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This paper proposes an original methodology to compute the regions of attraction in hyperbolic and polynomial nonlinear dynamical systems using the eigenfunctions of the discrete-time approximation of the Koopman operator given by the extended dynamic mode decomposition algorithm. The proposed method relies on the spectral decomposition of the Koopman operator to build eigenfunctions that capture the boundary of the region of attraction. The algorithm relies solely on data that can be collected in experimental studies and does not require a mathematical model of the system. Two examples of dynamical systems, a population model and a higher dimensional chemical reaction system, allows demonstrating the reliability of the results.

This paper considers a cooperative cruise control problem from a predictive control perspective. Online decision-making is used to be executed during the driving process based on the information obtained from the network. We formalize a synchronization problem approach from a predictive control theory using bargaining games to find an operating agreement between the vehicles. Finally, we test these results in an emulation environment in a hardware-in-the-loop system., Comment: 18 pages, 25 figures, journal paper

This paper presents a distributed data-driven control to regulate the voltage in an alternate current microgrid (MG). Following the hierarchical control frame for MGs, a secondary control for voltage is designed with a data-driven strategy using the Koopman operator. The Koopman operator approach represents the nonlinear behavior of voltage as a linear problem in the space of observables or lifted space. The representation in the lifted space is used together with linear consensus to design a model predictive control (MPC). The complete algorithm is proved in an MG model including changes in load, transmission lines, and the communication graph. The data-driven model regulates voltage using a distributed approach based only on local measurements, and includes reactive power constraints and control cost minimization., Comment: Title: This paper is an extention of previos results of another article that uses koopman for the MGs control Authors: Vladimir Toroa, Duvan Tellez-Castro, Eduardo Mojica-Nava, Naly Rakoto-Ravalontsalama Comments: 13 pages, 21 This paper uses the Koopman operator to identify an alternate current MG, the uses a linear predictor for MPC design

We develop an event-triggered control strategy for a weighted-unbalanced directed homogeneous robot network to reach a dynamic consensus in this work. We present some guarantees for synchronizing a robot network when all robots have access to the reference and when a limited number of robots have access. The proposed event-triggered control can reduce and avoid the periodic updating of the signals. Unlike some current control methods, we prove stability by making use of a logarithmic norm, which extends the possibilities of the control law to be applied to a wide range of directed graphs, in contrast to other works where the event-triggered control can be only implemented over strongly connected and weight-balanced digraphs. We test the performance of our algorithm by carrying out experiments both in simulation and in a real team of robots., Comment: 6 Pages, 4 Figures, IROS 2021

We consider the model of cooperative learning via distributed non-Bayesian learning, where a network of agents tries to jointly agree on a hypothesis that best described a sequence of locally available observations. Building upon recently proposed weak communication network models, we propose a robust cooperative learning rule that allows asynchronous communications, message delays, unpredictable message losses, and directed communication among nodes. We show that our proposed learning dynamics guarantee that all agents in the network will have an asymptotic exponential decay of their beliefs on the wrong hypothesis, indicating that the beliefs of all agents will concentrate on the optimal hypotheses. Numerical experiments provide evidence on a number of network setups., Comment: Submitted to ACC2021

Adaptive synchronization protocols for heterogeneous multi-agent network are investigated. The interaction between each of the agents is carried out through a directed graph. We highlight the lack of communication between agents and the presence of uncertainties in each system among the conventional problems that can arise in cooperative networks. Two methodologies are presented to deal with the uncertainties: A strategy based on robust optimal control and a strategy based on neural networks. Likewise, an input estimation methodology is designed to face the disconnection that any agent may present on the network. These control laws can guarantee synchronization between agents even when there are disturbances or no communication from any agent. Stability and boundary analyzes are performed. Cooperative cruise control simulation results are shown to validate the performance of the proposed control methods., Comment: 24 pages, 5 figures, Control & systems letters

