Discrete-Time Extended State Observer-Based Model-Free Adaptive Control Via Local Dynamic Linearization

Linearization is often used for control design of nonlinear systems but what degree of a linearization is sufficient for the controller design is always a question. Furthermore, most of the existing linearization methods aim to develop a completely linear model without retaining any nonlinearity and thus the unmodeled dynamics unavoidably exists due to omitted higher order terms. In this article, a local compact form dynamic linearization (local-CFDL) is developed at first to transform the original nonlinear nonaffine system into an affine structure consisting of both an unknown residual nonlinear time-varying term and a linearly parametric term affine to the control input. A discrete-time extended state observer (DESO) is introduced to estimate the unknown residual nonlinear time-varying term as a new extended state. Then, a local-CFDL-based DESO-model-free adaptive control (MFAC) is proposed where the estimation of DESO is incorporated to compensate for the disturbances and uncertainties. Furthermore, a local partial-form dynamic linearization (local-PFDL) is also presented using multi-lag inputs and partial derivatives. And, a corresponding local-PFDL-based DESO-MFAC is proposed utilizing additional control information to improve control performance. The two proposed methods are both data-driven and do not require any explicit model information. Theoretical analysis shows the robust convergence of the proposed methods in the presence of disturbances. Simulations verify the effectiveness of the proposed method and show that the local-PFDL-based DESO-MFAC outperforms the local-CFDL-based one owing to the use of additional control information.