Localized adaptive bounds for uncertain MIMO nonlinear system

A robust controller with localized adaptive bounds is proposed for a class of uncertain multiple-input-multiple-output nonlinear systems. Command filtered backstepping (CFBS) is used to design virtual control laws recursively. With spectral radius introduced into the control law, the assumption on nonsingularity of control coefficient matrix estimation is eliminated. Localized modification can overcome the parameter drift of standard σ-modification when states change and tracking errors are small. Adaptive bounding control is employed to compensate inherent approximation errors and external disturbances. It is proved that the proposed method can guarantee the boundedness of all signals in the closed-loop system theoretically. Simulation example demonstrates the effectiveness of the proposed method.