Advancements in Dynamic System Identification Methods

Markus Lindgren^*
*Correspondence: Markus Lindgren, Department of Computer Science,, Lund University, Lund 221 00, Sweden, Sweden, Email:

Introduction

System identification is a foundational discipline concerned with building mathematical models of dynamic systems from observed data. The field consistently pushes boundaries to address increasingly complex system behaviors, environmental noise, and operational constraints. Recent advancements span a wide array of techniques and applications, reflecting the diverse challenges encountered in engineering and scientific domains. One significant area of progress involves the refinement of methods for identifying state-space models. Researchers are exploring Kalman Filter-based prediction error techniques to achieve more precise model parameters [1].

What this really means is they're using a common estimation technique, the Kalman filter, to refine predictions and improve the accuracy of linear system models derived from data. This approach is particularly adept at handling measurement noise and unmeasured disturbances, which are ubiquitous in real-world applications, thereby leading to more reliable models. Here's the thing about nonlinear system identification: it's notoriously difficult. However, significant strides are being made, particularly with NARMAX (Nonlinear AutoRegressive Moving Average with eXogenous inputs) models [2].

This work provides a comprehensive overview of recent developments in structure detection, parameter estimation, and validation specifically tailored for these complex models. Understanding systems that do not behave linearly is crucial for many advanced control and prediction tasks. For linear systems, subspace identification methods are quite powerful, but their effectiveness can be hampered by correlated noise [3].

This article tackles exactly that, presenting new techniques for subspace identification of stochastic linear systems even when the noise isn't conveniently independent. This is important because real-world systems often exhibit complex noise characteristics that standard methods struggle to accurately model. Moving beyond purely linear models, Linear Parameter-Varying (LPV) systems allow parameters to change with operating conditions, offering a more nuanced representation of dynamic behavior. New data-driven identification methods are being introduced for these systems, especially in scenarios where the "scheduling variables" that dictate parameter changes are not directly known [4].

Being able to learn these complex relationships directly from data opens up new possibilities for modeling adaptive systems that operate across varying environments. Identifying systems while they're operating under closed-loop control presents a unique set of challenges because the input signals are no longer independent [5].

This article tackles the crucial problem of designing optimal input signals for closed-loop identification that provide strong performance guarantees. What this really means is ensuring that you get good model accuracy without destabilizing the system or compromising its normal operation. This balance between identification and control performance is vital in practical applications. Frequency domain methods remain a classic approach for system identification, offering profound insights into system dynamics. This work specifically looks at identifying Wiener-Hammerstein systems, a particular type of nonlinear model, directly in the frequency domain [6].

They use generalized orthonormal basis functions, which help simplify complex systems into manageable components, making the identification process more efficient and accurate. This technique offers an alternative lens for understanding system behavior. Bayesian methods offer a probabilistic perspective to system identification, inherently allowing for the quantification of uncertainty [7].

This paper explores Bayesian nonparametric system identification, leveraging Gaussian processes to model system behavior. This approach is powerful because it doesn't assume a fixed model structure upfront; instead, it lets the data guide the complexity of the model, which is often a big advantage for highly complex and poorly understood systems. Grey-box models represent an intelligent compromise, combining physical insights with data-driven elements. A method for grey-box system identification using sparse regression is presented, which is particularly useful for creating reduced-order models [8].

Let's break it down: sparse regression helps pick out only the most important model terms, leading to simpler, yet accurate, models. This is excellent for complex processes where full physical models are intractable but purely black-box models lack interpretability. The intersection of system identification and learning-based control is currently booming [9].

This survey provides a comprehensive look at how data-driven identification methods are being used to build models specifically for control applications that rely on machine learning. It highlights the challenges and opportunities in using real-world data to create models that are not just accurate but also suitable for robust and adaptive control strategies, bridging theory with practical implementation. Finally, identifying systems in real-time, especially for demanding applications like motor control, is incredibly challenging [10].

