  Among the existing works on enhancing system performance via prescribed
performance functions (PPFs), the decay rates of PPFs need to be predetermined
by the designer, directly affecting the convergence time of the closed-loop
system. However, if only considering accelerating the system convergence by
selecting a big decay rate of the performance function, it may lead to the
severe consequence of closed-loop system failure when considering the prevalent
actuator saturation in practical scenarios. To address this issue, this work
proposes a control scheme that can flexibly self-adjust the convergence rates
of the performance functions (PFs), aiming to achieve faster steady-state
convergence while avoiding the risk of error violation beyond the PFs'
envelopes, which may arise from input saturation and improper decay rate
selection in traditional prescribed performance control (PPC) methods.
Specifically, a performance index function (PIF) is introduced as a reference
criterion, based on which the self-adjusting rates of the PFs are designed for
different cases, exhibiting the following appealing features: 1) It can
eliminate the need to prespecify the initial values of the PFs. In addition, it
can also accommodate arbitrary magnitudes of initial errors while avoiding
excessive initial control efforts. 2) Considering actuator saturation, this
method can not only reduce the decay rates of the PFs when necessary to avoid
violation of the PFs, but also increase the decay rates to accelerate system
convergence when there is remaining control capacity. Finally, several
numerical simulations are conducted to confirm the effectiveness and
superiority of the proposed method.
