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13 pages, 297 KiB

Open AccessArticle

Characterization Results of Solution Sets Associated with Multiple-Objective Fractional Optimal Control Problems

by Savin Treanţă and Tareq Saeed

Mathematics 2023, 11(14), 3191; https://doi.org/10.3390/math11143191 - 20 Jul 2023

Viewed by 740

This paper investigates some duality results of a mixed type for a class of multiple objective fractional optimal control problems. More precisely, by considering the Wolfe- and Mond–Weir-type dualities, we formulate a robust mixed-type dual problem and, under suitable convexity assumptions of the [...] Read more.

This paper investigates some duality results of a mixed type for a class of multiple objective fractional optimal control problems. More precisely, by considering the Wolfe- and Mond–Weir-type dualities, we formulate a robust mixed-type dual problem and, under suitable convexity assumptions of the involved functionals, we establish some equivalence results between the solution sets of the considered models. Essentially, we investigate robust weak, robust strong, and robust strict converse-type duality results. To the best of the authors’ knowledge, robust duality results for such problems are new in the specialized literature. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

17 pages, 645 KiB

Open AccessArticle

Optimal Robust Tracking Control of Injection Velocity in an Injection Molding Machine

by Guoshen Wu, Zhigang Ren, Jiajun Li and Zongze Wu

Mathematics 2023, 11(12), 2619; https://doi.org/10.3390/math11122619 - 08 Jun 2023

Viewed by 1018

Abstract

Injection molding is a critical component of modern industrial operations, and achieving fast and stable control of injection molding machines (IMMs) is essential for producing high-quality plastic products. This paper focuses on solving an optimal tracking control problem of the injection velocity that [...] Read more.

Injection molding is a critical component of modern industrial operations, and achieving fast and stable control of injection molding machines (IMMs) is essential for producing high-quality plastic products. This paper focuses on solving an optimal tracking control problem of the injection velocity that arises in a typical nonlinear IMM. To this end, an efficient optimal robust controller is proposed and designed. The nonlinear injection velocity servo system is first approximately linearized at iteration points using the first-order Taylor expansion approach. Then, at each time node in the optimization process, the relevant algebraic Riccati equation is introduced, and the solution is used to construct an optimal robust feedback controller. Furthermore, a rigorous Lyapunov theorem analysis is employed to demonstrate the global stability properties of the proposed feedback controller. The results from numerical simulations show that the proposed optimal robust control strategy can successfully and rapidly achieve the best tracking of the intended injection velocity trajectory within a given time. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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18 pages, 1165 KiB

Open AccessArticle

Appearance-Based Gaze Estimation Method Using Static Transformer Temporal Differential Network

by Yujie Li, Longzhao Huang, Jiahui Chen, Xiwen Wang and Benying Tan

Mathematics 2023, 11(3), 686; https://doi.org/10.3390/math11030686 - 29 Jan 2023

Cited by 5 | Viewed by 2021

Abstract

Gaze behavior is important and non-invasive human–computer interaction information that plays an important role in many fields—including skills transfer, psychology, and human–computer interaction. Recently, improving the performance of appearance-based gaze estimation, using deep learning techniques, has attracted increasing attention: however, several key problems [...] Read more.

Gaze behavior is important and non-invasive human–computer interaction information that plays an important role in many fields—including skills transfer, psychology, and human–computer interaction. Recently, improving the performance of appearance-based gaze estimation, using deep learning techniques, has attracted increasing attention: however, several key problems in these deep-learning-based gaze estimation methods remain. Firstly, the feature fusion stage is not fully considered: existing methods simply concatenate the different obtained features into one feature, without considering their internal relationship. Secondly, dynamic features can be difficult to learn, because of the unstable extraction process of ambiguously defined dynamic features. In this study, we propose a novel method to consider feature fusion and dynamic feature extraction problems. We propose the static transformer module (STM), which uses a multi-head self-attention mechanism to fuse fine-grained eye features and coarse-grained facial features. Additionally, we propose an innovative recurrent neural network (RNN) cell—that is, the temporal differential module (TDM)—which can be used to extract dynamic features. We integrated the STM and the TDM into the static transformer with a temporal differential network (STTDN). We evaluated the STTDN performance, using two publicly available datasets (MPIIFaceGaze and Eyediap), and demonstrated the effectiveness of the STM and the TDM. Our results show that the proposed STTDN outperformed state-of-the-art methods, including that of Eyediap (by 2.9%). Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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13 pages, 1200 KiB

