  In this paper, we will consider a class of continuous-time stochastic control
systems with both unknown nonlinear structure and unknown disturbances, and
investigate the capability of the classical
proportional-integral-derivative(PID) controller in tracking time-varying
reference signals. First, under some suitable conditions on system nonlinear
functions, reference signals, and unknown disturbances, we will show that PID
controllers can be designed to globally stabilize such systems and ensure the
boundedness of the tracking error. Analytic design formulae for PID gain
matrices are also provided, which only involve some prior knowledge of the
partial derivatives of system structural nonlinear functions. Besides, it will
be shown that the steady-state tracking error hinges on three critical factors:
i) the change rate of reference signals and external disturbances; ii) the
intensity of random noises; iii) the selection of PID gains, and can be made
arbitrarily small by choosing PID gains suitably large. Finally, by introducing
a desired transient process which is shaped from the reference signal, we will
present a new PID tuning rule, which can guarantee both nice steady-state and
superior transient control performances.
