A study on the state and parameter cooperative estimation of nonlinear mechanical systems

In this paper, we propose a new state and parameter cooperative estimation design method for the nonlinear mechanical systems that can measure the configurations. The paper is based on a preceding state observer that is intrinsic to nonlinear mechanical systems and considers the case where a design parameter differs by some constant error from the real parameter. In the paper, we first confirmed through theory and simulation that the configurations estimated by the observer differ from those of the real dynamics. Then we confirm that modifying the parameter in a direction reducing the difference between the measured and estimated configurations can sufficiently estimate the real parameter, and we derive a parameter estimation equation based on it. Furthermore, we designed a new cooperative estimation method that estimates the system states and a parameter simultaneously in association with each other by adding this estimation equation to an intrinsic observer designed for mechanical systems. Numerical simulations show that it estimates an exact parameter value while ensuring convergence rates as much as the preceding observer.