Finite-time system identification, estimation and fault detection

Abstract

As an increasingly spoken-about topic in modern control engineering, the finite-time identification and estimation problems are dealt with in this thesis. Two kernel-based schemes are proposed that successfully achieve finite-time estimation for parameter and state respectively. Induced by suitably shaped kernels, the Volterra integral operators are used to avoid explicit time-differentiation and thus accomplish the finite-time estimation. Based on the pioneering works, the target of this thesis is to fully develop the kernel-based methodology and devise deadbeat schemes for several kinds of problems - thus enhancing the estimation speed.

Beyond the state estimation, a novel kernel-based estimation framework is designed to address the demand for parameter-state joint estimation. The system parameters and state variables are reconstructed simultaneously which removes the hierarchical correction process in conventional approaches. The proposed scheme is applied to construct a non-asymptotic fault diagnosis architecture for interconnected networks that shortens the fault diagnosis time.

As an important link from estimation to control systems, derivative estimation is dealt with based on Volterra integral operators. The problem is formulated in a state estimation prospect, thus the kernel-based scheme can be effective to obtain non-asymptotic numerical differentiation.

Deploying the kernel-based tools, a novel estimation scheme is designed to address the speed-demanding localization problem. Volterra operators and suitably shaped kernels ensure fast and robust estimation of the target position.

Moreover, the kernel-based methodology is applied to identify exponentially damped sinusoidal (EDS) signals in a comprehensive way. A new kernel is designed to reconstruct the initial conditions that allow identifying more parameters of the EDS than the existing methods.

The robustness of the above algorithms is analyzed by input-to-state stable characterization based on the internally stable realizations. Analysis of the numerical aspects provides hints to algorithm implementations. The effectiveness of the estimators is examined and compared with existing works via simulations.