Gradient-free numerical optimization-based extremum seeking control for multiagent systems

In this article, we develop a model- and gradient-free numerical optimization-based extremum seeking control scheme to solve the problem of formation control and target tracking in multiagent systems. Unlike in conventional gradient-based extremum seeking control, we do not make the strong assumption that the gradient and/or the Hessian of the objective function can be analytically computed from continuously measured system states. Rather, we employ a derivative-free numerical optimization method that directly builds an approximate model of the objective function. After showing the global convergence of the optimization algorithm, we use a regulator to drive the states of the system to the optimizer of the unknown performance function. We demonstrate the performance of the control scheme by simulations where we control three agents that are given a random initial position and are required to maintain an equilateral triangle formation while tracking and localizing a source signal with unknown spatial dynamics.