Prescribed-Time Control of Nonlinear Systems with Linearly Vanishing Multiplicative Measurement Noise

We present new prescribed-time designs for strict-feedback nonlinear systems with multiplicative measurement noise. When the noise is small and linearly vanishing, we first propose a new postulated feedback to solve the prescribed-time mean-square stabilization problem, then redesign the control gains, which is not only optimal with respect to a meaningful cost functional but also globally stabilizes the closed-loop system in the prescribed-time. When the noise is arbitrary large but vanishing faster than linearly, we develop a new control scheme to make the system achieve prescribed-time mean-square stabilization. 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, two simulation examples are given to illustrate the designs.