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.

In this paper we propose the application of a robust terminal sliding mode control with fast sliding surface to the ship control problem, which consists of leading the ship along the desired course via automatic changes in the rudder blade deflections. In spite of its robustness to system parameter variations and external disturbances, normal terminal sliding mode control (NTSMC) has a limitation of shattering the input rudder angle command particularly when the ship steering mechanism has a big time constant. Through comparative simulations, we show that the proposed controller with fast sliding surface outperforms NTSMC controller in reducing the chattering in the input signal and the initial swing of the rudder angle in the presence of external disturbances and model uncertainties.