Terminal adaptive control for a class of uncertain underactuated systems

Abstract

This paper presents a backstepping-based terminal adaptive control solution for a class of uncertain underactuated systems with two degrees of freedom. The control scheme developed in this work is based on the finite time stability approach for the terminal convergence of system outputs. Due to the physical restrictions associated with underactuated systems, classical backstepping approach is not applicable to this class of nonlinear systems and hence an approximate version is developed by designing a suitable error surface. Control term is developed in two steps: first, non-singular pseudo-control terms are developed for the dimensions of the configuration space and thereafter a feasible control term is designed to ensure the finite time convergence of error surface. The error surface is designed such that its finite time convergence in turn implies the terminal convergence of configuration variables. To ensure a well-defined control term over the entire state space, control components are embedded with corrective terms. Corrective terms are designed so as to avoid the singularity of the control term and to preserve the desired controller response up to certain extent. A fuzzy logic system is used for the approximation of unknown systems dynamics. Simulation results demonstrate the effectiveness of the control approach.