On Scheduled Space-Time Convergence: Sliding Mode Control Through the Scheduled Time Function

Previous researches on sliding mode control focus on the time or space domain, regardless of the combination of the two domains. This paper presents a new scheduled space-time barrier sliding mode control (SSTBSMC) scheme for disturbed systems. The SSTBSMC scheme is established based on the designed scheduled time function (STF). One uniqueness of the proposed scheme lies in that it ensures the scheduled space-time convergence, i.e., the sliding variable can converge into a scheduled space within a scheduled time. Besides, the scheduled space and time can be predetermined regardless of the initial condition and unified uncertainty. Moreover, the SSTBSMC scheme applies a more reasonable state-preserving upper bound assumption, removing the conservative assumption of constant upper bound on the unified uncertainty. In addition, the proposed scheme mitigates the overestimation of the control gain to attenuate chattering effect. The stability of the closed-loop disturbed system is verified by theoretical analysis. The effectiveness of the proposed scheme is confirmed through a series of simulations and experimental investigations.