Adaptive Neural Network Unified Control for General MIMO Underactuated Mechatronic Systems With Disturbances via Modified Normal Forms

The control problem of underactuated mechatronic systems is one of the key representatives of complex nonlinear dynamical systems. Starting from the dynamical structures of underactuated systems is usually one of the most direct and effective ways to design controllers. However, controllers developed for specific dynamic models are often difficult to be directly generalized to other underactuated systems. Moreover, due to the lack of control inputs, designing robust controllers for unmatched disturbances (acting on unactuated states) remains a challenging problem. Therefore, based on the Euler-Lagrange dynamics of multi-input-multi-output (MIMO) underactuated systems, this paper gives four coordinate transformations according to different configurations of the inertia matrix, which <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">extends</i> the Olfati transformation to some extent and finally <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unifies</i> underactuated systems into normal forms. A sliding manifold and an adaptive neural network sliding mode controller are developed with the derived normal forms, which improves transient performance and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">avoids</i> the chattering problem in traditional sliding mode controllers by combining an estimation error-driven adaptive law, a high-order sliding-mode differentiator, and the super-twisting algorithm. More importantly, the stability is guaranteed by Lyapunov techniques even in the presence of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">both</i> persistent matched disturbances and asymptotically vanishing unmatched disturbances. Furthermore, the proposed control strategy is applied to overhead cranes and tower cranes, whose superior control performance is verified by hardware experiments.