Adaptive backstepping control for a class of MIMO uncertain underactuated systems with input constraints

Abstract

This paper presents a backstepping methodology-based semi generic adaptive controller scheme for a class of multi-input multi-output (MIMO) uncertain underactuated systems in presence of actuator constraints. To develop a feasible controller scheme for multi-input multi-output underactuated systems, (n – p + 1) dimensions of the n dimensional configuration space are stabilised by using one dimension of the input space. This control term is developed by applying hierarchical methodology whereas as remaining p – 1 input dimensions are assigned as dedicated control terms to solve the control problem of remaining dimensions of the configuration space. Backstepping technique is used to develop the classical control terms whereas wavelet networks are used to approximate the uncertain dynamics as well as the nonlinear effects of actuator saturation. The proposed scheme, thus, relaxes the constraint of completely and accurately known system dynamics as well as the requirement of measuring the clipped portion of the control effort. A robust control term is used to attenuate the approximation error to a prescribed level. Uniform ultimate boundedness (UUB) stability of the closed loop system is verified in the Lyapunov sense. Simulation results illustrate the effectiveness of theoretical development.