Open AccessArticle

A Novel Zeroing Neural Network for Solving Time-Varying Quadratic Matrix Equations against Linear Noises

by Jianfeng Li, Linxi Qu, Zhan Li, Bolin Liao, Shuai Li, Yang Rong, Zheyu Liu, Zhijie Liu and Kunhuang Lin

Mathematics 2023, 11(2), 475; https://doi.org/10.3390/math11020475 - 16 Jan 2023

Cited by 1 | Viewed by 1413

Abstract

The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix [...] Read more.

The solving of quadratic matrix equations is a fundamental issue which essentially exists in the optimal control domain. However, noises exerted on the coefficients of quadratic matrix equations may affect the accuracy of the solutions. In order to solve the time-varying quadratic matrix equation problem under linear noise, a new error-processing design formula is proposed, and a resultant novel zeroing neural network model is developed. The new design formula incorporates a second-order error-processing manner, and the double-integration-enhanced zeroing neural network (DIEZNN) model is further proposed for solving time-varying quadratic matrix equations subject to linear noises. Compared with the original zeroing neural network (OZNN) model, finite-time zeroing neural network (FTZNN) model and integration-enhanced zeroing neural network (IEZNN) model, the DIEZNN model shows the superiority of its solution under linear noise; that is, when solving the problem of a time-varying quadratic matrix equation in the environment of linear noise, the residual error of the existing model will maintain a large level due to the influence of linear noise, which will eventually lead to the solution’s failure. The newly proposed DIEZNN model can guarantee a normal solution to the time-varying quadratic matrix equation task no matter how much linear noise there is. In addition, the theoretical analysis proves that the neural state of the DIEZNN model can converge to the theoretical solution even under linear noise. The computer simulation results further substantiate the superiority of the DIEZNN model in solving time-varying quadratic matrix equations under linear noise. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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19 pages, 1712 KiB

Open AccessArticle

Automatic Compression of Neural Network with Deep Reinforcement Learning Based on Proximal Gradient Method

by Mingyi Wang, Jianhao Tang, Haoli Zhao, Zhenni Li and Shengli Xie

Mathematics 2023, 11(2), 338; https://doi.org/10.3390/math11020338 - 09 Jan 2023

Viewed by 1608

Abstract

In recent years, the model compression technique is very effective for deep neural network compression. However, many existing model compression methods rely heavily on human experience to explore a compression strategy between network structure, speed, and accuracy, which is usually suboptimal and time-consuming. [...] Read more.

In recent years, the model compression technique is very effective for deep neural network compression. However, many existing model compression methods rely heavily on human experience to explore a compression strategy between network structure, speed, and accuracy, which is usually suboptimal and time-consuming. In this paper, we propose a framework for automatically compressing models through the actor–critic structured deep reinforcement learning (DRL) which interacts with each layer in the neural network, where the actor network determines the compression strategy and the critic network ensures the decision accuracy of the actor network through predicted values, thus improving the compression quality of the network. To enhance the prediction performance of the critic network, we impose the L

_{1}

norm regularizer on the weights of the critic network to obtain a distinct activation output feature on the representation, thus enhancing the prediction accuracy of the critic network. Moreover, to improve the decision performance of the actor network, we impose the L

_{1}

norm regularizer on the weights of the actor network to improve the decision accuracy of the actor network by removing the redundant weights in the actor network. Furthermore, to improve the training efficiency, we use the proximal gradient method to optimize the weights of the actor network and the critic network, which can obtain an effective weight solution and thus improve the compression performance. In the experiment, in MNIST datasets, the proposed method has only a 0.2% loss of accuracy when compressing more than 70% of neurons. Similarly, in CIFAR-10 datasets, the proposed method compresses more than 60% of neurons, with only 7.1% accuracy loss, which is superior to other existing methods. In terms of efficiency, the proposed method also cost the lowest time among the existing methods. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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15 pages, 1053 KiB

Open AccessArticle

Economic Dispatch for Smart Buildings with Load Demand of High Volatility Based on Quasi-Quadratic Online Adaptive Dynamic Programming

by Kairui Chen, Zhangmou Zhu and Jianhui Wang

Mathematics 2022, 10(24), 4701; https://doi.org/10.3390/math10244701 - 11 Dec 2022

Cited by 2 | Viewed by 1030

Abstract

In this paper, a quasi-quadratic online adaptive dynamic programming (QOADP) algorithm is proposed to realize optimal economic dispatch for smart buildings. Load demand of high volatility is considered, which is modeled by an uncontrollable state. To reduce residual errors of the approximation structure, [...] Read more.

