Adaptive regulation of high-order lower-triangular systems: an adding a power integrator technique

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In this paper, a new adaptive control technique called adding a power integrator is proposed, for a class of linearly parametrized high-order nonlinear systems that are of a lower-triangular structure, but neither feedback linearizable nor affine in the control input. Using the adaptive adding a power integrator technique as a basic design tool, we show how to explicitly construct, in a recursive manner, a smooth adaptive controller that solves the problem of adaptive regulation with global stability. The development of the adding a power integrator technique leads to a significant relaxation on the system nonlinearities such as feedback linearizability and affineness, which are known to be two standard hypotheses made in the existing nonlinear adaptive control schemes.