Thulasi Mylvaganam

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— A method to find approximate solutions to a class of nonzero-sum differential games without solving partial differential equations is introduced. The solution relies upon the use of a dynamic state feedback control law and the solution of algebraic equations. The two-player case is addressed before the N-player case is discussed and a numerical example(More)
— The problem of steering a team of agents from their initial positions to a predefined end-configuration while avoiding collisions is formulated as a differential game. A method for approximating the solution of the differential game is then presented, providing-Nash strategies. It is shown that approximate solutions are sufficient to guarantee that the(More)
The transient stability of a power grid characterized by regional aggregations is studied via robust mean-field games. The model involves a set of coupled Hamilton-Jacobi-Bellman-Isaacs equations and Fokker-Planck-Kolmogorov equations. The former describe the behavior of each single machine, while the latter model the population behavior in aggregate form.(More)
We consider a population of " crowd-averse " dynamic agents controlling their states towards regions of low density. This represents a typical dissensus behavior in opinion dynamics. Assuming a quadratic density distribution, we first introduce a mean-field game formulation of the problem, and then we turn the game into a two-point boundary value problem.(More)