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In solving the problem of asymptotic tracking and disturbance rejection, ithas been long always assumed that the reference to be tracked and thedisturbance to be rejected must be generated by an exosystem such as a finitedimensional exosystem with pure imaginary eigenvalues. The objective of thispaper is to solve such a tracking problem for the unstable Burgers' equationwithout this assumption. Our treatment of this problem is straightforward.Using the method of variable transform, the tracking problem is split into twoseparate problems: a simple Neumann boundary stabilization problem and adynamical Neumann boundary regulator problem. Unlike the existing literaturewhere the regulator problem is always kept independent, the stabilizationproblem here is simplified to an independent linear diffusion equation bymoving the instability term and the nonlinear term to the dynamical regulatorproblem, whereas the dynamical regulator problem does depend on thestabilization problem.  Thus we can first easily handle the stabilization problem and then solve thedynamical regulator problem by using the fundamental theory of partialdifferential equations. The boundary feedforward controller is explicitlyconstructed by using the reference, the disturbance and the solution of thestabilization problem while the boundary feedback controller is easily designedfor the linear diffusion equation without using a complex method such as thebackstepping method. It is proved that, under the designed feedback andfeedforward controllers, the tracking error converges to zero exponentially.This theoretical result is confirmed by a numerical example.

The exponential tracking and disturbance rejection for the unstable Burgers' equation with general references and disturbances