Filter-based Immersion and Invariance Adaptive Control of Nonlinear Systems

This paper proposes a novel filter-based immersion and invariance (I&I) adaptive method for nonlinear systems with additive disturbances and parameter uncertainties. The key innovation of the proposed method is a filter construction that involves the dynamics of the system, based on which the I&I parameter estimator with a sigma modification term is designed. Comparing existing I&I methods, the expression for the novel filter-based I&I estimator is given in terms of total derivatives rather than partial derivatives, which is no longer subject to the integrability condition. In combining the sigma modification term, the proposed parameter estimator also guarantee the uniformly ultimately bounded stability of the parameter estimation error when the system is disturbed, which cannot be achieved by the original I&I method. Furthermore, Lyapunov theory demonstrates that the proposed method can guarantee the stability of the nonlinear systems discussed in this paper. Simulation and experimental results confirm the effectiveness of the proposed method.