Optimal control of switched systems with multiple time-delays and a cost on changing control

Gong, Zhenfeng; Liu, Chongyang; Wang, Yujing

doi:10.3934/jimo.2017042

Cited by 26 publications

(12 citation statements)

References 23 publications

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“…Therefore, handling missing data properly is major part of data preprocessing. This type of data mainly includes includes a value or continuous value [28]. If a value is lost, it can be replaced by the mean value obtained from several sets of adjacent data.…”

Section: Electrolysis Process and Problemmentioning

confidence: 99%

Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production

Chen¹,

Li²,

Chen³

et al. 2019

Journal of Industrial &Amp; Management Optimization

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In this study, a new prediction algorithm is proposed, based on the collaborative two-dimensional forecast model (CTFM) that combines the traditional method and similarity search technique. The main idea of the algorithm is that the prediction of the change trend of the slope and the accumulated slope of the cell resistance as well as the useful knowledge obtained using the similarity search technique are used as the main criteria to calculate anode effect (AE)-prediction reliability. The accumulated mass deviation value is used as an auxiliary criterion to adjust the AE-prediction reliability. Finally, the current AE-process is marked according to the current AE-prediction reliability. The prediction model based on CTFM is tested on a real situation, in which multiple samples are extracted from the production of a 400 kA aluminum electrolysis cell. We observe that when the time advance of AE-prediction is within 20 ∼ 40 min, the accuracy rate of the CTFM algorithm is greater than 95% and the applicability of the method is excellent, showing a high prediction accuracy for different aluminum electrolysis cells.

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Section: Electrolysis Process and Problemmentioning

confidence: 99%

Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production

Chen¹,

Li²,

Chen³

et al. 2019

Journal of Industrial &Amp; Management Optimization

View full text Add to dashboard Cite

show abstract

“…Control parameterization method is a popular approach for solving general constrained optimal control problems [7,22,33,37,38]. This method involves approximating the control function by a piecewise constant function.…”

mentioning

confidence: 99%

On the optimal control problems with characteristic time control constraints

Yu¹,

Su²,

Bai³

2022

JIMO

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In this paper, we consider a class of optimal control problems with control constraints on a set of characteristic time instants. By applying the control parameterization technique, these constraints are imposed on the subdomains that contain the characteristic time points. The values of the control functions as well as the lengths for their corresponding subdomains become decision variables. Time-scaling transformation is an effective technique to optimize the length of each subdomain in a new time horizon. However, the characteristic time instants in the original time horizon become variable time instants in the new time horizon, and hence the control constraints imposed on these characteristic time points are difficult to be formulated in the new time horizon. We propose a surrogate condition and show that the characteristic time control constraints will be satisfied once the surrogate condition holds. Moreover, this surrogate condition is easy to formulate in the new time horizon. The resulting approximate problem can be readily solved by many existing computational methods for solving constrained optimal control problems. Finally, we conclude this paper by solving two examples.

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“…In recent years, switched systems [13,14,16] have drawn considerable attention due to their broad range of applications. In spite of the simplicity of each subsystem, switched systems may exhibit complicated dynamical behaviors because of the switching law between the subsystems.…”

mentioning

confidence: 99%

The viability of switched nonlinear systems with piecewise smooth Lyapunov functions

Lv¹,

Gao²,

Zhao³

2021

JIMO

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In this paper, we focus on the viability and attraction for switched nonlinear systems with nonsmooth Lyapunov functions. We determine the viable set and region of attraction for switched systems in which Lyapunov functions are piecewise smooth. The switching law is constructed by using the directional derivatives of a piecewise smooth Lyapunov function along the trajectories of the subsystems. Sufficient conditions are derived to guarantee the viability and attraction of switched nonlinear systems on the level set of a piecewise smooth Lyapunov function. We further extend the method to switched systems involving possible sliding motions. The approach in the paper provides a unified framework for studying viability and attraction with a systematic consideration of sliding motions. Finally, considering two certain classes of piecewise smooth functions, the related conditions of the viability and attraction for the level set are developed.2010 Mathematics Subject Classification. Primary: 93C10, 93C60; Secondary: 93C05.

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Optimal control of switched systems with multiple time-delays and a cost on changing control

Cited by 26 publications

References 23 publications

Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production

Anode effect prediction based on collaborative two-dimensional forecast model in aluminum electrolysis production

On the optimal control problems with characteristic time control constraints

The viability of switched nonlinear systems with piecewise smooth Lyapunov functions

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