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18 pages, 5284 KiB

Open AccessArticle

Disturbance Attenuation Trajectory Tracking Control of Unmanned Surface Vessel Subject to Measurement Biases

by Qijia Yao, Hadi Jahanshahi, Chengliang Liu, Ahmed Alotaibi and Hajid Alsubaie

Axioms 2023, 12(4), 361; https://doi.org/10.3390/axioms12040361 - 8 Apr 2023

Cited by 1 | Viewed by 1430

This article addresses trajectory tracking control of unmanned surface vessels (USVs) subject to position and velocity measurement biases. Unlike model uncertainties and external disturbances, measurement biases can lead to mismatched disturbances in system kinematics, rendering great difficulty to the USV control system design. [...] Read more.

This article addresses trajectory tracking control of unmanned surface vessels (USVs) subject to position and velocity measurement biases. Unlike model uncertainties and external disturbances, measurement biases can lead to mismatched disturbances in system kinematics, rendering great difficulty to the USV control system design. To overcome this problem, a disturbance attenuation controller was recursively synthesized by incorporating two disturbance observers into the backstepping control design. The stability argument shows that all error signals in the closed-loop system can regulate to the small neighborhoods about the origin. The proposed controller has two remarkable features: (1) By adopting two disturbance observers to estimate the mismatched and matched lumped disturbances, the proposed controller is robust against model uncertainties and external disturbances and insensitive to measurement biases. (2) Meanwhile, the proposed controller is structurally simple and user friendly. Lastly, comparative simulations were conducted to validate the obtained results. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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16 pages, 441 KiB

Open AccessArticle

Research on PDF Shape Control for Nonlinear Stochastic System Using an Approximate Solution of FPK Equation

by Lingzhi Wang, Kun Zhang, Fucai Qian and Xiaoli Zhang

Axioms 2023, 12(3), 303; https://doi.org/10.3390/axioms12030303 - 17 Mar 2023

Viewed by 1496

Abstract

In this paper, we developed a probability density function (PDF) shape control method for non-linear stochastic systems using a hybrid logistic function (HLF) as an approximate PDF of the state variable. First, the functional relationship between the hybrid logistic probability density function and [...] Read more.

In this paper, we developed a probability density function (PDF) shape control method for non-linear stochastic systems using a hybrid logistic function (HLF) as an approximate PDF of the state variable. First, the functional relationship between the hybrid logistic probability density function and the controller was established based on the Fokker–Planck–Kolmogorov (FPK) equation. Then, the optimal PDF shape controller derivation was completed using the optimization method and the inner product definition of Hilbert space. This approach is suitable for any non-linear stochastic system. To evaluate the effectiveness and performance of the proposed method, we conducted a comparison experiment with the multi-Gaussian closure (MGC) method and the exponential polynomial (EP) method. The experimental results show that, for different types of targeted PDFs (symmetric unimodal, asymmetric unimodal, bimodal, and trimodal shapes), the PDF shape controller obtained using the HLF approach can make the PDF shape of the state variable track the targeted PDF effectively. In particular, when the targeted PDF has an asymmetric or complex trimodal shape, the proposed technique has comparatively better control effects. Compared with the EP method, our method requires a much smaller number of parameters, greatly reducing the computational complexity while achieving the same control effects. This study provides another approach for controlling the PDF shape of state variables in non-linear stochastic systems, which has important research significance. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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16 pages, 2630 KiB

Open AccessArticle

Optimization of Leakage Risk and Maintenance Cost for a Subsea Production System Based on Uncertain Fault Tree

by Jianyin Zhao, Liuying Ma, Yuan Sun, Xin Shan and Ying Liu

Axioms 2023, 12(2), 194; https://doi.org/10.3390/axioms12020194 - 13 Feb 2023

Viewed by 1527

Abstract

Traditional fault tree analysis is an effective tool used to evaluate system risk if the required data are sufficient. Unfortunately, the operation and maintenance data of some complex systems are difficult to obtain due to economic or technical reasons. The solution is to [...] Read more.

Traditional fault tree analysis is an effective tool used to evaluate system risk if the required data are sufficient. Unfortunately, the operation and maintenance data of some complex systems are difficult to obtain due to economic or technical reasons. The solution is to invite experts to evaluate some critical aspect of the performance of the system. In this study, the belief degrees of the occurrence of basic events evaluated by experts are measured by an uncertain measure. Then, a system risk assessment method based on an uncertain fault tree is proposed, based on which two general optimization models are established. Furthermore, the genetic algorithm (GA) and the nondominated sorting genetic algorithm II (NSGA-II) are applied to solve the two optimization models, separately. In addition, the proposed risk assessment method is applied for the leakage risk evaluation of a subsea production system, and the two general optimization models are used to optimize the leakage risk and maintenance cost of the subsea production system. The optimization results provide a theoretical basis for practitioners to guarantee the safety of subsea production system. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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15 pages, 1537 KiB

Open AccessArticle

Condition-Based Maintenance Optimization Method Using Performance Margin

by Shuyu Li, Meilin Wen, Tianpei Zu and Rui Kang

Axioms 2023, 12(2), 168; https://doi.org/10.3390/axioms12020168 - 7 Feb 2023

Cited by 2 | Viewed by 1788

Abstract

As a maintenance strategy to reduce unexpected failures and enable safe operation, condition-based maintenance (CBM) has been widely used in recent years. The maintenance decision criteria of CBM in the literature mostly originate from statistical failure data or degradation states, few of which [...] Read more.

