Research Interest:

My research focuses on developing convex optimization-based computational methods and tools for analyzing and controlling dynamical systems. I have recently started exploring ways of integrating machine learning (convex and non-convex) methods in control theory to potentially solve problems that cannot be solved using classical/modern control methods.

List of Publications

My Thesis

• Analysis, Estimation, and Control of Partial Differential Equations Using Partial Integral Equation Representation. Link

Peer Reviewed

Book Chapter

• Shivakumar, S., Aukes, D. M., Berman, S., He, X., Fisher, R. E., Marvi, H., & Peet, M. (2021). Decentralized estimation and control of a soft robotic arm. Bioinspired Sensing, Actuation, and Control in Underwater Soft Robotic Systems, 229-246. Link

Journals

• Jagt, D., Shivakumar, S., Seiler, P., & Peet, M. (2022). Efficient Data Structures for Representation of Polynomial Optimization Problems: Implementation in SOSTOOLS. IEEE Control Systems Letters, 6, 3493-3498. Link

• Shivakumar, S., and Matthew Peet. A Computational Method for H₂-optimal Estimator and State Feedback Controller Synthesis for PDEs. IEEE Control Systems Letters. (In review) Link

• Shivakumar, S., Das, A., Weiland, S., & Peet, M. (2022). Extension of the partial integral equation representation to GPDE input-output systems. IEEE Transactions on Automatic Control. (In review) Link

Conference proceedings

• Shivakumar, S., Das, A., & Peet, M. (2023). Representation of linear PDEs with spatial integral terms as Partial Integral Equations. In 2023 American Control Conference (ACC) (pp. 1788-1793). IEEE. Link

• Peet, M., & Shivakumar, S. (2022). Control of Large-Scale Delayed Networks: DDEs, DDFs and PIEs. IFAC-PapersOnLine, 55(30), 97-102. Link

• Das, A., Shivakumar, S., Peet, M., & Weiland, S. (2020). Robust analysis of uncertain ODE-PDE systems using PI multipliers, PIEs and LPIs. In 2020 IEEE Conference on Decision and Control (CDC) (pp. 634-639). IEEE. Link

• Shivakumar, S., Das, A., & Peet, M. (2020). PIETOOLS: A MATLAB toolbox for manipulation and optimization of partial integral operators. In 2020 American Control Conference (ACC) (pp. 2667-2672). IEEE. Link

• Shivakumar, S., Das, A., Weiland, S., & Peet, M. (2020). Duality and H_∞-optimal control of coupled ODE-PDE systems. In 2020 IEEE Conference on Decision and Control (CDC) (pp. 5689-5696). IEEE. Link

• Shivakumar, S., Das, A., Weiland, S., & Peet, M. (2019). A generalized LMI formulation for input-output analysis of linear systems of ODEs coupled with PDEs. In 2019 IEEE Conference on Decision and Control (CDC) (pp. 280-285). IEEE. Link

• Das, A., Shivakumar, S., Weiland, S., & Peet, M. (2019). H_∞ optimal estimation for linear coupled PDE systems. In 2019 IEEE Conference on Decision and Control (CDC) (pp. 262-267). IEEE. Link

• Peet, M., Shivakumar, S., Das, A., & Weiland, S. (2019). Discussion paper: A new mathematical framework for representation and analysis of coupled PDEs. IFAC-PapersOnLine, 52(2), 132-137. Link

• Shivakumar, S., & Peet, M. (2019). Computing input-output properties of coupled linear PDE systems. In 2019 American Control Conference (ACC) (pp. 606-613). IEEE. Link

• Doroudchi, A., Shivakumar, S., Fisher, R. E., Marvi, H., Aukes, D., He, X., … & Peet, M. (2018). Decentralized control of distributed actuation in a segmented soft robot arm. In 2018 IEEE Conference on Decision and Control (CDC) (pp. 7002-7009). IEEE. Link

Unpublished/Not peer-reviewed

• Baker, L. S., Shivakumar, S., Armbruster, D., Platte, R. B., & Zlotnik, A. (2023). Linear System Analysis and Optimal Control of Natural Gas Dynamics in Pipeline Networks. (To be submitted) Link

• Shivakumar, S., Das, A., Weiland, S., & Peet, M. (2023). H_∞-optimal control of coupled ODE-PDE systems using PIE framework and LPIs. IEEE Transactions on Automatic Control. (To be submitted) Link

• Wu, S., Peet, M., Shivakumar, S., & Hua, C. (2020). H_∞-optimal estimation in the PIE framework for systems with multiple delays and sensor noise. (To be submitted) Link

• Shivakumar, S., Jagt, D., Braghini, D., Das, A., & Peet, M. (2021). PIETOOLS 2022: User Manual. arXiv e-prints, arXiv-2101. Link

• Wu, S., Shivakumar, S., Peet, M., & Hua, C. (2020). H_∞-Optimal Observer Design for Linear Systems with Delays in States, Outputs and Disturbances. arXiv preprint arXiv:2004.04482. Link

• Das, A., Shivakumar, S., Weiland, S., & Peet, M. (2018). Representation and stability analysis of PDE-ODE coupled systems. arXiv preprint arXiv:1812.07186. Link

Talks/Presentations

• Representation of linear PDEs with spatial integral terms as Partial Integral Equations. In 2023 American Control Conference (ACC). IEEE.

• PIETOOLS: A MATLAB toolbox for manipulation and optimization of partial integral operators. In 2020 American Control Conference (ACC). IEEE.

• Duality and H_∞-optimal control of coupled ODE-PDE systems. In 2020 IEEE Conference on Decision and Control (CDC). IEEE.

• A generalized LMI formulation for input-output analysis of linear systems of ODEs coupled with PDEs. In 2019 IEEE Conference on Decision and Control (CDC). IEEE.

• Computing input-ouput properties of coupled linear PDE systems. In 2019 American Control Conference (ACC). IEEE.

• Decentralized control of distributed actuation in a segmented soft robot arm. In 2018 IEEE Conference on Decision and Control (CDC). IEEE.