Dynamic uncertainty propagation analysis framework for nonlinear control problem based on manifold learning and optimal polynomial method and its application on active suspension system

Abstract

A novel uncertainty propagation method based on manifold learning and optimal polynomial model is proposed to quantify and analyze the dynamic uncertainties of the nonlinear feedback control system. To deal with the multiple objectives and constraints of the nonlinear control problem, a barrier Lyapunov-function-based nonlinear filtered backstepping controller is developed and applied to active suspension system to obtain superior ride comfort performance under limited structural constraints. Considering the errors in the production, manufacturing, and assembly, the probability density function is employed to quantify the structural parameter uncertainties in the nonlinear control system. Moreover, to reveal the dynamic propagation mechanism of uncertainties in the system with nonlinearity, the manifold learning method is proposed to reduce the dimensionality of the dynamic system to avoid the complexity of uncertainty propagation. Simultaneously, data-driven optimal polynomial model is utilized to accurately approximate the internal mechanism of nonlinear filtered backstepping control system. Based on that, the response uncertainties of the nonlinear control system are accurately and quickly quantified through dynamic moment information and uncertain fluctuation space. Finally, an active suspension system with nonlinearities and uncertainties is developed to verify the effectiveness of the controller with improved ride comfort and better handling safety and the superiority of the framework in terms of efficiency and accuracy of the dynamic uncertainty propagation analysis for nonlinear control problem.