- Cyber-Physical Systems
- Fundamental limitations for control of dynamical systems over networks:
- Control and optimization over uncertainty networks:
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We have discovered a systematic framework for analyzing and designing network-controlled systems in the presence of uncertainty.
The main contribution of this work is to understand fundamental tradeoffs that arise in the control of linear and nonlinear dynamical systems over networks in the presence of uncertainty.
- Off-road Autonomy and Robotics
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This research focuses on developing a systematic data-driven analytical and computational framework for the navigation of autonomous vehicles in the off-road environment. The data-driven tools are based on linear operator theory involving Koopman and Perron-Frobenius operators. The developed framework is tested on an experimental platform consisting of an F1TENTH vehicle, 1/5th scale Hunter SE. We are currently implementing the framework for full-scale Warthog and MRZR vehicles.
- Network Power System
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In applications involving network power systems, our research work is focused on a couple of different problems, which include real-time stability monitoring, stochastic stability and performance analysis of power systems in the presence of uncertain renewable, robust distributed optimization of a distributed system, data-driven analytics involving linear operator theoretic methods for reduced order modeling, and cyber security of power grid. We have discovered data-driven methods based on the dynamical system theory for the real-time rotor angle and power system voltage stability monitoring using time-series data from Phasor Measurement Units (PMUs).
- Operator theoretic methods for data-driven analysis and control of dynamical systems
- Duality in stability and control from linear operator perspective:
- Spectral Koopman methods for analysis and control:
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We have introduced novel operator theoretical methods for stability analysis and optimal control design for dynamical systems.
The proposed research aims to discover methods based on the spectral analysis of the Koopman operator for the data-driven analysis and synthesis of nonlinear systems.
- Information Flow and Control Over Networks
- Information-based causality measure in a dynamical system:
- Control of information flow over networks:
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Information flow and causality are the most fundamental concepts for analyzing and designing various engineering and natural sciences systems.
Information flow among nodes in a complex network describes the overall cause-effect relationships among the nodes. It provides a better understanding of the contributions of these nodes, individually or collectively, towards the underlying network dynamics.