Event-based global asymmetric constraint control for p-normal systems with unknown control coefficients

Abstract

The global asymmetric predetermined performance control (APPC) problem for p-normal systems with time-varying unknown control coefficients is studied. To address the challenges posed by these unknown time-varying control coefficients, a new unified Nussbaum function is proposed. This function is applicable to all cases where the system power is an odd positive ratio, not just those greater than or equal to one. In order to remove the restriction on the initial values of system, a variable transformation mechanism is designed, enhancing the applicability of the control strategy. Additionally, by incorporating the sign of the error signal into the error transformation mechanism, the constraint boundaries can be switched based on the sign of error. This introduces non-differentiability issues, which are effectively managed through the design of the virtual controller. Furthermore, to optimize energy transmission efficiency, we develop an adaptive event-triggered (AET) mechanism that dynamically adjusts the triggered threshold based on the tracking error. We also provide lemmas to demonstrate that all signals within the system are bounded and that the tracking error remains within the asymmetric boundaries. Finally, two examples are given to verify the effectiveness of the proposed algorithm.