Recursive gain controller for strict feedback systems

Abstract

This paper presents a new solution to the ‘explosion of complexity’ problem arising from the repeated derivations of the virtual controls in Standard Backstepping approach. It is inspired by the principle of separation and is based on the use of ‘fictitious’ signals. This solution avoids the use of filters to approximate the virtual controls first derivatives as it is done both in Command Filtered Backstepping and Dynamic Surface Control and ensures global and exponential convergence of the tracking errors to zero within balls of radii that can be made as small as desired. This proposed solution, referred to as Recursive Gain Controller, is applicable to more wider class of strict feedback systems as it requires less conservative assumptions. Simulation results are given to illustrate the effectiveness of the proposed approach. It is shown that the Recursive Gain Controller has better performance than the Standard Backstepping approach.