Koopman System Approximation Based Optimal Control of Multiple Robots -- Part II: Simulations and Evaluations

Understand

This report presents the results of a simulation study of the linear model and bilinear model approximations of the Koopman system model of the nonlinear utility functions in optimal control of a 3-robot system.

• In such a control problem, the nonlinear utility functions are maximized to achieve the control objective of moving the robots to their target positions and avoiding collisions.
• With the linear and bilinear model approximations of the utility functions, the optimal control problem is solved, based on the approximate model state variables rather than the original nonlinear utility functions.
• This transforms the original nonlinear game theory problem to a linear optimization problem.