In this paper, a quasi-quadratic online adaptive dynamic programming (QOADP) algorithm is proposed to realize optimal economic dispatch for smart buildings. Load demand of high volatility is considered, which is modeled by an uncontrollable state. To reduce residual errors of the approximation structure, a quasi-quadratic-form parametric structure was designed elaborately with a bias term to counteract effects of uncertainties. Based on action-dependent heuristic dynamic programming (ADHDP), an implementation of the QOADP algorithm is presented that involved obtaining optimal economic dispatch for smart buildings. Finally, hardware-in-loop (HIL) experiments were conducted, and the performance of the proposed QOADP algorithm is superior to that of two other typical algorithms. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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18 pages, 2455 KiB

Open AccessArticle

Remaining Useful Life Prediction Based on Multi-Representation Domain Adaptation

by Yi Lyu, Qichen Zhang, Zhenfei Wen and Aiguo Chen

Mathematics 2022, 10(24), 4647; https://doi.org/10.3390/math10244647 - 08 Dec 2022

Cited by 6 | Viewed by 1398

Abstract

All current deep learning-based prediction methods for remaining useful life (RUL) assume that training and testing data have similar distributions, but the existence of various operating conditions, failure modes, and noise lead to insufficient data with similar distributions during the training process, thereby [...] Read more.

All current deep learning-based prediction methods for remaining useful life (RUL) assume that training and testing data have similar distributions, but the existence of various operating conditions, failure modes, and noise lead to insufficient data with similar distributions during the training process, thereby reducing RUL prediction performance. Domain adaptation can effectively solve this problem by learning the cross-domain invariant features of the source domain and target domain to reduce the distribution difference. However, most domain adaptive methods extract the source domain and target domain features into a single space for feature alignment, which may leave out effective information and affect the accuracy of prediction. To address this problem, we propose a data-driven approach named long short-term memory network and multi-representation domain adaptation (LSTM-MRAN). We standardize and process the degraded sensor data with a sliding time window, use LSTM to extract features from the degraded data, and mine the time series information between the data. Then, we use multiple substructures in multi-representation domain adaptation to extract features of the source domain and target domain from different spaces and align features by minimizing conditional maximum mean difference (CMMD) loss functions. The effectiveness of the method is verified by the CMAPSS dataset. Compared with methods without domain adaptation and other transfer learning methods, the proposed method provides more reliable RUL prediction results under datasets with different operating conditions and failure modes. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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15 pages, 3557 KiB

Open AccessArticle

A Guaranteed Approximation Algorithm for QoS Anypath Routing in WMNs

by Weijun Yang, Xianxian Zeng and Guanyu Lai

Mathematics 2022, 10(23), 4557; https://doi.org/10.3390/math10234557 - 01 Dec 2022

Cited by 3 | Viewed by 906

Abstract

Anypath routing is a hot research topic for QoS guarantee in wireless mesh networks (WMNs). According to time-varying characteristics of WMNs and the idea of anypath routing, a system network modeling method is proposed to address the multiple constrained optimization anypath problem. It [...] Read more.

Anypath routing is a hot research topic for QoS guarantee in wireless mesh networks (WMNs). According to time-varying characteristics of WMNs and the idea of anypath routing, a system network modeling method is proposed to address the multiple constrained optimization anypath problem. It focuses on the application of WMNs; under various QoS constraints, it satisfies a specific constraint and approaches other QoS constraints from an approximate perspective. A heuristic multi-constrained anypath algorithm with a time complexity as Dijkstra is proposed for the problem, and the algorithm is proved to be a K-1 approximation algorithm. The feasibility of the algorithm is verified, then its computational efficiency and performance are evaluated through simulation experiments, respectively. According to the application characteristics of wireless networks, the algorithm is suitable for WMNs and has good compatibility with existing routing protocols. Full article

(This article belongs to the Special Issue Learning-Based Control and Nonlinear Optimization: Theory, Models, Algorithms, and Applications)

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