Adaptive constraint-following control for uncertain nonlinear mechanical systems with measurement error

This study proposes an adaptive constraint-following control scheme for an uncertain nonlinear mechanical system. The concerned system is required to follow a class of (holonomic and nonholonomic) equality constraints. Uncertainties (possibly fast time-varying) exist in the dynamics equation and the equality constraints. Meanwhile, the system contains state measurement errors. Both the uncertainties and measurement errors are assumed to be bounded. Based on Udwadia-Kalapa approach and a saturation type adaptive law, an adaptive control scheme is proposed to drive the system to follow the prescribed constraints approximately. Through Lyapunov minimax analysis, it is proved that the resulting control guarantees the uniform boundedness and uniform ultimate boundedness of the closed-loop constrained mechanical system despite the presence of the uncertainties and the measurement errors. Numerical simulations of the vehicle lateral motion control are presented. The results validate the effectiveness of the proposed methodology.

Automated summary

This study introduces an adaptive constraint-following control scheme for an uncertain nonlinear mechanical system, which aims to approximately follow prescribed constraints using adaptive control. Through Lyapunov minimax analysis, it is demonstrated that the resulting control ensures the uniform boundedness and uniform ultimate boundedness of the system, despite uncertainties and measurement errors.