My doctoral dissertation studies the impact of reaction delays on the dynamics of connected vehicle systems. In the context of human-driven vehicles, our work provides phenomenological insight into real-world phenomena such as "phantom jams." In the context of self-driven vehicles, our work provides design guidelines for appropriate choice of control parameters. In addition to avoiding collision, these guidelines also account for the following: (i) stability of the entire connected vehicle system, (ii) robustness to uncertainty in parameters, (iii) jerk-free vehicular motion, and (iv) quick equilibration of the connected vehicle system. These results are obtained by modeling the dynamics of individual vehicles using delay differential equations. Mathematically, our work provides novel conditions for stability and convergence of solutions to the differential equations. Additionally, our work provides appropriate corrections to existing results. Post PhD, we proposed a design methodology for a simple generic controller that can stabilize connected vehicle systems. The main tools used here pertain to time-delay systems and non-linear control design. We choose between time-domain and spectral-domain approaches appropriately, based on the insight obtained. This has led to 5 conference and 2 journal publications, with an additional manuscript currently under revision at the IMA Journal of Applied Mathematics. This body of work has been carried out with my Ph.D. advisors Dr. Krishna Jagannathan and Dr. Gaurav Raina and my Ph.D. colleague Dr. Sreelakshmi Manjunath.

Traditional design of control systems assumes that control information is communicated over an ideal communication medium. Similarly, network protocol design is typically oblivious to the information contained in the packets that it transmits. However, a control-communication co-design is a necessity to enhance the performance of the overall system. Thus, I have pursued two lines of thought in this area, one based on a deterministic analysis and the other on a stochastic analysis.

In the first approach, we consider a number of plant-controller pairs communicating over a limited number of noisy channels. In this scenario, we provide simple LMI-based conditions that the scheduler and the controllers must obey for all plant-controller pairs to be stabilized. We predominantly make use of Lyapunov-based tools from switched systems theory to obtain these results. We also provide an algorithm to implement such a scheduler. This work has led to a conference publication in IEEE CDC 2019, and was carried out in collaboration with Dr. Rachel Kalpana Kalaimani and Mr. Kiran Rokade at IIT Madras.

In the other approach, we consider a Gauss-Markov source being estimated over a lossy network. Traditionally, scheduling of packets of over networks make use of only the so-called "age of information" or "freshness" of packets. We show that, for our scenario, scheduling packets based on an appropriately defined "value of information" is optimal; that is, it yields minimum estimation error. While such a result was shown via simulations in the literature, ours is the first work to supply an analytical proof for the same. To that end, we make use of tools from the theory of optimal control. This work is in collaboration with Prof. P.R. Kumar and Dr. Rahul Singh, and was presented at the Allerton 2019 conference.

Security of CPSs has been an important topic of study due to the serious impact that it can have. In this context, a first step is to detect attacks when they occur. While the majority of the literature focuses on communication-related "external" attack, it is imperative that CPSs be designed to tackle rogue "internal" attacks as well. In this context, the dynamic watermarking technique and the related detection tests have been proved to work efficiently for linear stochastic dynamical systems. In this thread, I am involved in implementing and testing of these tests for non-linear systems. As a prototypical example of process control systems, we have implemented and studied the detection tests on a water-tank set up. This implementation is carried out using MATLAB and Simulink. Similarly, we have implemented these detection tests on a real-life Lincoln MKZ autonomous car. In each of these cases, the attacks are correctly detected in a reasonable amount of time. This work is in collaboration with Prof. P.R. Kumar, Dr. Swaminathan Gopalswamy, Dr. Woo-Hyun Ko, Dr. Satchidananda Bharadwaj, Mr. Lantian Shangguan, Mr. Kenny Chour and Mr. Jaewon Kim, and has led to a publication in IEEE Transactions on Industrial Electronics. 

A recent thread on detection of Distributed Denial of Service (DDoS) attacks is based on using reduced number of features for quicker detection without a loss of accuracy. To that end, the Shapley value-based explainer SHAP is used for feature reduction. It is shown that SHAP not only reduces the number of features needed to detect an attack but also have over 99% accuracy. Thus, we show that the proposed SHAP-based DDoS detector is faster and more accurate. This work is in collaboration with my Ph.D. student, C Cynthia, and my Ph.D. colleague Dr. Debayani Ghosh, and has led to a publication in ICOAI 2023.

In the context of the futuristic Unmanned Aerial Vehicle (UAV) systems, air traffic control plays a central role in ensuring safety of the airborne UAVs. Prof. P.R. Kumar's group, of which I was a part as a Post Doc, has proposed an architecture for air traffic control that provably guarantees safety of all airborne UAVs. The proposed architecture consists of several independent and mutually interacting modules. My work concerned the communication module that allows UAVs to exchange critical control and positional information in real time. In particular, I have proposed and implemented a simple and efficient communication protocol using Java that runs on a middleware called Etherware. The next logical step is to test the overall air traffic control architecture on real-life drones. This work is in collaboration with Prof. P.R. Kumar, Dr. Satchidananda Bharadwaj, Dr. Woo-Hyun Ko, Mr. Jaewon Kim and Ms. Neagin Santi.

In addition to my research on CPSs, post Ph.D., I have also studied stability, convergence and bifurcation properties of time-delay systems that arise out of application domains of physiology and economics. Specifically, we have performed a thorough and systematical mathematical analysis of the Mackey-Glass and Lasota models for change in concentration of blood cells in physiology, and the Kaldor-Kalecki model for business cycles in economics. We have conducted a local stability analysis for these models, and also shown that they undergo a loss of local stability via a Hopf bifurcation. We have also studied robustness properties of these models to parametric uncertainty. Thus, our work provides insight into these physical processes. This work was carried out at IIT Madras with Dr. Gaurav Raina and my Ph.D. colleague Dr. Sreelakshmi Manjunath, and the manuscripts are currently under preparation.