Persistent identification of time-varying systems

Wang, Le Yi

doi:10.1109/9.553688

Cited by 31 publications

(2 citation statements)

References 45 publications

(66 reference statements)

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“…Once again it revealed certain large irreducible identification errors that seemed to be far too conservative for engineering problems. As a result, after I introduced persistent identification problems [7], first in the deterministic worst-case scenario, I thought to try stochastic noises but keep unmodelled dynamics in a worst-case sense in a combined framework. At that time, my knowledge on stochastic systems was limited to some self-studied courses and a few courses at McGill University such as Peter Caines's "Stochastic Control Systems".…”

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A lifelong friendship and fruitful collaboration: A journey of more than 30 years with George Yin

Wang

2024

NACO

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This article highlights my lifelong friendship and collaboration with George Yin on developing new methodologies in diversified fields in control theory and their branches, as well as their engineering and medical applications. It explains the roots and motivations in initiating these problems and George's critical contributions in applying his extensive expertise in stochastic systems to bring these challenging pursuits to fruitful new frameworks and methodologies.George and I have collaborated for more than 30 years on problems in the intersection of applied mathematics and engineering. The themes of our joint work have always been motivated strongly by engineering systems, evolving with emerging technologies. They are mostly focused on theoretical aspects in control systems and their branches, aiming for new frameworks and methodologies that deal with different types of uncertainties, information, and complexity.George started his work at Wayne State University (WSU) in 1987 in the Mathematics Department, three years prior to my faculty position in the Department of Electrical Engineering of WSU in 1990. While I knew George around my PhD graduation via friends, conferences, and occasional interactions, our actual joint work started in the mid 1990s, and then it quickly became much more intensive and comprehensive. 1. Backgrounds. Our collaboration has the roots in many aspects of my lifelong pursuit of dealing with uncertainties, information, and complexity, both in theory and in applications. Some themes were initiated well before my PhD graduation, and others were due to my personal interests, and still others stemmed from the unique locations of WSU as well as my personal connections. These may be summarized in the following three background categories.1. Integration of Deterministic and Stochastic Frameworks. During the final years of my PhD program at McGill University, my supervisor, George Zames, started to think about possibility of employing both deterministic and stochastic frameworks to treat uncertainties. In the late 1980s, many people in the field of H ∞ control tried to extend the H ∞ robust control theory to the

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“…1. Persistent Identification with Combined Unmodelled Dynamics, Model Mismatch, and Stochastic Noise [4,7,8]. Common system identification has a given starting time t 0 for data collection.…”

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A lifelong friendship and fruitful collaboration: A journey of more than 30 years with George Yin

Wang

2024

NACO

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Model reference adaptive control system design for linear time-varying systems with unstructured and bounded varying functions

Hidaka¹,

Ohmori²,

Sano³

2000

Elect. Eng. Jpn.

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In recent years, many methods of model reference adaptive control system (MRACS) for a linear time‐varying (LTV) plant have been proposed. These methods assumed that the structure of plant parameters is known in advance. However, it is difficult to get a priori information of plant parameters. In this paper, an MRACS design for an LTV system based on high‐order estimator (HOE) is proposed. By applying dynamic certainty equivalence (DyCE) to LTV plants, a new MRAC law of LTV system is derived without knowing the structure of the plant parameters. The MRACS law is generated by using high‐order derivatives of an estimated parameter, so that robust HOE with a normalization signal and σ modification for the system introduced. Our proposed method can attain better performance than conventional methods, such as estimation with variable forgetting factor (VF) and the gradient projection method (GPM). The robust HOE establishes the boundedness of all of the estimated parameters under the condition that the estimated parameter and the first derivative of the parameter are bounded. It is shown that all signals in the adaptive loop are bounded and the output error converges to a closed set. The proposed method is compared to the familiar schemes, the gradient projection method and the estimation based on forgetting factor through numerical simulations, and the effectiveness of our proposed method is shown. © 2000 Scripta Technica, Electr Eng Jpn, 130(4): 87–98, 2000

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Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics, observation bias, and nonlinear model mismatch

Kan

Yin

Wang

2012

Adaptive Control & Signal

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SUMMARYThis work focuses on tracking and system identification of systems with regime‐switching parameters, which are modeled by a Markov process. It introduces a framework for persistent identification problems that encompass many typical system uncertainties, including parameter switching, stochastic observation disturbances, deterministic unmodeled dynamics, sensor observation bias, and nonlinear model mismatch. In accordance with the ‘frequency’ of the parameter switching process, we divide the problems into two classes. For fast‐switching systems, the switching parameters are stochastic processes modeled by irreducible and aperiodic Markov chains. Because accurately tracking real‐time parameters in such systems is not possible because of the uncertainty principles, the effect of parameter switching is evaluated on their average by the stationary distribution of the Markovian chain and estimated by the least squares algorithms. We derive upper and lower bounds on identification errors, which characterize how identification accuracy depends on the earlier uncertainty terms. When the system parameters switch their values infrequently in a probabilistic sense, their values can be tracked based on input/output observations. Stochastic approximation algorithms with adaptive step sizes are used for such systems. Simulation studies are carried out to demonstrate that slowly varying parameters could be tracked with reasonable accuracy.Copyright © 2012 John Wiley & Sons, Ltd.

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Persistent identification of time-varying systems

Cited by 31 publications

References 45 publications

A lifelong friendship and fruitful collaboration: A journey of more than 30 years with George Yin

A lifelong friendship and fruitful collaboration: A journey of more than 30 years with George Yin

Model reference adaptive control system design for linear time-varying systems with unstructured and bounded varying functions

Persistent tracking and identification of regime‐switching systems with structural uncertainties: unmodeled dynamics, observation bias, and nonlinear model mismatch

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