Multivariable Finite-Time Composite Neural Control via Prescribed Performance for Error Norm

Abstract

This work investigates finite-time tracking control for a multi-input–multi-output plant with multisource uncertainties. A multivariable finite-time prescribed performance control scheme is proposed, where the norm of the tracking error vector is constrained with a prescribed bound. Due to the positiveness of the norm of the error vector, a novel error transformation is given to transform the “constrained” problem into an equivalent “unconstrained” problem. Meanwhile, the composite neural adaptive law is established to attenuate the effect of multisource uncertainties. The parametric perturbations are counteracted by neural adaptive terms. Time-varying uncertain control gains and external disturbances in the multivariable systems are compensated by adaptively estimating their bounds and applying the Lyapunov control design. To tackle the practical tracking problem, the aforementioned method is integrated into a dynamic-surface-based backstepping framework. Additionally, the practical quaternion-based attitude tracking problem is addressed, in which a quaternion-based form of error-norm constraint is constructed to express the generality and scalability of our proposed.