@article{kar_bai_chakrabortty_2023, title={Reinforcement Learning based Approximate Optimal Control of Nonlinear Systems using Carleman Linearization}, ISSN={["2378-5861"]}, DOI={10.23919/ACC55779.2023.10156057}, abstractNote={We develop a policy iteration-based model-free reinforcement learning (RL) control for nonlinear systems with single input. First, Carleman linearization, a commonly used linearization technique in the Hilbert space, is applied to express the nonlinear system as an infinite-dimensional Carleman state-space model, followed by derivation of an online state-feedback RL controller using state and input data in this infinite-dimensional space. Next, the practicality of using any finite-order truncation of this controller, and the corresponding closed-loop stability of the nonlinear plant is established. Results are validated using two numerical examples, where we show how our proposed method provides solutions close to the optimal control resulting from the model-based Carleman controllers. We also compare our controller to alternative data-driven methods, showing its advantage in terms of shorter learning time.}, journal={2023 AMERICAN CONTROL CONFERENCE, ACC}, author={Kar, Jishnudeep and Bai, He and Chakrabortty, Aranya}, year={2023}, pages={3362–3367} }
 @article{minster_saibaba_kar_chakrabortty_2021, title={EFFICIENT ALGORITHMS FOR EIGENSYSTEM REALIZATION USING RANDOMIZED SVD}, volume={42}, ISSN={["1095-7162"]}, DOI={10.1137/20M1327616}, abstractNote={Eigensystem Realization Algorithm (ERA) is a data-driven approach for subspace system identification and is widely used in many areas of engineering. However, the computational cost of the ERA is dominated by a step that involves the singular value decomposition (SVD) of a large, dense matrix with block Hankel structure. This paper develops computationally efficient algorithms for reducing the computational cost of the SVD step by using randomized subspace iteration and exploiting the block Hankel structure of the matrix. We provide a detailed analysis of the error in the identified system matrices and the computational cost of the proposed algorithms. We demonstrate the accuracy and computational benefits of our algorithms on two test problems: the first involves a partial differential equation that models the cooling of steel rails, and the second is an application from power systems engineering.}, number={2}, journal={SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS}, author={Minster, Rachel and Saibaba, Arvind K. and Kar, Jishnudeep and Chakrabortty, Aranya}, year={2021}, pages={1045–1072} }
 @article{kar_chakrabortty_2021, title={LSTM based Denial-of-Service Resiliency for Wide-Area Control of Power Systems}, ISSN={["2165-4816"]}, DOI={10.1109/ISGTEUROPE52324.2021.9640193}, abstractNote={Denial-of-Service (DoS) attacks in wide-area control loops of electric power systems can cause temporary halting of information flow between the generators, leading to closed-loop instability. One way to counteract this issue would be to recreate the missing state information at the impacted generators by using the model of the entire system. However, that not only violates privacy but is also impractical from a scalability point of view. In this paper, we propose to resolve this issue by using a model-free technique employing neural networks. Specifically, a long short-term memory network (LSTM) is used. Once an attack is detected and localized, the LSTM at the impacted generator(s) predicts the magnitudes of the corresponding missing states in a completely decentralized fashion using offline training and online data updates. These predicted states are thereafter used in conjunction with the healthy states to sustain the wide-area feedback until the attack is cleared. The approach is validated using the IEEE 68-bus, 16-machine power system.}, journal={2021 IEEE PES INNOVATIVE SMART GRID TECHNOLOGY EUROPE (ISGT EUROPE 2021)}, author={Kar, Jishnudeep and Chakrabortty, Aranya}, year={2021}, pages={313–317} }