Xinen Liu

This paper proposes a bounded H _∞ control scheme with prescribed performance for strictly feedback-controlled nonlinear systems under unknown initial tracking conditions. By introducing a novel algebraic saturation function, the scheme eliminates the reliance on precise initial state information inherent in traditional prescribed performance control, ensuring convergence to a small neighborhood of the equilibrium point even when the initial value of the tracking error is unknown. By combining the barrier Lyapunov function, the backstepping method, and neural networks, a novel dynamic threshold event triggering mechanism is designed, which significantly reduces the control update frequency and works in concert with bounded H _∞ control theory to enhance system robustness. Simulation results demonstrate that in a second-order robotic arm control system, the proposed method converges within 0.5 s regardless of whether the initial value of tracking error lies within the constraint boundary, satisfying the predefined transient performance requirements. Furthermore, the number of trigger events is 43.9% of that for a fixed threshold, 49.1% of that for a relative threshold, and 85.9% of that for a dynamic threshold.

This paper investigates the problem of adaptive event-triggered control with prescribed performance for a class of strictly feedback-controlled nonlinear systems with unknown initial tracking conditions. To overcome the dependence of traditional prescribed performance control on the system’s initial tracking conditions, this paper introduces a novel algebraic saturation function that first maps tracking error initial values of arbitrary magnitude to a bounded interval and then imposes predefined performance constraints on this bounded interval. This strategy ensures that, even when the system’s initial state is unknown, the tracking error still converges to a small neighborhood near the equilibrium point in accordance with the prescribed performance. Furthermore, the strategy employs a fixed-threshold event-triggered mechanism, which effectively reduces the system’s update frequency and alleviates the communication load. Furthermore, by combining a logarithmic barrier Lyapunov function with neural network-based unknown function approximation techniques, this strategy proposes an adaptive prescribed performance event-triggered controller that is independent of the system’s initial state, in other words, independent of the initial tracking conditions. Simulation results validate the effectiveness and superiority of the proposed controller.

This paper proposes a novel active disturbance rejection prescribed performance controller for a class of strictly feedback nonlinear systems under unknown initial tracking conditions. By introducing a novel algebraic saturation function, the initial value of tracking error is transformed into a bounded range, effectively overcoming the limitation of traditional prescribed performance control that requires prior knowledge of the initial value of tracking error. To address the differential explosion issue arising from the backstepping method, this paper employs dynamic surface processing techniques. The integration of active disturbance rejection control with prescribed performance control significantly enhances the robustness of nonlinear systems. The designed controller ensures that closed-loop systems under unknown initial tracking conditions converge to any small neighborhood near the origin within finite time. The system output satisfies the requirements of the prescribed performance function and exhibits excellent suppression capability against external disturbances.