Prescribed-time prescribed performance control for stochastic nonlinear input-delay systems with arbitrary bounded initial error

The issue of adaptive prescribed-time prescribed performance control (PTPPC) for stochastic nonlinear input-delay systems with arbitrary bounded initial error is discussed in this paper. With the help of prescribed-time prescribed performance function (PTPPF) and a novel switching model-based error transformation function, the proposed method can ensure that the tracking error reaches the specified accuracy within an arbitrary prescribed time, and another significant advantage is that it removes the restriction that the initial error must be within the constrained boundary of existing prescribed performance control (PPC) methods. In addition, an auxiliary system is introduced to manipulate the input delay, which eliminates the limitations of computational complexity and small delays in the Padé approximation method. By combining backstepping with neural network approximation technology, a novel controller is raised, under which the tracking accuracy and convergence time can be pledged, and the whole signals of closed-loop system are bounded in probability. Simulation experiments testify the effectiveness of the control approach.