High-Gain Adaptive Control With Switching Derivation Order and Its Application to a Class of Multiagent Systems

This article presents the design and analysis of a switching high-gain adaptive control scheme for a class of nonlinear systems. Adaptation is included in the scheme to estimate the controller gains, using differential equations whose order can switch between 1 (integer order) and some real number (fractional order) in the interval (0, 1), depending on the error level. This switching strategy permits obtaining lower values for controller gains due to fractional orders, resulting in improved robustness, while simultaneously guaranteeing fast convergence of the state to the origin due to the integer order, leading to a better balance between system behavior and control energy efficiency. Applications to multiagent systems are presented to illustrate the potential of the proposed scheme.