This paper focuses on adaptive real-time system identification for permanent magnet synchronous motors driven by variable frequencies. The core challenge here is dealing with rapidly changing dynamics, and the proposed adaptive method ensures the model stays accurate enough to maintain high-performance control despite these variations. This work underscores the practical need for responsive and adaptable identification techniques.

Description

System identification stands as a cornerstone in control engineering and related disciplines, providing the necessary mathematical models to understand, predict, and control dynamic processes. The pursuit of more accurate and robust models continually drives research into new methodologies and applications. A foundational aspect involves the identification of linear state-space models, where methods like the Kalman Filter-based prediction error technique are refined to enhance accuracy [1]. This approach is particularly valuable for its ability to effectively manage measurement noise and unmeasured disturbances, ensuring that the derived model parameters are as precise as possible for dynamic system analysis.

For systems that exhibit complex behaviors not captured by linear approximations, nonlinear system identification is essential. Advancements in NARMAX (Nonlinear AutoRegressive Moving Average with eXogenous inputs) models offer crucial tools for this domain [2]. This includes significant progress in detecting the underlying structure, estimating parameters, and validating these intricate models, which are vital for truly understanding systems that operate outside linear assumptions. Furthermore, while subspace identification methods are highly effective for linear systems, they face hurdles when confronted with correlated noise. New techniques are specifically developed to address this, enabling robust subspace identification for stochastic linear systems even when noise dependencies are prominent [3]. Real-world environments frequently present such complex noise characteristics, making these methods highly relevant.

Beyond purely linear or strictly nonlinear models, Linear Parameter-Varying (LPV) systems offer a powerful intermediate framework, allowing system parameters to evolve with operational changes. Recent efforts focus on data-driven identification methods for LPV systems, particularly when the 'scheduling variables' — the conditions dictating parameter shifts — are not directly observable [4]. The ability to infer these relationships from data alone marks a significant step forward for modeling adaptive and condition-dependent systems. Simultaneously, identifying systems under closed-loop control introduces unique complexities as input signals lose their independence. Here, research emphasizes the design of optimal input signals to achieve reliable closed-loop identification, aiming to guarantee model accuracy without risking system instability or disrupting normal operation [5]. This ensures practical applicability in active control environments.

Alternative and complementary perspectives also continue to evolve. Frequency domain methods, long recognized for providing deep insights into system dynamics, are being adapted for more specialized nonlinear models. For instance, specific techniques utilize generalized orthonormal basis functions for frequency-domain identification of Wiener-Hammerstein systems [6]. This simplifies the characterization of complex nonlinearities by breaking them down into manageable components. On a different front, Bayesian methods introduce a probabilistic framework, offering not just parameter estimates but also a quantification of uncertainty. Bayesian nonparametric system identification, using Gaussian processes, is particularly powerful because it allows the model's complexity to be determined by the data itself, rather than imposing a fixed structure, which is a substantial advantage for systems with unknown or highly variable dynamics [7].

Hybrid modeling approaches also offer significant benefits. Grey-box models combine the best of both worlds: incorporating physical insights where available and filling in gaps with data-driven components. A notable development in this area uses sparse regression for grey-box system identification, specifically targeting the creation of reduced-order models [8]. Sparse regression helps in selecting only the most salient model terms, resulting in models that are simpler, more interpretable, yet still highly accurate. This is especially useful for complex industrial processes where full physical models are often intractable. Moreover, the synergy between system identification and learning-based control is flourishing. A comprehensive survey highlights how data-driven identification methods are becoming instrumental in building models for control applications that leverage machine learning [9]. This area focuses on ensuring identified models are not only accurate but also suitable for robust and adaptive control strategies in real-world scenarios.

Finally, the demand for real-time performance in system identification remains high for critical applications. For example, adaptive real-time system identification is being developed for variable-frequency-driven permanent magnet synchronous motors [10]. The challenge here is to maintain model accuracy despite rapidly changing dynamics, which is crucial for sustaining high-performance control. These adaptive methods ensure that the system model is continuously updated and reliable, even in dynamic operating conditions, underscoring the practical utility and ongoing evolution of identification techniques across diverse engineering domains.

