Time optimal feedback control of linear systems and minimum time consensus of multiple interacting double integrators

In first part, we review a recently developed method to compute the time optimal feedback control for state transfer of a class of single input linear time invariant systems with constrained input. The time optimal control is known to switch between upper and lower limits of constraints based on switching surfaces in state space which are available in parametric form (not useful for feedback). We use Groebner basis to eliminate these parameters and obtain an implicit representation of switching surface which is useful for state-feedback based switching.

In second part, We give a method to compute the minimum time to consensus for multiple double integrator agents interacting with each other over a complete graph. The method uses intersection of attainable sets and Helly's theorem to show that, for a group of N>3 agents only two or three agents determine the final time to consensus and consensus state. This part is a joint work with a fellow PhD student Ameer K. Mulla and Professor Debraj Chakraborty.