Research

My research focuses on the analysis and control of nonlinear dynamical systems on/of complex networks. In general, complex networks can be modeled by nonlinear hybrid systems with constraints in a graph-theoretical framework, where collective behavior emerges with possible different properties of the individual agents. Recently, the distributed pervasive available information of these networked systems have lead to data-driven modeling techniques to efficiently improve the robust operation. From a theoretical point of view, my goal is to develop efficient, adaptive, and scalable algorithms in the intersection of distributed optimization, network games, network science, and control theory. These theoretical results attempt to deal with several relevant engineering challenges such as multi-energy systems, large-scale processes, and multi-agent systems in complex environments.

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Research Topics

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Population Games and its Applications

In modern technological systems, one of the main challenges is related to the coordination of large-scale population of subsystems that exhibit different individual behaviors while interacting with each other. The multiagent framework has emerged as one way to overcome the main issues associated with networked systems. In the context of multiagent systems, game-theoretical methods, and in particular population games, have appear as a useful modeling tool, where self-interested non-cooperative agents wish to maximize their welfare. A remarkable advantage of distributed population dynamics compared to others distributed learning algorithms in games is the inclusion of coupled constraints. This property has been exploited for solving dynamic resource-allocation problems.

A fundamental resource-allocation problem in smart grids is the economic dispatch in microgrids. To solve a dynamic economic dispatch problem in microgrids using population games, we have developed a hierarchical management strategy in [J35]. I was also part of a featured IEEE Control Systems Magazine article addressing three crucial engineering problems associated with smart cities solved by population games: smart lighting, optimal dispatch in microgrids, and control of urban drainage systems [J70]. Based on these results, and as part of the activities of the IEEE Control Systems Society Technical Committee on Smart Grids, a book chapter was published in [BC87].

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Analysis and Synthesis of Switched Nonlinear Systems

My research on switched systems started with my PhD dissertation. At the time, most of the literature was focused on switched linear systems. To deal with the nonlinearities, I have investigated how semi-algebraic geometry and convex optimization could be used to analyze and control switched nonlinear systems by means of embedding it into a continuous polynomial representation. Once the system has this representation, I have used the Theory of Moments to transform the nonlinear system into a relaxed convex formulation mode appropriate to be solved by high-performance numerical algorithms [J27]. For the stability analysis of switched nonlinear system, I have followed the same embedding technique and proposed a polynomial approach to deal with the stability analysis of switched non-linear systems under arbitrary switching using dissipation inequalities. With this method and from a theoretical point of view, I provided an alternative way to search for a common Lyapunov function for switched non-linear systems [J16].

In the context of microgrids, I have proposed a switched control algorithm for a DC microgrid and, in collaboration with Prof. Miguel Castilla and Juan M. Rey, an experimental validation was implemented and published in [J83].

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Complex Networks and Synchronization in Multiagent Systems

Cyber-physical energy systems are large-scale and complex systems that involve a wide number of electrical devices that are interconnected by physical and communication networks. In this interdisciplinary research, we have first focused our attention on distributed frequency synchronization [J77]. We have used the Kuramoto oscillator to model these nonlinear phenomena. The topology that describes the interaction between oscillators may not be connected due to environmental limitations or link failures. We have proposed a consensus-based control strategy that forces the network to follow a virtual agent with a constant frequency, and where only few agents have access to the leader state. The controller is based on the exchange of information between the oscillators through a communication network.

On the other hand, we have begun to study how network science can be applied to engineering problems. With my PhD student Catalina Caro in collaboration with Prof. David J. Hill, we have been working on qualifying transmission line significance on cascading failures using cut-sets, and cascading collapse of power networks under minimum cut-set-based attacks.

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Current and Future Research Directions

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Data-Driven Learning for Synthesis of Networks

A fundamental topic in dynamical networks is the identification of the dynamics of/on the network, where the information of network topology and the dynamics of the nodes is partially or completely unknown, and only limited time series are available from direct measures. Therefore, the reverse engineering problem of predicting network structure and dynamics from data is crucial. We have been studying operator-theoretic methods for network reconstruction, in particular the Koopman operator approach as a unified framework to the analysis of high dimensional systems including modeling and analysis of subsystems. The Koopman operator is an infinite dimensional linear operator that obtain the information about the nonlinearities through the evolution of observables of the state space. We would like to extend this framework to incorporate more complex scenarios such as subsystems modeled by hybrid differential-algebraic equations, network with time-varying topology, uncertainty in the measures, and heterogeneous agents.

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Large-Scale Optimization and Operator-Theoretic Methods

Distributed optimization algorithms have shown several benefits over centralized algorithms in important cyber-physical problems. In the context of smart grids, we have been working on new modeling perspective to integrate devices of different nature. Recently, we have proposed 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.

In this promising research area of distributed optimization, we plan to tackle several issue related to real systems. On the one hand, traditional distributed optimization algorithms are model-based (constraints, payoff function, etc.), but this assumption imposes some limitations when we intend to apply the results in real scenarios, where there is model uncertainty or partially knowledge of the system is available. In these cases, the unknown nonlinear dynamics of the agents can be reconstructed through a data-driven transformation. We intend to use the Koopman operator approach with its spectrum approximated by data-driven regressions using variations or improvements of the extended dynamic mode decomposition to deal with model nonlinearities and uncertainties. It would also be interesting to study the relationship between statistical learning and the operator-theoretical framework, and their application to distributed optimization algorithms with uncertainties. On the other hand, when the agents are non-cooperative (or partially cooperative), network games have emerged as a promising approach to model this collective behavior in a distributed way. This work is based on the work that has been developed in population games including monotone operator to guarantee convergence under dynamical constraints.

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Multiplex Networks and Engineering Applications

One of the new challenges in complex networks concerns the topological and dynamical characterization of systems composed of two or more interconnected networks. A natural extension to describe a set of coupled layered networks is the concept of multiplex network. This concept can be used to model modern engineering applications where systems of systems or networks of networks emerge. Several applications have been identified where these phenomena are pervasive such as networked microgrids, multi-energy systems (power, gas, and district heating networks), multi-mode transportation systems, among others. For this research, we expect to extend the developed distributed optimization and network games algorithms to control these multiplex networks with constraints.