Robust Time-Varying Output Formation Control for Swarm Systems with Nonlinear Uncertainties

Abstract

Time-varying output formation control problems for high-order time-invariant swarm systems are studied with nonlinear uncertainties and directed network topology in this paper. A robust controller which consists of a nominal controller and a robust compensator is applied to achieve formation control. The nominal controller based on the output feedback is designed to achieve desired time-varying formation properties for the nominal system. And the robust compensator based on the robust signal compensator technology is constructed to restrain nonlinear uncertainties. The time-varying formation problem is transformed into the stability problem. And the formation errors can be arbitrarily small with expected convergence rate. Numerical examples are provided to illustrate the effectiveness of the proposed strategy.

A Proposed System for Multi-UAVs in Remote Sensing Operations

“…Then, rewriting the controller input as standing for nominal and robust parts. Solving for the Laplacian transformation for a time-varying output model, as mentioned in [ 6 , 7 ], gives: where L and are the Laplacian transformation and transform inverse, respectively; the term is a standard remarking for Laplacian transformation matrix; and is the Laplacian form of , in which both and a are positive constants equal to or bigger than the transformation matrix power. Following the solution performed in previous works [ 22 , 23 , 24 ], controller update parameters that update the system’s error ( ) matrix could be defined as .…”

“…Their results affirm that the sliding mode controller behaves fantastically, independent of the potential functions and the tracking term aims for the controller to follow the target. In [ 6 ], the authors performed a numerical study of robust algorithms for a time-varying swarm with nonlinear external errors. To solve the instabilities, they first expanded the observation matrix for a consensus problem, and the “n” employing a robust compensator and a nominal controller, the system converged to stability with small errors; however, their solution does not support a dynamic switch formation, and no practical work was performed.…”