Improving Transient Performance of Nussbaum Gain-based Controllers with Barrier Liapunov Functions

Haris E. Psillakis


Adaptive control, Nussbaum gains, Nonlinear systems


Nussbaum gains are typically adopted in control schemes to stabilize nonlinear systems with unknown control directions. These controllers guarantee stability but suffer from poor transient performance. In this paper, barrier Lyapunov functions are proposed to improve transient behavior and confine the output response within desired barrier functions. This is made possible through modified Nussbaum parameter update laws that provide fast parameter changes whenever the trajectory approaches the barrier. The results are applied to design a backstepping controller for a class of uncertain strict-feedback nonlinear systems with specific output constraints and unknown control directions. Rigorous arguments prove that the overall scheme is stable and the output is confined within the barrier limits. Simulation results illustrate the effectiveness of the proposed approach.

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