Advancements in Linear System Identification: A Study of Modern Techniques
Parth Joshi
Maharaja Sayajirao University of Baroda, Vadodara
Bhavna Shah
Dhirubhai Ambani Institute of Information and Communication Technology (DA-IICT), Gandhinagar
Keywords: Linear System Identification, Subspace-Based Methods, Frequency-Domain Methods, Regularization Techniques, Machine Learning Approaches, Bayesian Methods, Computational Resources
Abstract
Linear System Identification (LSI) is a pivotal procedure in control engineering, aiming to construct an accurate model of a system from observed input-output data. Contemporary techniques for LSI have incorporated advancements in computational power and machine learning algorithms. Subspace-Based Methods represent an evolution from classical identification methods such as ARX or ARMAX models. These methods analyze the system's input-output data by identifying its state-space representation, offering the ability to manage multiple-input and multiple-output systems without an excessive computational load. Noteworthy methods include N4SID (Numerical algorithms for state-space system IDentification) and MOESP (Multivariable Output Error State Space). Frequency-Domain Methods involve the conversion of time-domain input-output data into frequency-domain data, facilitating an understanding of the system's dynamic behavior. These methods are particularly beneficial when the system exhibits non-minimum phase behavior or when noise affects the measurements. Modern methods include spectral analysis and the use of frequency response functions. Regularization Techniques are designed to address overfitting and underfitting issues that frequently occur during the system identification process. By incorporating a regularization term into the loss function, it is feasible to control the model's complexity, thereby achieving a balance between the model's fit and its complexity. Examples include Ridge Regression and Lasso Regression. Machine Learning Approaches have been applied to system identification due to advancements in computational power and the emergence of machine learning. Techniques such as Support Vector Machines (SVM), Artificial Neural Networks (ANN), and Deep Learning can manage complex nonlinear systems and provide robust identification of linear systems, albeit requiring substantial data for training. Bayesian Methods offer a probabilistic framework for system identification, integrating uncertainty in both the model and measurements. These methods can manage the system's nonlinearity and provide uncertainty estimates for the model parameters. Examples include Gaussian Processes and Markov Chain Monte Carlo. The choice of an appropriate method for a specific system identification task necessitates a thorough understanding of the system's dynamics and the characteristics of these methods, considering the nature of the system under study, the availability and quality of data, and the computational resources available.
