Event-triggered sampling-based singularity-free fixed-time control for nonlinear systems subject to input saturation and unknown control directions

In this paper, the issue of event-triggered fixed-time tracking control is investigated for a class of nonlinear systems subject to unknown control directions (UCDs) and asymmetric input saturation. Firstly, to cope with the design challenge imposed by nondifferential saturation nonlinearity in the system, the asymmetric saturation function is approached by introducing a smooth nonlinear function with respect to the control input signal. Secondly, a variable separation technique lemma is developed to remove the restrictive growth conditions that must be fulfilled by the nonlinear functions, and a new practically fixed-time stability lemma with more accurate upper-bound estimate of the settling time is put forward by means of the Beta function. Then, a technical lemma regarding a class of type-B Nussbaum functions (NFs) with unique properties is introduced, which avoids specific NFs-based complex stability analysis. Moreover, in compensation for the sampling error incurred by the event-triggered mechanism under UCDs, an adaptive law is skillfully constructed to co-design the fixed-time control law and the event-triggered mechanism. The results show that the controlled system is practically fixed-time stable (PFxTS), the tracking error can converge to a small neighborhood of the origin in a fixed time, and the saturation constraint is satisfied while reducing the communication burden. Finally, the effectiveness of the practically fixed-time stability criterion and control method developed in this study are verified by two simulation examples.