A recently developed method for synthesizing time optimal feedback control policies for linear time invariant systems with bounded inputs will be briefly reviewed. This technique involves converting the associated equations in to polynomials using appropriate variable substitution, and then using Gröbner basis based elimination methods to synthesize a nested time optimal feedback control law. Currently the method is limited to systems with rational distinct eigenvalues. The developed method will be then applied to solve the following problems: (1) Distributed Computation of Minimum Time Consensus for Multi-Agent Systems (2) Computing the Nash equilibrium feedback control policies for two player time optimal pursuit evasion games. (3) Computing decentralized feedback control for min-max time consensus tracking of multi-agent systems that are communicating over directed graphs. A short description of our efforts to set up an outdoor multi-quadcopter testbed for experimentally verifying the developed theory will also be presented.
Debraj Chakraborty received his BE in Electrical Engineering from Jadavpur University, Kolkata, India in 2001, MTech in Electrical Engineering from IIT Kanpur, Kanpur, India in 2003 and PhD in Electrical and Computer Engineering from University of Florida Gainesville, USA in 2007 respectively. Thereafter he joined the Department of Electrical Engineering, Indian Institute of Technology Bombay where he is currently an Assistant Professor. His research interests include optimal control, linear systems and control applications.