Adaptive unit vector control of multivariable systems using monitoring functions

Abstract

SummaryAn adaptive sliding‐mode unit vector control approach based on monitoring functions to deal with disturbances of unknown bounds is proposed. An uncertain multivariable linear system is considered with a quite general class of nonsmooth disturbances. Global stabilization/tracking is demonstrated using either state or output feedback. The proposed adaptation method makes the control gain less conservative, becoming large enough when the disturbance grows and becoming smaller when it decreases, leading to reduced chattering effects. In contrast to previous methods, the new switching scheme is able to guarantee a prespecified transient time, maximum overshoot, and steady‐state error for multivariable uncertain plants. The proposed technique is applied to the trajectory tracking control of a surface vessel subjected to ocean currents, wind, and waves. Simulations are presented to show the performance of the new adaptation scheme in this adverse scenario of possibly growing, temporarily large, or vanishing exogenous disturbances.