Rodrigo A. González

Rodrigo A. González, Cristian R. Rojas, James S. Welsh

The indirect approach to continuous-time system identification consists in estimating continuous-time models by first determining an appropriate discrete-time model. For a zero-order hold sampling mechanism, this approach usually leads to a transfer function estimate with relative degree 1, independent of the relative degree of the strictly proper real system. In this paper, a refinement of these methods is developed. Inspired by indirect PEM, we propose a method that enforces a fixed relative degree in the continuous-time transfer function estimate, and show that the resulting estimator is consistent and asymptotically efficient. Extensive numerical simulations are put forward to show the performance of this estimator when contrasted with other indirect and direct methods for continuous-time system identification.

Zhihe Zhuang, Rodrigo A. González, Hongfeng Tao et al.

An inherent assumption of perfect tracking in iterative learning control (ILC) is that there exists an ILC input such that the generated output can track the desired trajectory reference. This assumption may fail in practice, which gives rise to desired but untrackable tasks. This paper gives an end-to-end ILC design for repetitive untrackable tasks in closed-loop systems. The reference input is trial-to-trial updated together with the ILC feedforward input based on the measurement data. This two-player behavior of the closed-loop ILC system is investigated from a cooperative game perspective. A sufficient condition for the two-player end-to-end ILC to have a lower cost than the one-player norm optimal ILC (NOILC) is discovered. Finally, a numerical example is given to verify the effectiveness of the developed method.

Enrico Dozzi, Tom Oomen, Rodrigo A. González

Traditional system identification with multisine inputs relies on uniform sampling and periodic excitation to preserve Fourier orthogonality and avoid spectral leakage, limiting its use in scenarios with irregular sampling or nonperiodic inputs. This work investigates continuous-time system identification under nonperiodic multisine excitation and nonuniform sampling. We develop a nonparametric frequency response function estimator suited to such conditions and design irregular sampling schemes that enhance the informativeness of measurements and reduce spectral leakage. The proposed sampling scheme improve the statistical accuracy of system identification in settings where periodic excitation is impractical.

Rodrigo A. González, Cristian R. Rojas

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $χ^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, we present a problem-dependent finite-time bound on the deviation probability of any fixed linear combination of the estimated parameters of the AR$(n)$ process. We discuss extensions and limitations of our approach.