Nonlinear state and parameter estimation using derivative information: A Lie-Sobolev approach

The implementation of nonlinear control depends on the accuracy of the system model, which, however, is often restricted by parametric and structural uncertainty in the underlying dynamics. In this paper, we propose methods of estimating parameters and states that aim at matching the identified model and the true dynamics not only in the direct output measurements, i.e., in an L²-sense, but also in the higher-order time derivatives of the output signals, i.e., in a Sobolev sense. A Lie-Sobolev gradient descent-based observer-estimator and a Lie-Sobolev moving horizon estimator (MHE) are formulated, and their convergence properties and effects on input–output linearizing control and model predictive control (MPC) respectively are studied. Advantages of Lie-Sobolev state and parameter estimation in nonlinear processes are demonstrated by numerical examples and a reactor with complex dynamics.