A Framework for Prescribed-Time Control Design via Time-Scale Transformation

Abstract

This letter presents a unified framework for the design of prescribed-time controllers under timevarying input and state constraints for normal-form unknown nonlinear systems with uncertain input gain. The proposed approach is based on a time-domain mapping method by which any infinite-time system can be corresponded to a prescribed-time system and vice versa. It is shown that the design of a constrained nonasymptotic prescribed-time controller can be reduced to the asymptotic control design for an associated constrained infinitetime system. Fa à di Bruno's formula and Bell polynomials are used for a constructive representation of the associated infinite-time system. The presented results are not confined to a particular mapping function, which adds to the flexibility of the proposed scheme. It is shown that necessary and sufficient conditions on the uniform (practical) prescribedtime stability and attractivity can be obtained as corollaries of the main result.