Continuous-time System Identification
Refined Instrumental Variables and Sampling Assumptions
Time: Thu 2022-05-05 14.00
Location: F3, Lindstedtsvägen 26 & 28, Stockholm
Subject area: Electrical Engineering
Doctoral student: Rodrigo A. González , Reglerteknik
Opponent: Professor Marion Gilson-Bagrel,
Supervisor: Professor Cristian R. Rojas, Reglerteknik
Continuous-time system identification deals with the problem of building continuous-time models of dynamical systems from sampled input and output data. There are two main approaches in this field: indirect and direct. In the indirect approach, a suitable discrete-time model is first determined, and then it is transformed into continuous-time. On the other hand, the direct approach obtains a continuous-time model from the sampled data without an intermediate discrete-time model. In both approaches there exists a dichotomy between discrete-time data and continuous-time models, which can induce robustness issues and complications in the theoretical analysis of identification methods. These difficulties are addressed in this thesis.
First, we consider the indirect approach to continuous-time system identification. For a zero-order hold sampling mechanism, this approach usually leads to an excess of model zeros when the true system has a relative degree greater than one. Inspired by the indirect prediction error method, we propose an indirect-approach estimator that guarantees stability in the model and enforces the desired number of poles and zeros in the continuous-time transfer function estimate.
The second part of this thesis concerns the asymptotic properties and extensions of direct continuous-time identification methods. We provide a comprehensive statistical analysis of the simplified refined instrumental variable method for continuous-time systems (SRIVC), which is a widely-used direct identification algorithm that applies an adaptive prefiltering to the sampled input and output data. We prove that the SRIVC estimator is generically consistent and asymptotically efficient under some mild conditions when taking into account the intersample behavior of the signals in the analysis, and we give conditions under which these statistical properties are not achieved. An extended analysis is provided for when the model is over-parameterized. Later, we propose and analyze the statistical properties of an extension of the SRIVC estimator that can deal with input signals that cannot be interpolated exactly via hold reconstructions. The standard SRIVC estimator and its extension for arbitrary inputs, together with other refined instrumental variable methods, are also investigated in closed-loop settings and are further enhanced to deal with the identification of unstable systems.
The last part of this thesis focuses on the analysis and identification of continuous-time systems subject to band-limited input excitations. The non-causal behavior of the band-limited discrete-time equivalent system is studied in detail, and the findings are later used for designing novel non-parametric and parametric identification methods for when the input is band-limited. Special treatment is given to identification with continuous-time multisine inputs. For that case, we investigate fundamental relations between prediction error methods, optimal refined instrumental variables, and interpolation and approximation of frequency response function estimates.
All of the methods and theoretical results are accompanied by extensive simulation tests that verify our findings.