Improved Adaptive Compensation of Unmatched Multisinusoidal Disturbances in Uncertain Nonlinear Plants

The paper addresses the problem of adaptive compensation of unmatched disturbance in nonlinear parametrically uncertain systems presented in parametric-strict-feedback form. The disturbance is modeled as a vector of unmeasurable multisinusoidal functions with a priori unknown amplitudes, frequencies and phases. The proposed solution is based on observer-based disturbance parameterization, modular back-stepping design and special adaptation algorithm (identifier) with memory regressor extension. New adaptation algorithm proposed has two important properties. First, it has improved parametric convergence achieved by regressor recording over past period of time. Recording is provided by involving a linear SISO filter into the structure of the algorithm. Second, inclusion of this filter allows us to calculate the high-order time derivatives of the adjustable parameters used directly in virtual and actual control laws.