Nonlinear control; Information theory in control; Model reduction of Markov models; Large population games; Symmetry-methods in Dynamical Systems; Building systems; Biological systems
I work at the intersection of nonlinear dynamical systems and control theory: Topics include analysis of fundamental limitations in control of nonlinear systems, model reduction methods for complex systems, and phase transition and learning in large-scale dynamic games. My recent research involves analysis of phase transition in non-cooperative dynamic games with a large number of agents. The work aggregates concepts and techniques from nonlinear dynamical systems, game theory, and statistical mechanics to provide new tools for understanding complex interconnected systems. Specifically, a variant of the classical Kuramoto oscillator model is considered in a novel game-theoretic setting for control. It is shown that the synchronization of coupled oscillators can be interpreted as a solution of a non-cooperative dynamic game. The theoretical research is important to several applications in neuroscience, biology, economics, and large-scale engineering systems. On the technology side, my recent research includes applications to systems biology and integrated energy efficient building systems. Prior to joining Illinois, I worked at the United Technologies Research Center (UTRC) in the area of modeling and control of combustion instabilities in jet engines and afterburners. The state-of-the-art in control of rotating wave combustion instabilities in jet engines and afterburners is based on a “symmetry breaking” solution that I invented together with my colleagues at UTRC.
Deng, K., P. G. Mehta, and S. P. Meyn, "Optimal Kullback-Leibler Aggregation via the Spectral Theory of Markov Chains," accepted subject to minor changes in IEEE Transactions on Automatic Control.
Hao, H., P. Barooah, and P. G. Mehta, "Stability Margin Scaling of Distributed Formation Control as a Function of Network Structure," accepted subject to minor changes in IEEE Transactions on Automatic Control.
Sun, Y. and P. G. Mehta, "The Kullback-Leibler Rate Pseudo-Metric for Comparing Dynamical Systems," to appear in IEEE Transactions on Automatic Control, 55:7, 1585-1598, July 2010.
Sun, Y. and P. G. Mehta, "Bode-like Fundamental Performance Limitations in Control of Nonlinear Systems," IEEE Transactions on Automatic Control, 55:6, 1390-1405, June 2010.
Vaidya, U., P. G. Mehta, and U. Shanbhag, "Nonlinear Stabilization via Control Lyapunov Measure," IEEE Transactions on Automatic Control, 55:6, 1314-1328, June 2010.
Yin, H., P. Wang, T. Alpcan and P. G. Mehta, "Hopf Bifurcation and Oscillations in Communication Networks with Heterogeneous Delays," Automatica, 45:10, 2358-2367, October 2009.
Mehta, P. G., "Controlling Combustion," IEEE Control Systems Magazine, 29:4, 14-17, August 2009.
Barooah, P., P. G. Mehta, and J. Hespanha, "Mistuning-based Control Design to Improve Closed-loop Stability of Vehicular Platoons," IEEE Transactions on Automatic Control, 54:9, 2100-2113, Sept 2009.
Alpcan, T., P. Wang, P. G. Mehta, and T. Basar, "A Non-equilibrium Analysis and Control Framework for Active Queue Management," Automatica, 44:10, 2474-2486, October 2008.
Mehta, P. G., U. Vaidya, and A. Banaszuk, "Markov Chains, Entropy, and Fundamental Limitations in Nonlinear Stabilization," IEEE Transactions on Automatic Control, 53:3, 784-791, April 2008.
Vaidya, U. and P. G. Mehta, "Lyapunov Measure for Almost Everywhere Stability," IEEE Transactions on Automatic Control, 53:1, 307-324, March 2008.