Kybernetika 50 no. 3, 450-469, 2014

Constraint robust adaptive stabilization for a class of lower triangular systems with unknown control direction

Jianglin Lan, Weijie Sun and Yunjian PengDOI: 10.14736/kyb-2014-3-0450


This paper studies the constrained robust adaptive stabilization problem for a class of lower triangular systems with unknown control direction. A robust adaptive feedback control law for the systems is proposed by incorporating the technique of Barrier Lyapunov Function with Nussbaum gain. Such a controlled system arises from the study of the constrained robust output regulation problem for a class of output feedback systems with the unknown control direction and a nonlinear exosystem. An application of the constrained robust adaptive stabilization design leads to the solution of the constrained robust output regulation problem in the sense that the output tracking error is constrained within the prescribed barrier limit while asymptotically approaching to zero and the closed loop signals are all bounded for all the time. A numerical example is provided to illustrate the performance of the proposed control.


output regulation, nonlinear exosystem, Nussbaum gain, Barrier Lyapunov Function


93E12, 62A10


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