Desired Dynamics-Based Generalized Inverse Solver for Estimation Problems

An important task for estimators is to solve the inverse. However, as the designs of different estimators for solving the inverse vary widely, it is difficult for engineers to be familiar with all of their properties and to design suitable estimators for different situations. Therefore, we propose a more structurally unified and functionally diverse estimator, called generalized inverse solver (GIS). GIS is inspired by the desired dynamics of control systems and understanding of the generalized inverse. It is similar to a closed-loop system, structurally consisting of nominal models and an error-correction mechanism (ECM). The nominal models can be model-based, semi-model-based, or even model-free, depending on prior knowledge of the system. In addition, we design the ECM of GIS based on desired dynamics parameterization by following a simple and meaningful rule, where states are directly used in the ECM to accelerate the convergence of GIS. A case study considering a rotary flexible link shows that GIS can greatly improve the noise suppression performance with lower loss of dynamic estimation performance, when compared with other common observers at the same design bandwidth. Moreover, the dynamic estimation performances of the three GIS approaches (i.e., model-based, semi-model-based, and model-free) are almost the same under the same parameters. These results demonstrate the strong robustness of GIS (although by means of the uniform design method). Finally, some control cases are studied, including a comparison with DOB and ESO, in order to illustrate their approximate equivalence to GIS.