Adaptive Practical Prescribed‐Time Control for Stochastic Nonlinear Systems With Input Saturation

ABSTRACT This paper studies the practical prescribed‐time control issue for stochastic nonlinear systems under input saturation and unmeasurable states. Different from existing finite‐ or fixed‐time control schemes that rely on fractional power output feedback, the developed prescribed‐time control only uses regular output feedback. The key to the proposed control scheme is to design an improved time‐varying constraining function such that the original prescribed‐time control issue can be transformed into one with deferred constraints on tracking error, which alleviates the restrictions on initial conditions of the system. Simultaneously, the space between tracking error and constraint boundaries is mapped into a bounded interval, so as to avoid the uncontrollable phenomenon due to the delayed constraints. Utilizing the mean‐value theorem, the design difficulties induced by input saturation are addressed without needing prior knowledge of the bound. Then, a novel observer‐based adaptive prescribed‐time controller is devised so that the tracking error converges to a predefined range in a prescribed time, in which both settling time and accuracy can be set freely regardless of initial values. Finally, the validity of the presented method is proved by two simulation examples.