Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms

Adaptive robust control (ARC) of MIMO nonlinear systems transformable to tw o semi-strict feedback forms are considered. The forms can have both parame tric uncertainties and uncertain nonlinearities such as external disturbanc es. In addition, the forms allow coupling and appearance of parametric unce rtainties in the input matrix of each layer. Furthermore, the usual assumpt ion on the linear parametrization of the state equations is relaxed to the extent that the forms are applicable to the control of some mechanical syst ems. To deal with the complexity and difficulties caused by the coupling an d the appearance of parametric uncertainties in the input matrices, an ARC Lyapunov function-an extension of the adaptive control Lyapunov function (a clf)-is used to formalize the viewpoint and the achievable results of the r ecently proposed ARC approach. Two backstepping designs via ARC Lyapunov fu nctions are presented. The results are then used to construct specific ARC control laws for MIMO nonlinear systems in the semi-strict-feedback forms. By using trajectory initialization, the resulting ARC law achieves a guaran teed output tracking transient performance and final tracking accuracy in g eneral. while keeping all physical states and control inputs bounded. In ad dition, the control law achieves asymptotic output tracking in the presence of parametric uncertainties without using a discontinuous or infinite-gain feedback term. (C) 2001 Elsevier Science Ltd. All rights reserved.