Prescribed-Time Nonlinear Control with Multiplicative Noise

We study the prescribed-time design problem for strict-feedback nonlinear systems with multiplicative measurement noise. With the assumption that the noise is small and linearly vanishing, we propose a new postulated feedback to solve the prescribed-time mean-square stabilization problem. In contrast to the existing stochastic prescribed-time designs, the merit of our design is that it can effectively deal with multiplicative measurement noise. The existence of measurement noise makes the design rather challenging since the resulting process noise intensity, in closed loop, depends on the feedback gains and even goes to infinity. Finally, a simulation example is given to illustrate the design.