Adaptive prescribed performance control for uncertain nonlinear HOFA systems with time delay

This paper focuses on the adaptive prescribed performance control problem for high-order fully actuated (HOFA) system with state time-delay. Different from the existing results, an adaptive prescribed performance control method is proposed to ensure that the HOFA system with state time-delay can achieve semi-globally practical finite-time stability. Moreover, it is worth mentioning that the control method ensures both the steady-state performance of the system and the dynamic performance of the system within a finite time. In addition, the settling time of this paper is independent of design parameters and initial conditions. Hence, it can be set to any value. Finally, a practical example of a thermoacoustic unstable system in the Rijke tube is used to verify the effectiveness and feasibility of the scheme.