| Boundary control is an important part of the modern control theory , which has been emphasized in the control theory field and has been extensively studied and developed . Recently people more and more take notice on the boundary control of Burgers equation KdV equation KdVB equation and KS equation. Firstly, this paper studies a class of nonlinear evolution equation- KS equation . The problem of global exponential stabilization by boundary feedback for the KS equation on the domain (0,1) is considered . The existence and uniqueness of the solution with the help of the Banach fixed point theorem and the theory of operator semigroups are verified .The global exponential stability of KS equation and the global exponential stability and asymptotical stability of macro KS equation with the given boundary feedbacks are proved .Secondly , we studies an other class of nonlinear evolution equation: Mkdv-Burgers equation. We study backstepping boundary control of Mkdv-Burgers equation with actuator dynamics. The existence and uniqueness of the Mkdv-Burgers equation solution are verified. With the help of Lyapunov analysis , we prove that all these signals are sufficiently regular and the close-loop system including the boundary dynamics is globally L~2, H~1 and H~3 stable and well posed.
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