Finite-time system identification, estimation and fault diagnosis
The field of system identification and estimation has developed dramatically in the past few decades. In practical cases, the knowledge about the system and its environment, which is necessary for designing a control strategy, is seldom an available as a priori. For example, the parameters or the states of the system is not measurable or, in another case, the function governing the system is available but so complex that the model might be limited. It is often feasible to acquire the lacking knowledge by experiment on the system, e.g. sampling and signal feedback, to reconstruct the systems. Estimators and observers which are able to estimate the parameters and states of the system based on feedback signals, are designed to adaptively obtain knowledge of the system.
Different estimation and identification approaches are devised for linear systems and non-linear systems. Nevertheless, these approaches are designed in an asymptotic fashion, i.e. the convergence of the estimation is always asymptotic with time and the estimated parameters will reach respect true values in the infinite time span. In order to perform a better control, it is often desirable to commit a non-asymptotic method for system identification and estimation.
This research aims at exploring several paradigms towards novel approaches of finite-time system identification, estimation and fault diagnosis, which is suitable for systems under both noise-free and noise scenario. The main goal of this project is to find out non-asymptotic approaches through which the estimation is able to converge in finite time, showing no restrictions to the use of initial conditions, sampled-data or discrete technique. The project will involve mathematical analysis and the extensive simulation of the proposed algorithms. We expect that the outcome scheme of the project will have a satisfactory performance in terms of the convergence rate, adaptability and noise attenuation.
The following figures show the result of the non-asymptotic estimation of multi-sinusoidal signals based on Volterra kernel function.
Figure 1. Time behaviour of parameter estimation