Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems

Chaudhary, Naveed Ishtiaq; Khan, Zeshan Aslam; Kiani, Adiqa Kausar; Raja, Muhammad Asif Zahoor; Chaudhary, Iqra Ishtiaq; Peinto, Carla M.A.

doi:10.1016/j.chaos.2022.112611

Cited by 19 publications

(6 citation statements)

References 67 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…1 In recent years, with the development of engineering technology, several novel algorithms have emerged in the field of system identification. For example, the auxiliary model identification method 2,3 uses the observable information of the system to build an auxiliary model. Then the output of the model is used to replace unmeasured variables of the system.…”

Section: Literature Reviewmentioning

confidence: 99%

“…That is, when either System 1 or System 2 updates its parameters, the central unit updates the auxiliary matrix immediately. This means that it needs to use the parameters from the previous moment to compute the matrix A without waiting for system 2 and obtain the new parameters theta 2 . In other words, when any task obtains observations, it will partially modify the matrix Θ and compute A.…”

Section: Distributed Asynchronous Multi-task Online Sparse Identifica...mentioning

confidence: 99%

See 1 more Smart Citation

Distributed online multi‐task sparse identification for multiple systems with asynchronous updates

Zhang,

Luan,

Ding

et al. 2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

Simultaneous online identification of the structure and parameters for multiple systems can use the multi‐task learning to share parameter sparse patterns across different identification tasks to improve the estimation accuracy. To reduce the communication and computational burden, improve the convergence rate and increase the reliability of the identification task, a distributed asynchronous multi‐task sparse identification algorithm is proposed. The alternating minimization algorithm is applied to design a distributed multi‐task loss function. Then by constructing the auxiliary matrix and transforming the sparse constraint on the parameter matrix to the constructed auxiliary matrix, the asynchronous parameter update and sparse model update can be realized. The algorithm uses a recursive form to complete online identification which is feasible to analyze. After proving the convergence of the identification algorithm, we present an example to support the theoretical analysis and show the advantages of the proposed algorithm.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Distributed Asynchronous Multi-task Online Sparse Identifica...mentioning

confidence: 99%

Distributed online multi‐task sparse identification for multiple systems with asynchronous updates

Zhang,

Luan,

Ding

et al. 2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

show abstract

“…In recent decades, fractional calculus has been a significant mathematical technique used to represent critical challenges in various areas, including science, technology, and engineering such as, optimal power flow problems 17 , nonlinear output-error systems 18 , recommender systems with chaotic ratings behavior 19 , parameter estimation of nonlinear control autoregressive systems 20 , power management involving wind-load chaos and uncertainties 21 , Schrodinger equations 22 , 23 and shallow water waves 24 . The power-law function is involved in the Liouville–Caputo fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

Khan

Ahmad

Shah

et al. 2023

Sci Rep

View full text Add to dashboard Cite

In this paper, the newly developed Fractal-Fractional derivative with power law kernel is used to analyse the dynamics of chaotic system based on a circuit design. The problem is modelled in terms of classical order nonlinear, coupled ordinary differential equations which is then generalized through Fractal-Fractional derivative with power law kernel. Furthermore, several theoretical analyses such as model equilibria, existence, uniqueness, and Ulam stability of the system have been calculated. The highly non-linear fractal-fractional order system is then analyzed through a numerical technique using the MATLAB software. The graphical solutions are portrayed in two dimensional graphs and three dimensional phase portraits and explained in detail in the discussion section while some concluding remarks have been drawn from the current study. It is worth noting that fractal-fractional differential operators can fastly converge the dynamics of chaotic system to its static equilibrium by adjusting the fractal and fractional parameters.

show abstract

“…For dual‐rate Hammerstein‐Volterra systems, Zong et al solved the problem of the incomplete identification data caused by the dual‐rate sampling through using the auxiliary model method and proposed an auxiliary model‐based hybrid particle swarm‐gradient algorithm 43 . Chaudhary et al studied an auxiliary model‐based normalized variable initial value fractional least mean square algorithm for input nonlinear output‐error system by using the auxiliary model identification idea 44 …”

Section: Introductionmentioning

confidence: 99%

“…43 Chaudhary et al studied an auxiliary model-based normalized variable initial value fractional least mean square algorithm for input nonlinear output-error system by using the auxiliary model identification idea. 44 The iterative methods update the parameters of the systems through using a batch of measurement data and are suitable for off-line identification. [45][46][47][48][49][50] In contrast, the recursive methods can real-timely estimate the parameters of the systems and are suitable for online identification through capturing the real-time information from actual production processes.…”

Section: Introductionmentioning

confidence: 99%

Highly‐computational hierarchical iterative identification methods for multiple‐input multiple‐output systems by using the auxiliary models

Xing

Ding

Pan

2023

Intl J Robust & Nonlinear

View full text Add to dashboard Cite

The identification of multiple‐input multiple‐output (MIMO) systems is an important part of designing complex control systems. This article studies an auxiliary model least squares iterative (AM‐LSI) algorithm for MIMO systems. With the expansion of the system scale and limitations of the computer resources, there is an urgent need for an identification algorithm that provides higher computational efficiency. To address this issue, this article further derives a hierarchical identification model and proposes a new auxiliary model hierarchical least squares iterative (AM‐HLSI) algorithm for MIMO systems by applying the hierarchical identification principle. Through the analysis of the computational efficiency, the AM‐HLSI algorithm has higher computational efficiency than the AM‐LSI algorithm. Additionally, the feasibility of the AM‐LSI and AM‐HLSI algorithms is validated by a simulation example.

show abstract

Design of auxiliary model based normalized fractional gradient algorithm for nonlinear output-error systems

Cited by 19 publications

References 67 publications

Distributed online multi‐task sparse identification for multiple systems with asynchronous updates

Distributed online multi‐task sparse identification for multiple systems with asynchronous updates

Dynamics of chaotic system based on circuit design with Ulam stability through fractal-fractional derivative with power law kernel

Highly‐computational hierarchical iterative identification methods for multiple‐input multiple‐output systems by using the auxiliary models

Contact Info

Product

Resources

About