Robust Adaptive Backstepping Control with Improved Parametric Convergence

Abstract The paper addresses the problem of performance improvement of robust adaptive backstepping control for a class of disturbed nonlinear systems presentable in parametric-strict-feedback form. The proposed solution is based on backstepping procedure reducing to actual control and an error model. Later motivates design of robust σ-modification of adaptation algorithm with improved parameters tuning of the actual control. Tuning improvement is achieved by applying Kreisselmeier’s scheme of adaptation algorithm with memory regressor extension (MRE). MRE is provided by involving a linear filter into adaptation algorithm. On the one hand this filter records the regressor over past period of time (with some forgetting) and, as a result, accelerates the tuning of control. On the other hand the filter allows to generate the higher order time derivatives of adjustable parameters used for calculation of virtual and actual controls. The actual control obtained is robust with respect to disturbance, is free from overparameterization, does not contain tuning functions and completely compensates for nonlinear dynamics together with uncertainties of the plant. The efficiency of proposed solution is demonstrated via simulation.