Prescribed-Time Optimal Control with Error Constraints

Tracking control of nonlinear systems (Chen 2023; Zhang et al. 2023), a fundamental control problem, is widely employed in adaptive control due to its ability to achieve real-time reference signal tracking and its strengths in high efficiency and extensive operational range. Despite its focus on steady-state performance, a key limitation of tracking control (Gao et al. 2023) lies in its general neglect of transient performance. Furthermore, quantifying and characterizing such transient requirements remains a considerable challenge. Moreover, poor transient response, exemplified by severe overshoot, poses a serious threat to the structural components of various mechanical systems. Therefore, optimizing transient performance is essential in numerous engineering and control applications (Liu et al. 2024, 2023) to ensure system stability and safety. In response to the aforementioned requirements,significant research efforts (Ren et al. 2023; Su et al. 2023) have been produced, motivated by the development of an effective control strategy known as prescribed performance control (PPC). Initially proposed by Bechlioulis and Rovithakis (2008), the PPC approach employs a judiciously designed error transformation function and a prescribed performance function to meet specific control requirements. Owing to its advantages in high tracking accuracy and superior performance, PPC has prompted significant research interest and proven effective across numerous control fields (Li et al. 2020; Qiu et al. 2019; Dai et al. 2019). However, these results generally ensure asymptotic stability, meaning the system achieves stability only as time approaches infinity.