Adaptive Fuzzy Control of Underactuated Switched Systems With Disturbance Observation and Actuated/Unactuated Motion Constraints

Abstract

With the increasingly wide applications of underactuated systems, the necessary switching actions in complex multiple-mode tasks may induce overlarge errors, chattering, or even instability. In different working scenarios, there usually exist different plant parameters, dynamic characteristics, and external disturbances, which may further degrade operation performance. To this end, this article designs a learning-based adaptive fuzzy switching controller to compensate for uncertainties online in various modes and realize exponential convergence of actuated states. During multiple-mode operations, both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">actuated</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> constraints are guaranteed by constructing integral constraint terms as time-variant gains, which introduce control energy in advance, to drive all state variables to converge to their desired values, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">rather than</i> direct braking force that may destroy the transient performance of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unactuated</i> states (e.g., residual payload swing induced by rapid braking in cranes). Further, when underactuated systems suffer from matched/mismatched disturbances, a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">model-independent</i> disturbance observer is elaborately designed to improve anti-disturbance performance, ensure the boundedness of closed-loop signals, and restrict all variables <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in every mode</i> . Based on Lyapunov methods and the concept of average dwell time, the closed-loop stability of entire switched systems is theoretically analyzed and proven; then, the effectiveness of the proposed switching controllers is verified by hardware experiments.