Research Description




My research is motivated by the dearth of scalable techniques for the analysis and synthesis of various large-scale complex systems; notably, the ones which tackle design and decision making in a single framework. Utilizing concepts from control, graph theory and combinatorial optimization, the main objective is to develop new design tools and algorithms that can harness the physical dynamics of such systems to meet the specified large-scale control objectives with performance guarantees. The systems of interest are neural-systems, and  distributed control systems that require the embedding of pervasive intelligence and scalable decision-making; a particularly relevant infrastructure being the electrical power network as it transitions to the smart grid of the future, and multi-agent networks.

Neurosciences and Control

My motivation is drawn from the following questions:
  • How to model brain dynamics?
  • What is the minimum number of probes to ensure brain dynamics observability?
  • Is there a relation between electroencephalogram (EEG), structural and functional connectivity?
  • What is the interplay between the micro-meso-macroscopic scales in brain activity?
  • How to develop cyber-physical devices to attenuate the effects of neuronal disorders (e.g. epilepsy)?

Closed-loop Electroencephalography-based (EEG) Neurostimulation Devices

Most of today's neurostimulation devices have discharging strategies that are empirically determined. Therefore, these devices do not take into consideration the specific brain's dynamics nor response to a sequence of discharges. Hence, we seek model-based schemes that enable a personalized discharge scheme that minimizes the interaction with the brain, which leads to more autonomy of the neurostimulation device. 

Epilepsy and Neurostimulation

Mapping Structural into Functional Connectivity

One of the major challenges nowadays is to characterize the human connectome. There are several methods to characterize the connectome, where two of the most common ones are the structural and functional connectivity. On one hand, structural connectivity is characterized by white matter tracts physically interconnecting brain regions and is typically measured in vivo in humans using diffusion tensor imaging (DTI). On the other hand, functional connectivity is a statistical measure of correlation (or covariation) between functional magnetic resonance imaging (fMRI) signals obtained from discrete brain regions (usually anatomically defined). Although it is tempting to assume that one can ascertain the nature of structural connections present by examining the strength of functional connections and vice versa. It has long been observed that functional connectivity can be detected between brain regions in the absence of direct structural connectivity. Consequently, one of the major questions is as follows
: are structural and functional connectivity related, and, if so, how? Learn more about this topic in Contributions and challenges for network models in cognitive neuroscience, by Olaf Sporns, Nature Neuroscience, 2014.

How a piano can help us understanding the inner working of the human brain?

Re-Thinking Wearable Technology

State-of-the-art electroencephalogram (EEG) wearable technology relies on signal processing and machine learning tools to capture mainly temporal features that can be linked to a specific task. Our approach aims to introduce new models capable of capturing spatiotemporal dependencies, to be later used to determine which regions need to be sensed, and which data contains more 'information'. Subsequently, we can leverage these insights to re-think wearable technology, by possible minimizing the number of sensors prescribed to monitor brain dynamics, which implies a smaller energy requirement and, hence, more autonomy. Furthermore, due to the spatiotemporal 'fingerprints' captured by our model, we are able to enhance the functionality of current technology. Thus, improving the reliability of the interaction between brain-machine and brain-machine-brain interfaces, with potential applications to neurological disorders (e.g. epilepsy) by improving the current neurostimulators. Alternatively, the improvement of this technology enables a real-time embedding into the current technology world. Therefore, this technology will ultimately enable the improvement of people's life quality.

Proactive Brain Interfacing

Analysis, Design, and Optimization of
Large-Scale Networked Dynamical Systems

Some of the fundamental questions I am interested to address are as follows:

  • What is the smallest subset of state variables that need to be actuated to ensure controllability?
  • What is the smallest subset of state variables that we need to measure to ensure observability?
  • Which subset of measured state variables needs to be provided to the actuators (and which actuators) to ensure arbitrary pole placement using decentralized control?

Additionally, the above questions can be addressed under privacy requirements and/or adversarial environments, so I am also interested in addressing these while considering the following:

  • How to exchange task-specific data without compromising private information?
  • How to design the sensing infrastructure to make the system resilient against malicious adversarial attacks?

Actuation-Sensing Selection

A major focus area of my research involves the optimization and assessment of intrinsic elementary system theoretic constructs, such as controllability and observability, from a design point of view, and, in particular, in non-classical information and operation scenarios. For instance, we are interested in understanding and characterizing the sparsest inputs (actuators) and sparsest outputs (sensors) to ensure controllability and observability, when physical parameters are not accurately known. In other words, we want to assess structural controllability and observability that ensures that almost all realizations of the plant matrices with a given structure (sparsity) are controllable and observable, respectively.

Actuation-Sensing-Communication Co-Design

Due to geographic nature of distributed systems or design constraints, given a system that is controllable
and observable, it is desirable to only provide a relatively small subset of the measurements to some
actuators. Thus, we ask the following fundamental question: Which subset of measured state variables needs to be provided to the actuators (and which actuators) to ensure arbitrary pole placement using decentralized control?

It is well known that in static output feedback, if all the measurements are forwarded to all the actuators, arbitrary performance (i.e., pole placement) can be enforced as long as the system is controllable and observable. Nevertheless, if a single measurement is disregarded by an actuator, then there is a demand for theoretical and numerical methods (suitable for large-scale systems) to assert that decentralized control for arbitrary performance is still possible. Nevertheless, it is known that such performance is closely related with the notion of fixed modes, which are the modes of the closed-loop system that use static output feedback and are kept unchanged by varying the gain that satisfies a pre-specified information pattern. Thus, we seek to determine and design information patterns in large-scale dynamic systems that have no structural fixed modes, i.e., fixed modes originated by the structure of the system plant matrices.

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