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Associate Professor
Palaj, Gandhinagar
Gujarat 382 355
Email: cdpahlajani [at] iitgn.ac.in
Education:
Ph.D. in Mathematics, University of Illinois at Urbana-Champaign, October 2007.
Thesis Advisor: Richard B. Sowers.
M.S. in Mathematics, University of Illinois at Urbana-Champaign,
May 2003.
B.S.E. in Engineering Physics, University of Michigan at Ann Arbor, August 1999.
Research Interests:
Probability Theory and Stochastic Processes, Dynamical Systems, Control Theory, Homogenization
My doctoral dissertation was on stochastic averaging for a planar Hamiltonian system with skew random perturbations (i.e., something similar to skew Brownian motion); see (5) below. I have also worked on multiscale stochastic models of gene regulatory networks (9), and on some problems of decision making for Poisson processes motivated by applications in nuclear detection (6),(7),(8).
I am currently interested in stochastic processes that arise in hybrid dynamical systems. Examples include systems with:
Switching, e.g., a power electronic circuit which is governed by different differential equations depending on the ON/OFF state of a switch; see (3).
Sampling, e.g., a system evolving in continuous time according to a differential equation while being controlled by a digital computer which (necessarily) works in discrete time; see (1),(2) below.
Impacts/Resetting, e.g., bouncing ball, walking robot
I have also gotten interested recently in some problems of homogenization for stochastic processes.
Ph.D. Students
Current
Ashif Khan
Graduated
Shivam Dhama (Postdoctoral Associate Lecturer in Dept. of Mathematics and Statistics at Boston University, USA, starting July 2023)
Preprints:
Chetan D. Pahlajani. Periodic homogenization for switching diffusions (submitted). Preprint on ArXiv
Journal Publications:
Shivam Dhama and Chetan D. Pahlajani. Fluctuation analysis for a class of nonlinear systems with fast periodic sampling and small state-dependent white noise. Journal of Differential Equations, 362 (2023), pp. 438-483. (link to article)
Shivam Dhama and Chetan D. Pahlajani. Approximation of linear feedback control systems with small random noise and fast periodic sampling. Mathematical Control and Related Fields, vol. 13, issue 3 (2023), pp. 852-872. (link to article)
Chetan D. Pahlajani. Randomly perturbed switching dynamics of a DC/DC converter. Discrete and Continuous Dynamical Systems Series B, vol. 22, no. 2, pp. 569-584, March 2017 (link to journal).
Optimal navigation for vehicles with stochastic dynamics. Shridhar K. Shah, Herbert G. Tanner and Chetan D. Pahlajani. IEEE Transactions on Control Systems Technology, vol. 23, issue 5 (2015), pp. 2003-2009.
Stochastic averaging for a Hamiltonian system with skew random perturbations. Chetan D. Pahlajani. Journal of Theoretical Probability, vol. 28, issue 3, September 2015, pp. 1165-1226 (link to journal).
Performance bounds for mismatched decision schemes with Poisson process observations. Chetan D. Pahlajani, Jianxin Sun, Ioannis Poulakakis, and Herbert G. Tanner. Systems and Control Letters, 75 (2015), pp. 69-76 (link to journal).
Error probability bounds for nuclear detection: Improving accuracy through controlled mobility. Chetan D. Pahlajani, Jianxin Sun, Ioannis Poulakakis and Herbert G. Tanner. Automatica, vol. 50, issue 10 (2014), pp. 2470-2481 (link to journal).
Networked decision making for Poisson processes with applications to nuclear detection. Chetan D. Pahlajani, Ioannis Poulakakis and Herbert G. Tanner. IEEE Transactions on Automatic Control, vol. 59, no. 1 (2014), pp. 193-198 (link to journal).
Stochastic reduction method for biological chemical kinetics using time-scale separation. Chetan D. Pahlajani, Paul J. Atzberger and Mustafa Khammash. Journal of Theoretical Biology, 272 (2011), pp. 96-112 (link to journal).
Peer-reviewed Conference Publications:
Asymptotic analysis of discrete-time models for linear control systems with fast random sampling. Shivam Dhama and Chetan D. Pahlajani. 2021 Seventh Indian Control Conference (ICC), 359-364. (Shivam won Best Student Paper Award at the Seventh ICC for this work).
Decision-making accuracy for networks of sensors observing time-inhomogeneous Poisson processes. Chetan D. Pahlajani, Indrajeet Yadav, Herbert G. Tanner, and Ioannis Poulakakis. Distributed Autonomous Robotic Systems: the 13th International Symposium. Springer Tracts in Advanced Robotics 6, pages 177-190, 2018.
Error probabilities and threshold selection in networked nuclear detection. Chetan D. Pahlajani, Jianxin Sun, Ioannis Poulakakis and Herbert G. Tanner. 2013 IEEE Conference on Decision and Control, pp. 5450-5455.
Decision making in sensor networks observing Poisson processes. Chetan D. Pahlajani, Ioannis Poulakakis and Herbert G. Tanner. 2013 IEEE Mediterranean Conference on Control and Automation, pp. 1230-1235.
Stochastic receding horizon control for robots with probabilistic state constraints. Shridhar Shah, Chetan D. Pahlajani and Herbert G. Tanner. 2012 IEEE International Conference on Robotics and Automation, pp. 2893-2898.
Probability of success in stochastic robot navigation with state feedback. Shridhar Shah, Chetan D. Pahlajani and Herbert Tanner. 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3911-3916 (invited paper).
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