Prescribed-Time Exact Tracking for a Class of Nonlinear Systems

Prescribed time is an appealing but ambitious performance specification for many time-critical applications. Within the prescribed time, accurately reaching a moving target naturally becomes a more demanding goal. In this letter, we address prescribed-time exact tracking for nonlinear systems. The tracking only works within the prescribed time, differently from the conventional tracking. First, a temporal transformation is performed on the original system, to convert prescribed-time exact tracking in finite horizon to asymptotic tracking in a new infinite horizon. Then, a new vector of augmented reference signals is worked out, with the goal of forcing the difference between such a vector and the state vector of the original system to converge to zero with a desired speed. By scaling the difference to reduce convergence to boundedness, a new weakly time-varying system is obtained which is instrumental for the design of the control law for the original system. In addition, two refined pseudo functions are integrated into Lyapunov functions, thus avoiding the use of completing the square in the design of the control law. The main result is illustrated by a simulation example, after an extension to a class of systems admitting input-matched uncertainties.