An I & I Adaptive Redesign Approach for Asymptotic Stability without PE

Abstract

This paper proposes an adaptation redesign approach of the immersion and invariance (I&I) adaptive control to achieve asymptotic stability of the controlled plant and the parameter estimator at the desired equilibrium. The key idea is to employ the technique of generalized parameter estimation-based observer on the parameter estimation error dynamics by applying the indirect I & I adaptive control scheme, yielding a linear regression equation, from which the adaptive law can be redesigned. As a result, it is shown that globally exponential parameter convergence can be guaranteed under an interval excitation (IE) condition, which is much weaker than the conventionally required persistent excitation. Under a stabilizability assumption, an adaptation-redesigned feedback control law can be designed to achieve global asymptotic stability at the desired equilibrium point under the IE condition. The proposed adaptive control approach is applied to a class of parameteric strict-feedback systems without overparameterization, which is needed by the standard I & I adaptive control.