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Barrier Lyapunov Function and constraint adaptive output regulation problem for a class of nonlinear systems

In this paper, we present an output feedback control design of constraint adaptive output regulation problem for a class of nonlinear systems with unknown exosystems. We first transform this problem into a regulation problem with output constraint by the employment of adaptive internal model principle. Then, we use the Barrier Lyapunov Function technique to solve such a regulation problem. Finally, we prove that the constraint adaptive output regulation without constraint violation is achieved while all the signals of the closed loop system are bounded and the estimated parameter for the unknown exosystems converges to its real value. A numeral example is provided to illustrate the performance of the proposed control.