The cooperative control applied to vehicles allows the optimization of traffic on the roads. There are many aspects to consider in the case of the operation of autonomous vehicles on highways since there are different external parameters that can be involved in the analysis of a network. In this paper, we present the design and simulation of adaptive control for a platoon with heterogeneous vehicles, taking into account that not all vehicles can communicate their control input, and in turn include structured nonlinear uncertainty input parameters., Comment: 6 pages, 4 figures, conferencce paper

The modernization of the power system introduces technologies that may improve the system's efficiency by enhancing the capabilities of users. Despite their potential benefits, such technologies can have a negative impact. This subject has widely analyzed, mostly considering for-profit electric utilities. However, the literature has a gap regarding the impact of new technologies on non-profit utilities. In this work, we quantify the price of anarchy of non-profit utilities, that is, the cost caused by lack of coordination of users. We find that users, in the worst case, can consume up to twice the optimal demand, obtaining a small fraction of the optimal surplus. For this reason, we leverage the theory of mechanism design to design an incentive scheme that reduces the inefficiencies of the system, which preserves the privacy of users. We illustrate with simulations the efficiency loss of the system and show two instances of incentive mechanism that satisfy either budget balance and budget deficit., Comment: 17 pages, 3 figures, accepted in the International Journal of Electrical Power and Energy Systems

The shift of power systems toward a smarter grid has brought devices such as distributed generators and smart loads with an increase of the operational challenges for the system operator. These challenges are related to the real-time implementation as well as control and stability issues. We present a distributed transactive control strategy, based on the projected consensus algorithm, to operate the distributed energy resources and smart loads of a power system toward optimal social welfare. We consider two types of agents: Generators, and smart loads. Each agent iteratively optimizes its local utility function based on local information obtained from its neighbors and global information obtained through the network of agents. We show convergence analysis and numerical results for the proposed method., Comment: Necsys2018

Most demand management approaches with non-mandatory policies assume full users' cooperation, which may not be the case given users' beliefs, needs and preferences. In this paper we propose a mechanism for demand management including incentives both with and without money. The mechanism is validated by means of simulation, modeling the consumers as a finite multiagent system which evolves until a stable state, and social incentives diffusion using opinion dynamics., Comment: draft

Networks out of equilibrium display dynamics characterized by multiple equilibria and sudden transitions. These transitions arise when each node leaves its natural stable state and joins to an organized global activation behavior. In this paper, we study local patterns near regime shifts in Network Synchronization and Self-Organized Criticality (SOC) by a Koopman spectrum data-driven approach. To illustrate these ideas, we use synchronized behavior from an Integral-and-Fire oscillators (IFO) system and SOC in the Bak-Sneppen model., Comment: paper accepted in CCAC 2017

The physical interconnection of spatial distributed biochemical systems has some advantages when dealing with large-scale problems that require separated agents to be con- trolled locally but with an overall objective. The analysis and control of such systems becomes a difficult task, because of the nonlinear nature of the dynamics of the individual subsystems, and the added complexity due to the interconnection. Therefore, analysis tools from a data-driven perspective are employed in contrast with the analytical classical way that becomes intractable once the subsystems grow in size or complexity., Comment: 7 pages, 3 figures

In this work we investigate the inefficiency of the electricity system with strategic agents. Specifically, we prove that without a proper control the total demand of an inefficient system is at most twice the total demand of the optimal outcome. We propose an incentives scheme that promotes optimal outcomes in the inefficient electricity market. The economic incentives can be seen as an indirect revelation mechanism that allocates resources using a one-dimensional message space per resource to be allocated. The mechanism does not request private information from users and is valid for any concave customer's valuation function. We propose a distributed implementation of the mechanism using population games and evaluate the performance of four popular dynamics methods in terms of the cost to implement the mechanism. We find that the achievement of efficiency in strategic environments might be achieved at a cost, which is dependent on both the users' preferences and the dynamic evolution of the system. Some simulation results illustrate the ideas presented throughout the paper., Comment: 38 pages, 9 figures, submitted to journal