Robust adaptive prescribed performance control for nonlinear systems with arbitrary initial states

The initial state of nonlinear MIMO strict feedback systems is often unpredictable and random, and existing prescribed performance control (PPC) techniques can only guarantee system output constraints within a fixed initial value performance boundary. In this paper, an adaptive PPC method tailored for nonlinear systems was introduced, enabling the system stable tracking regardless of the arbitrary initial states. To guarantee that the tracking error consistently meets the prescribed performance boundary(PPB) envelope, we introduce a nonlinear mapping between the initial value of the prescribed performance functions(PPFs) and the system tracking errors, resulting in an asymmetric time-varying performance boundary. Building upon this foundation, an adaptive PPC scheme is proposed under the backstepping framework, integrated with a nonlinear disturbance observer (NDO). This method ensures that the tracking error remains within the desired PPB, regardless of external disturbances or system initial states. To prevent ‘complexity explosion’, a dynamic surface control (DSC) technology is employed to filter the virtual control signals of each subsystem. Furthermore, the ultimate uniform boundedness of the closed-loop signal has been demonstrated, and a practical flight vehicles roll control case was introduced to validate the efficacy of the proposed method.