en.Wedoany.com Reported - Researchers Kong Y Z, Wu X Q, Mao B, et al. have achieved global performance-guaranteed finite-time exact tracking control for strict-feedback nonlinear systems with actuator faults using a sliding mode control method, and have solved the challenge of unknown virtual control direction.

Trajectory tracking is a fundamental problem in the control field. Traditional methods for handling strict-feedback nonlinear systems can typically only guarantee asymptotic convergence or uniform boundedness of the tracking error, making it difficult to meet the demands of high-precision, fast control. Finite-time exact tracking control offers advantages such as fast convergence speed, high control accuracy, and strong robustness, showing great potential for practical engineering applications. Actuator faults are a key factor affecting system reliability. Although existing fault-tolerant control methods can handle uncertain nonlinear systems with actuator faults, they generally lack strict guarantees on transient performance. Prescribed performance control constrains system transient and steady-state performance by constructing funnel-type performance functions, but its integration with fault-tolerant control still faces challenges. Within the framework of strict-feedback nonlinear systems, designing a control strategy that simultaneously achieves finite-time exact tracking, guarantees prescribed performance indices, and possesses fault tolerance still requires overcoming the limitations of traditional methods on initial conditions, effectively handling uncertainties in the system, and ensuring the boundedness of all closed-loop signals while achieving exact tracking within a finite time.

To address these issues, this study, for the first time, achieves global performance-guaranteed finite-time exact tracking control for strict-feedback nonlinear systems with actuator faults using a sliding mode control method, and successfully solves the key problem of unknown virtual control direction. The main contributions include: achieving finite-time exact tracking, whereas existing research typically only achieves asymptotic tracking or bounded tracking control; handling the problem of unknown virtual control direction, expanding the applicability of the control scheme; and proposing a tan-type error transformation method and a Lyapunov-like function, which eliminate the inherent initial condition constraints and error surface effects of traditional control methods, while ensuring the global boundedness of all closed-loop signals.

The study validates the effectiveness and superiority of the method through numerical simulations. In Experiment 1, using a disturbance-free pendulum system, compared with a method that can only guarantee uniformly bounded errors, the results show that the proposed controller can achieve finite-time convergence of the tracking error to zero while maintaining prescribed performance, allowing the output to track the reference signal more quickly.

In Experiment 2, using a pendulum system subject to external disturbances, the proposed controller is compared with an existing robust controller. The results show that the baseline method can only achieve uniform boundedness of the tracking error, whereas the proposed controller can drive the tracking error to zero within a finite time while maintaining prescribed performance constraints, demonstrating superior transient performance and faster convergence speed.

The simulation results confirm that the proposed controller can achieve finite-time exact tracking of the reference signal in the presence of actuator faults, component faults, and external disturbances, with convergence speed and overshoot superior to existing methods. Researchers Kong Y Z, Wu X Q, Mao B, et al. published a paper in Science China Information Sciences (Chinese journal name: 《中国科学：信息科学》), titled "Performance-guaranteed finite-time exact-tracking of strict-feedback systems with actuator faults".