Mean-Nonovershooting Control of Stochastic Nonlinear Systems

We present mean-nonovershooting tracking control designs for stochastic strict-feedback nonlinear systems. Compared with the existing stochastic nonlinear tracking designs, the advantage of our design is that arbitrary reference trajectories can be tracked "from below." We first consider a special class of stochastic nonlinear systems where the diffusion terms satisfy the linear growth condition and the drift terms are in special triangular forms. A new controller is designed to guarantee that the mean of the system output can asymptotically track a given trajectory without overshooting while keeping all of the states mean-square bounded. In this case, an appealing feature in our design is that strict mean-nonovershooting tracking is achieved while the existing results on nonlinear systems with deterministic disturbance can only achieve practical nonovershooting tracking. Then, we design a new controller for general stochastic strict-feedback nonlinear systems to ensure that the mean of overshoot can be tuned to be arbitrarily small while all the states of the closed-loop system remain bounded in probability. In this case, the new design ingredient is that our control gains are independent of the initial conditions of system states, and the initial conditions of derivatives of the reference trajectory. This is in contrast with the existing results on corresponding deterministic systems whose control gains heavily rely on these initial conditions. Finally, two simulation examples are given to illustrate the stochastic nonlinear nonovershooting tracking designs.