Adaptive Control Solution for a Class of MIMO Uncertain Underactuated Systems with Saturating Inputs

Abstract

This paper addresses the issue of controller design for a
class of multi-input multi-output (MIMO) uncertain underactuated
systems with saturating inputs. A systematic controller framework,
composed of a hierarchically generated control term, meant to
ensure the stabilization of a particular portion of system dynamics
and some dedicated control terms designed to solve the tracking
problem of the remaining system dynamics is presented. Wavelet
neural networks are used as adaptive tuners to approximate the
system uncertainties also to reshape the control terms so as to deal
with the saturation nonlinearity in an antiwindup paradigm.
Gradient based tuning laws are developed for the online tuning of
adjustable parameters of the wavelet network. A Lyapunov based
stability analysis is carried out to ensure the uniformly ultimately
bounded (UUB) stability of the closed loop system. Finally, a
simulation is carried out which supports the theoretical
development.