A New Robust Adaptive Control for Uncertain Nonlinear Systems

A novel adaptive control with $\sigma$-modification on the basis of immersion and invariance (I&I) theory is proposed for a class of uncertain nonlinear systems in the paper. The idea is inspired by two difficulties of conventional adaptive control encountered in engineering applications. One is the difficulty of adaptive law design coming from the construction of Lyapunov function. The other is the unpredictable unstable phenomena of adaption under non-parametric uncertainties. The proposed method can be applied to deal with these problems, which is a beneficial attempt to facilitate the practical implication of adaptive control. It turns out to be a structured design method without requiring a Lyapunov function and robust to non-parametric uncertainties. Moreover, constrained command filter backstepping is adopted to meet the amplitude and rate constraints on the states and actuators. The effectiveness of the proposed control method is illustrated by a numerical simulation.

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