) , *MATHEMATICAL models - Abstract
We investigate performance deterioration in linear consensus networks subject to external stochastic disturbances. The expected value of the steady state dispersion of the states of the network is adopted as a performance measure. We develop a graph-theoretic methodology to relate structural specifications of the coupling graph of a linear consensus network to its performance measure. We explicitly quantify several inherent fundamental limits on the best achievable levels of performance and show that these limits of performance are emerged only due to the specific interconnection topology of the coupling graphs. Furthermore, we discover some of the inherent fundamental tradeoffs between notions of sparsity and performance in linear consensus networks. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
50. On the Effect of Collaborative and Antagonistic Interactions on Synchronization and Consensus in Networks of Conspecific Agents.
- Author
-
Roy, Subhradeep and Abaid, Nicole
- Subjects
- *
SOCIAL network theory , *SOCIAL systems , *SYNCHRONIZATION , *SWITCHING theory , *STOCHASTIC convergence - Abstract
While the vast majority of work on consensus and synchronization considers only collaborative interactions among the agents, antagonistic interactions may play important roles in coordination of social systems. In this work, we define a composite model over a stochastically-switching network capturing both collaborative and antagonistic interactions. We consider a general class of agents, so-called conspecifics, defined in terms of a common distribution for their interaction capacity and the weights they ascribe to interactions. We find closed form expressions for necessary and sufficient conditions for consensus, the rate of convergence to consensus, and conditions for stochastic synchronization. This model is further extended to composite topologies capable of capturing any number of independent interaction modes. Results demonstrate the presence of antagonistic interactions may help the system to achieve consensus and synchronization which is not possible in presence of only collaborative interactions and, at times, enables convergence at a faster rate. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
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