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In this paper, the problem of prescribed performance control (PPC) for heterogeneous vehicular platoons with saturation input is investigated. The occurrence of actuator saturation may lead to tracking errors beyond the given performance boundary, which may further cause the performance degradation or even instability. To this end, two modified fixed-time performance functions (MFxTPFs) are designed, based on which a PPC method is proposed to make the performance boundary can be autonomously adjusted when saturation occurs, while reducing the overshoot of the tracking error, and ensuring that the tracking errors converge to the prescribed region in a predefined time. An adaptive fixed-time sliding mode control (FxTSMC) scheme, wherein a fixed-time auxiliary system is introduced to compensate the saturation approximate error, is given based on the PPC method, guaranteeing both fixed-time individual vehicle stability and fixed-time string stability. In such a way, the restriction that convergence time depends on initial conditions is eliminated. Also, the phenomenon of singularity is avoided and a faster convergence rate is obtained. The effectiveness of the scheme is illustrated by numerical simulations.
Gao et al. (Mon,) studied this question.