Prescribed‐time control with explicit reference governor for a class of constrained cascaded systems

Abstract

AbstractDifferent from both finite‐time control (where the settling time depends on the initial condition) and fixed‐time control (whose settling time is subject to an upper bound but varies due to uncertainties and nonlinearities), the prescribed‐time control achieves regulation in prescribed finite time, even under uncertain nonlinearities. This article investigates the prescribed‐time regulation problem for a class of cascaded systems with integral form and control input constraints. The establishment of prescribed‐time property consists of the prescribed‐time regulation controller and prescribed‐time explicit reference governor (PT‐ERG), both of which satisfy the prespecified time requirement. For an elegant implementation, the feasibility for the separate design of controller and governor is guaranteed through a developed prescribed‐time cascaded stable theory. For the prescribed‐time controller, the proposed smooth time‐varying controller provides the prescribed‐time convergence based on a residual‐time‐dependent scaling transformation. For the PT‐ERG dealing with the control input constraints, a reference trajectory with a fixed minimum convergence rate provides an elegant compromise between performance and constraints which keeps the constraint satisfied and tracking errors in an invariant set. Both theoretical analysis and numerical simulations verify the effectiveness of the proposed control scheme.