Parameter Estimation Algorithms and Its Applications

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (31 December 2018)

Special Issue Editors


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Guest Editor
1. Faculty of Mechanical & Electrical Engineering, Kunming University of Science & Technology, Kunming 650500, China
2. Department of Mechanical Engineering, University of Bristol, Bristol BS8 1TH, UK
Interests: adaptive control; parameter estimation; nonlinear control and applications

E-Mail Website
Guest Editor
School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, China
Interests: system identification; numerical algorithm; signal processing; system modeling

Special Issue Information

Dear Colleagues,

Many practical engineering problems can be addressed, provided that the precise models of the studied plants are known. This practically orientated need has stimulated the development of an emerging topic: System identification. As a key subject in the system identification, parameter estimation has been widely studied since 1960, and many algorithms have been used in the practice. However, there are still certain issues to be further revisited and addressed. This has stimulated recently increasing research interests and developments on advanced learning and adaptation for parameter estimation.

The open access journal Algorithms will host a Special Issue on “Parameter Estimation Algorithms and Its Applications”.

This Special Issue aims at providing a specific opportunity to review the state-of-the-art of Parameter Estimation Algorithms. Authors are invited to present new algorithms, frameworks, software architectures, experiments and applications aimed at bringing new information about relevant theory and techniques of parameter estimation. All original papers related to parameter estimation and their application are welcome. In particular, we encourage authors to introduce new results for synthesizing estimation and optimization into practical systems, e.g., multi-agent systems, smart grid, population systems, multi-agent systems, UAVs, human–robot interactions, etc.

Prof. Dr. Jing Na
Prof. Dr. Feng Ding
Prof. Dr. Quan Min Zhu
Guest Editors

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Keywords

  • Adaptive parameter estimation
  • System identification
  • Gradient algorithm
  • Least squares algorithm
  • Black-box identification
  • Grey-box identification
  • Bio-inspired learning and adaptation
  • Convergence and consistency
  • Kernel based identification

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Published Papers (8 papers)

