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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.

Recursive gain controller for strict feedback systems