  In solving the problem of asymptotic tracking and disturbance rejection, it
has been long always assumed that the reference to be tracked and the
disturbance to be rejected must be generated by an exosystem such as a finite
dimensional exosystem with pure imaginary eigenvalues. The objective of this
paper is to solve such a tracking problem for the unstable Burgers' equation
without this assumption. Our treatment of this problem is straightforward.
Using the method of variable transform, the tracking problem is split into two
separate problems: a simple Neumann boundary stabilization problem and a
dynamical Neumann boundary regulator problem. Unlike the existing literature
where the regulator problem is always kept independent, the stabilization
problem here is simplified to an independent linear diffusion equation by
moving the instability term and the nonlinear term to the dynamical regulator
problem, whereas the dynamical regulator problem does depend on the
stabilization problem.
  Thus we can first easily handle the stabilization problem and then solve the
dynamical regulator problem by using the fundamental theory of partial
differential equations. The boundary feedforward controller is explicitly
constructed by using the reference, the disturbance and the solution of the
stabilization problem while the boundary feedback controller is easily designed
for the linear diffusion equation without using a complex method such as the
backstepping method. It is proved that, under the designed feedback and
feedforward controllers, the tracking error converges to zero exponentially.
This theoretical result is confirmed by a numerical example.
