Control Through Leadership of Cucker-Smale Model with Time Delay.

Abstract

In this thesis, we study multi-agent models with time delay that describe behaviors or movements of natural living such as bird flocks, fish school and human community ete. In this thesis, we focus on two of well-known multi-agent models that are swarming model and Cucker-Smale model. We investigate the stability of swarming model with time delay under the Morse potential function. We also outline altenative proof of CuckerSmale model with time delay using Lyapunov function. We derive sufficient optimality conditions for the Cucker-Smale model with time delay by adding one controlled leader into the system. We design two stategies of optimal control problems 1) leader agent reaches a target at final time 2) leader agent follows desired trajectory. These two optimal control problems cannot be solved numerically using a conventional gradient descent method. Therefore, in this thesis, we propose a modification of gradient descent method using new technique in unconstraint optimization step. Our new approach allows us to investigate behaviors of agents in the optimal control problem. The simulations are presented to compare behaviors of agents in considered optimal control problems.