Research

My research goal is to obtain a better understanding of how large-scale engineering systems work, on various levels and in a number of different applications: power systems, communication networks, and manufacturing systems, etc. This is a brief overview of what I think and things I’ve been doing lately; for more details see my list of publications.

Unknown state and sparse input estimation: Knowledge of the state and exogenous inputs is significant for monitoring and controlling real-world systems. Unfortunately, this information is often unavailable and needs to be extracted from noisy data. Assuming the system input is known, the celebrated Kalman filter produces optimal state estimates. But such an assumption fails to hold in many emerging applications: sensor and actuator faults and malignant attacks in critical infrastructures, acoustic systems, and mechanical systems; unknown deterministic dynamics that cannot be modeled as stochastic noise; and unmeasured couplings in networked systems. Therefore, in these scenarios, there is a need to estimate the inputs either to improve the state estimates’ accuracy or to ensure that the system is not excited by unwanted inputs.

The problem of state and input estimation in control theory is broadly referred to as system inversion and has a rich history. However, several existing techniques are limited to noise-free linear time-invariant systems with more outputs than inputs. My research addresses this limitation by developing new recursive algorithms that extend to time-varying noisy descriptor systems with large number of inputs than outputs. To this aim, I use tools from compressed sensing, systems theory, sparsity-promoting optimization algorithms, and concentration inequalities. In my recent work, I studied the statistical performance of the group LASSO algorithm for the unknown state and input estimation in terms of system invariant zeros and certain orthogonality conditions on system transfer functions. More details can be found in Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach and A Complex-LASSO Approach for Localizing Forced Oscillations in Power Systems

Structure learning in large-scale network systems: Networks capture interactions among entities or subsystems of complex systems and have thus found several applications in scientific and engineering disciplines. Examples range from engineering systems (e.g., power, water, and transportation networks) to biological systems (e.g., gene regulatory, protein-protein interaction, and brain networks). In these and several other applications, the network structure (i.e., the presence or absence of edges between entities) is often unknown and needs to be estimated from data for real-time management and control. But, unfortunately, the data is often corrupted by adversarial noise, and importantly, the number of samples is way less than the number of edges to be estimated. Nevertheless, we overcome the above limitation by exploiting the physics and structure in real-world network systems. Specifically, building on the recent advances in convex regularized estimators, we have developed and studied novel estimators to reconstruct network structures in systems obeying conservation laws, electric power distribution networks with hidden nodes, control of coarsely measured systems, and tree-like graphical models. Our results highlighted identifiability limits and suggested new ways (for e.g., convex-concave estimators) for rigorously studying structure learning in networks with minimal data.

Security of cyber-physical systems: Integrating cyber and communication technologies in physical processes not only enabled practitioners to use the resources efficiently, but also opened a gateway for attackers to launch cyber attacks, including the 2016 Ukraine Power grid attack and the 2021 Colonial oil pipeline attack. Notably, a successful attack can lead to the shutdown of an entire facility, whose effects can be devastating and long-lasting. E.g., in the 2016 Ukraine power grid attack, 250 thousand customers were left without power and other emergency services for six hours. Consequently, there is a need for intelligent attack detection and mitigation strategies. In my doctoral dissertation, I primarily focused on the former and developed theory to understand (i) why and when a decentralized attack detector, although having limited knowledge of the system model, can outperform a centralized detector?; (ii) why for specific network systems detection performance improves as sensors are moved away from the proximity of input attacks?; and (iii) the system degradation due to random and periodic attacks. In short, my research results provided engineering insights into the performance limits of existing attack detectors, which, I believe, will have an impact on designing data-driven detectors. The ultimate goal of my research is to develop robust and scalable attack detection methods, either model- or data-based, by exploiting system dynamics and high-dimensional statistical machine learning techniques.

• [.pdf] “Network theoretic analysis of maximum a posteriori detectors for optimal input detection,” 2022
• [.pdf] “Deflection-based attack detection for network systems,” 2021
• [.pdf] “On a security vs privacy trade-off in interconnected dynamical systems,” 2021
• [.pdf] “On the robustness of data-driven controllers for linear systems,” 2020
• [.pdf] “Centralized versus decentralized detection of attacks in stochastic interconnected systems,” 2020
• [.pdf] “A probabilistic approach to design switching attacks against interconnected systems,” 2019
• [.pdf] “Cross-layer codesign for secure cyber-physical systems,” 2016

Applications to power systems: Replacing fossil-fuel-based energy sources with inverter-based renewable energy sources (e.g., solar and wind) is good for planet Earth. Yet, recent research showed that this deep integration is threatening the dynamic and steady-state performance of the power systems (e.g., see this interesting article on Great Britain’s power outage). Thus, there is a great need to address several issues, such as stability, cyber-security, and estimation and control for this modern inverter-dominated grid. My research contributes to these aspects by (i) identifying the topology of a distribution network with limited PMUs; (ii) quickly localizing forced oscillations in bulk power systems; (iii) estimating model parameters for control in low-inertia grids; and (iv) real-time identification and synthesis of fake attacks using PMU measurements. I already listed a few related papers (with pdf links) in the paragraphs above.

Random and Toeplitz matrices, and linear algebra: Most of my research involves using concepts, techniques, and results from linear algebra and matrix theory. While I was/am working on research problems, I started to appreciate beautiful abstract results in Random matrices and Toeplitz matrices (e.g., the asymptotic distribution of spectrum and their splitting behavior), complex Hermitian matrices (e.g., square roots of these matrices), polynomial matrices, and operator theoretic notions in linear algebra. In my book of problems (my precious!) I listed some interesting questions, which seem unsolved yet. I’m waiting for the right time to strike them. Interested? Please shoot me an email.