Prescribed-time control of the nonholonomic integrator with input-delay by periodic delayed feedback

In this paper, the problem of prescribed-time control of the nonholonomic integrator with input delays is investigated. First, the relationship between the prescribed time T and the solvability of the prescribed time control problem is explored. Next, for systems with known input delays, two novel control strategies based on periodic delayed feedback (PDF) are proposed. Both methods avoid distributed delays and guarantee that the system state converges to the origin from any initial condition precisely at the prescribed time. Furthermore, for systems with unknown input delays, a novel PDF is proposed, which also does not involve any distributed delays, and effectively addresses the prescribed-time control problem for such systems. Finally, the efficiency of the proposed approaches is validated through simulation results.