Conclusion

The field of system identification is seeing continuous advancements, tackling various complexities in modeling dynamic systems. For instance, a Kalman Filter-based prediction error method refines linear state-space models, specifically addressing challenges posed by measurement noise and unmeasured disturbances to yield more precise parameters. This is a foundational task in dynamic system identification. Moving to the challenging realm of nonlinear systems, advancements in NARMAX models provide an extensive overview of structure detection, parameter estimation, and validation. Identifying stochastic linear systems becomes more complex when correlated noise is present. New techniques in subspace identification are emerging to handle such scenarios, which are common in real-world applications where noise characteristics are intricate. Another area of focus involves Linear Parameter-Varying (LPV) systems, where parameters adapt to operating conditions. Data-driven identification methods are being developed, especially for cases where the scheduling variables that govern these parameter changes are not directly known, enabling new possibilities for adaptive system modeling. When systems operate under closed-loop control, identifying them becomes particularly tricky due to dependent input signals. Optimal input signal design is a crucial area of research, aiming to ensure high model accuracy without compromising system stability. Frequency domain methods, a classic approach, are also evolving, specifically for identifying nonlinear Wiener-Hammerstein systems using generalized orthonormal basis functions, which simplifies complex system analysis. A probabilistic perspective comes from Bayesian nonparametric system identification, employing Gaussian processes. This approach is powerful because it allows the data to determine the model's complexity rather than assuming a fixed structure upfront. Grey-box models, which blend physical insights with data, are being enhanced through sparse regression to create accurate, reduced-order models. This helps bridge the gap between complex physical models and purely black-box data-driven ones. The integration of data-driven identification with learning-based control is a booming area, highlighting how models built from real-world data can support robust and adaptive control strategies. Finally, adaptive real-time system identification is crucial for applications like variable-frequency-driven permanent magnet synchronous motors, where rapidly changing dynamics demand constantly updated and accurate models for high-performance control.

Acknowledgement

None

Conflict of Interest

None

References

Rong C, K. JÅ, M. AA. "Kalman Filter Based Prediction Error Method for Identification of State-Space Models".Automatica 123 (2021):109312.

Indexed at, Google Scholar, Crossref

Stephen AB, Stephen C, Dan C. "Advances in nonlinear system identification using NARMAX models".Mech. Syst. Signal Process. 162 (2022):108000.

Indexed at, Google Scholar, Crossref

Chengwen L, Xiaoteng H, Zhaojun Z. "Subspace Identification for Stochastic Linear Systems with Correlated Noise".IEEE Trans. Autom. Control 66 (2021):384-391.

Indexed at, Google Scholar, Crossref

S. SC, J. CACL, M. RML. "Data-driven identification of linear parameter-varying systems with unknown scheduling".Automatica 146 (2022):110582.

Indexed at, Google Scholar, Crossref

T. S, D. K, L. P. "Optimal input design for closed-loop system identification with performance guarantees".Automatica 114 (2020):108846.

Indexed at, Google Scholar, Crossref

Y. A, K. B, J. S. "Frequency-domain identification of Wiener-Hammerstein systems using generalized orthonormal basis functions".Automatica 140 (2022):110228.

Indexed at, Google Scholar, Crossref

Christophe C, Frédéric E, Lennart L. "Bayesian nonparametric system identification with Gaussian processes".Automatica 124 (2021):109395.

Indexed at, Google Scholar, Crossref

Zheng X, Xinyu Y, Yu L. "Grey-box system identification using sparse regression for reduced-order models".J. Process Control 124 (2023):102980.

Indexed at, Google Scholar, Crossref

Gabriele A, Alberto B, Dario P. "Data-driven system identification for learning-based control: A survey".Annu. Rev. Control 53 (2022):206-220.

Indexed at, Google Scholar, Crossref

Mohamed K, Samir J, Tobias G. "Adaptive real-time system identification for variable-frequency-driven permanent magnet synchronous motors".Automatica 125 (2021):109405.

Indexed at, Google Scholar, Crossref