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Research

28 pages, 8107 KiB  
Article
Parameter Estimation, Robust Controller Design and Performance Analysis for an Electric Power Steering System
by Van Giao Nguyen, Xuexun Guo, Chengcai Zhang and Xuan Khoa Tran
Algorithms 2019, 12(3), 57; https://doi.org/10.3390/a12030057 - 5 Mar 2019
Cited by 7 | Viewed by 6492
Abstract
This paper presents a parameter estimation, robust controller design and performance analysis for an electric power steering (EPS) system. The parametrical analysis includes the EPS parameters and disturbances, such as the assist motor parameters, sensor-measurement noise, and random road factors, allowing the EPS [...] Read more.
This paper presents a parameter estimation, robust controller design and performance analysis for an electric power steering (EPS) system. The parametrical analysis includes the EPS parameters and disturbances, such as the assist motor parameters, sensor-measurement noise, and random road factors, allowing the EPS stability to be extensively investigated. Based on the loop-shaping technique, the system controller is designed to increase the EPS stability and performance. The loop-shaping procedure is proposed to minimize the influence of system disturbances on the system outputs. The simplified refined instrumental variable (SRIV) algorithm, least squares state variable filter (LSSVF) algorithm and instrumental variable state variable filter (IVSVF) algorithm are applied to reduce the model mismatching between the theoretical EPS models and the real EPS model, as the EPS parameters can be accurately identified based on the experimental EPS data. The performance of the proposed method is thus compared to that of the proportional-integral-derivative (PID) test bench results for the EPS system. The experimental results demonstrated that the proposed loop-shaping controller provides good tracking performance while ensuring the stability of the EPS system. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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19 pages, 592 KiB  
Article
Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems
by Yong-Hong Lan, Jun-Jun Xia and Yue-Xiang Shi
Algorithms 2019, 12(1), 20; https://doi.org/10.3390/a12010020 - 10 Jan 2019
Cited by 23 | Viewed by 4239
Abstract
In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L [...] Read more.
In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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17 pages, 828 KiB  
Article
Parametric Estimation in the Vasicek-Type Model Driven by Sub-Fractional Brownian Motion
by Shengfeng Li and Yi Dong
Algorithms 2018, 11(12), 197; https://doi.org/10.3390/a11120197 - 4 Dec 2018
Cited by 5 | Viewed by 3238
Abstract
In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion: d X t = ( μ + θ X t ) d t + d S t H , t 0 with [...] Read more.
In the paper, we tackle the least squares estimators of the Vasicek-type model driven by sub-fractional Brownian motion: d X t = ( μ + θ X t ) d t + d S t H , t 0 with X 0 = 0 , where S H is a sub-fractional Brownian motion whose Hurst index H is greater than 1 2 , and μ R , θ R + are two unknown parameters. Based on the so-called continuous observations, we suggest the least square estimators of μ and θ and discuss the consistency and asymptotic distributions of the two estimators. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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14 pages, 338 KiB  
Article
Iterative Identification for Multivariable Systems with Time-Delays Based on Basis Pursuit De-Noising and Auxiliary Model
by Junyao You and Yanjun Liu
Algorithms 2018, 11(11), 180; https://doi.org/10.3390/a11110180 - 6 Nov 2018
Cited by 7 | Viewed by 2623
Abstract
This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem [...] Read more.
This paper focuses on the joint estimation of parameters and time-delays of the multiple-input single-output output-error systems. Since the time-delays are unknown, an effective identification model with a high dimensional and sparse parameter vector is established based on overparameterization. Then, the identification problem is converted to a sparse optimization problem. Based on the basis pursuit de-noising criterion and the auxiliary model identification idea, an auxiliary model based basis pursuit de-noising iterative algorithm is presented. The parameters are estimated by solving a quadratic program, and the unavailable terms in the information vector are updated by the auxiliary model outputs iteratively. The time-delays are estimated according to the sparse structure of the parameter vector. The proposed method can obtain effective estimates of the parameters and time-delays from few sampled data. The simulation results illustrate the effectiveness of the proposed algorithm. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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17 pages, 698 KiB  
Article
The Bias Compensation Based Parameter and State Estimation for Observability Canonical State-Space Models with Colored Noise
by Xuehai Wang, Feng Ding, Qingsheng Liu and Chuntao Jiang
Algorithms 2018, 11(11), 175; https://doi.org/10.3390/a11110175 - 1 Nov 2018
Cited by 1 | Viewed by 2963
Abstract
This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise [...] Read more.
This paper develops a bias compensation-based parameter and state estimation algorithm for the observability canonical state-space system corrupted by colored noise. The state-space system is transformed into a linear regressive model by eliminating the state variables. Based on the determination of the noise variance and noise model, a bias correction term is added into the least squares estimate, and the system parameters and states are computed interactively. The proposed algorithm can generate the unbiased parameter estimate. Two illustrative examples are given to show the effectiveness of the proposed algorithm. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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12 pages, 408 KiB  
Article
Parameter Estimation of a Class of Neural Systems with Limit Cycles
by Xuyang Lou, Xu Cai and Baotong Cui
Algorithms 2018, 11(11), 169; https://doi.org/10.3390/a11110169 - 26 Oct 2018
Cited by 2 | Viewed by 2442
Abstract
This work addresses parameter estimation of a class of neural systems with limit cycles. An identification model is formulated based on the discretized neural model. To estimate the parameter vector in the identification model, the recursive least-squares and stochastic gradient algorithms including their [...] Read more.
This work addresses parameter estimation of a class of neural systems with limit cycles. An identification model is formulated based on the discretized neural model. To estimate the parameter vector in the identification model, the recursive least-squares and stochastic gradient algorithms including their multi-innovation versions by introducing an innovation vector are proposed. The simulation results of the FitzHugh–Nagumo model indicate that the proposed algorithms perform according to the expected effectiveness. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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10 pages, 2579 KiB  
Article
Online Adaptive Parameter Estimation for Quadrotors
by Jun Zhao, Xian Wang, Guanbin Gao, Jing Na, Hongping Liu and Fujin Luan
Algorithms 2018, 11(11), 167; https://doi.org/10.3390/a11110167 - 25 Oct 2018
Cited by 9 | Viewed by 3105
Abstract
The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be [...] Read more.
The stability and robustness of quadrotors are always influenced by unknown or immeasurable system parameters. This paper proposes a novel adaptive parameter estimation technology to obtain high-accuracy parameter estimation for quadrotors. A typical mathematical model of quadrotors is first obtained, which can be used for parameter estimation. Then, an expression of the parameter estimation error is derived by introducing a set of auxiliary filtered variables. Moreover, an augmented matrix is constructed based on the obtained auxiliary filtered variables, which is then used to design new adaptive laws to achieve exponential convergence under the standard persistent excitation (PE) condition. Finally, a simulation and an experimental verification for a typical quadrotor system are shown to illustrate the effectiveness of the proposed method. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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15 pages, 1199 KiB  
Article
Estimating the Volume of the Solution Space of SMT(LIA) Constraints by a Flat Histogram Method
by Wei Gao, Hengyi Lv, Qiang Zhang and Dunbo Cai
Algorithms 2018, 11(9), 142; https://doi.org/10.3390/a11090142 - 18 Sep 2018
Cited by 1 | Viewed by 3362
Abstract
The satisfiability modulo theories (SMT) problem is to decide the satisfiability of a logical formula with respect to a given background theory. This work studies the counting version of SMT with respect to linear integer arithmetic (LIA), termed SMT(LIA). Specifically, the purpose of [...] Read more.
The satisfiability modulo theories (SMT) problem is to decide the satisfiability of a logical formula with respect to a given background theory. This work studies the counting version of SMT with respect to linear integer arithmetic (LIA), termed SMT(LIA). Specifically, the purpose of this paper is to count the number of solutions (volume) of a SMT(LIA) formula, which has many important applications and is computationally hard. To solve the counting problem, an approximate method that employs a recent Markov Chain Monte Carlo (MCMC) sampling strategy called “flat histogram” is proposed. Furthermore, two refinement strategies are proposed for the sampling process and result in two algorithms, MCMC-Flat1/2 and MCMC-Flat1/t, respectively. In MCMC-Flat1/t, a pseudo sampling strategy is introduced to evaluate the flatness of histograms. Experimental results show that our MCMC-Flat1/t method can achieve good accuracy on both structured and random instances, and our MCMC-Flat1/2 is scalable for instances of convex bodies with up to 7 variables. Full article
(This article belongs to the Special Issue Parameter Estimation Algorithms and Its Applications)
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