As a maintenance strategy to reduce unexpected failures and enable safe operation, condition-based maintenance (CBM) has been widely used in recent years. The maintenance decision criteria of CBM in the literature mostly originate from statistical failure data or degradation states, few of which can directly and effectively reflect the current state and analyze condition monitoring data, maintenance measures, and reliability together at the same time. In this paper, we introduce the performance margin as a decision criterion of CBM. We propose a condition-based maintenance optimization method using performance margin. Considering a CBM optimization problem for a degrading and periodically inspected component, a newly developed performance margin degradation model is established when three different maintenance measures become involved. Maintenance measure effect factors, maintenance decision vectors, and maintenance measure threshold vectors are developed to update the degradation model. And to build a maintenance optimization model, both cost and loss related to maintenance decision problems and reliability obtained by performance margin have been taken into consideration. Finally, a numerical example is provided to illustrate the proposed optimization method. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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24 pages, 5352 KiB

Open AccessArticle

Uncertain Programming Model for the Cross-Border Multimodal Container Transport System Based on Inland Ports

by Junchi Ma, Xifu Wang, Kai Yang and Lijun Jiang

Axioms 2023, 12(2), 132; https://doi.org/10.3390/axioms12020132 - 28 Jan 2023

Cited by 7 | Viewed by 2138

Abstract

The importance of inland ports in promoting current cross-border trade is increasingly recognized. In this work, we aim to design the entire network for the cross-border multimodal container transport system based on inland ports. Unlike previous studies, we consider strong uncertainty in cross-border [...] Read more.

The importance of inland ports in promoting current cross-border trade is increasingly recognized. In this work, we aim to design the entire network for the cross-border multimodal container transport system based on inland ports. Unlike previous studies, we consider strong uncertainty in cross-border transportation demand to be caused by a variety of realistic factors such as the global economic situation, trade policies among countries, and global epidemics, etc. To handle the demand uncertainty, we develop an uncertain programming model for the considered cross-border multimodal container transportation network design problem to minimize the expectation of the total costs, including carbon emissions, by imposing two types of chance constraints for capacity limitations. Under mild assumptions, we further convert the proposed uncertain model into its equivalent deterministic one, which can be solved by off-the-shelf solvers such as CPLEX, Gurobi, and Lingo. Finally, we illustrate the applicability of the proposed model by taking the Huaihai Economic Zone-Europe multimodal container transport system as a real-world case study. The computational results provide valuable suggestions and policy guidance regarding four issues: the inland port locations, the transportation route choices, the strategies for reducing the total cost, and the schemes for improving network performance against uncertain demand. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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17 pages, 362 KiB

Open AccessArticle

A Game—Theoretic Model for a Stochastic Linear Quadratic Tracking Problem

by Vasile Drăgan, Ivan Ganchev Ivanov and Ioan-Lucian Popa

Axioms 2023, 12(1), 76; https://doi.org/10.3390/axioms12010076 - 11 Jan 2023

Cited by 2 | Viewed by 1508

Abstract

In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them [...] Read more.

In this paper, we solve a stochastic linear quadratic tracking problem. The controlled dynamical system is modeled by a system of linear Itô differential equations subject to jump Markov perturbations. We consider the case when there are two decision-makers and each of them wants to minimize the deviation of a preferential output of the controlled dynamical system from a given reference signal. We assume that the two decision-makers do not cooperate. Under these conditions, we state the considered tracking problem as a problem of finding a Nash equilibrium strategy for a stochastic differential game. Explicit formulae of a Nash equilibrium strategy are provided. To this end, we use the solutions of two given terminal value problems (TVPs). The first TVP is associated with a hybrid system formed by two backward nonlinear differential equations coupled by two algebraic nonlinear equations. The second TVP is associated with a hybrid system formed by two backward linear differential equations coupled by two algebraic linear equations. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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19 pages, 4107 KiB

Open AccessArticle

A Joint Location–Allocation–Inventory Spare Part Optimization Model for Base-Level Support System with Uncertain Demands

by Peixuan Li, Meilin Wen, Tianpei Zu and Rui Kang

Axioms 2023, 12(1), 46; https://doi.org/10.3390/axioms12010046 - 1 Jan 2023

Cited by 3 | Viewed by 1890

Abstract

This paper copes with a joint Location-Allocation-Inventory problem in a three-echelon base-level spare part support system with epistemic uncertainty in uncertain demands of bases. The aim of the paper is to propose an optimization model under the uncertainty theory to minimize the total [...] Read more.

This paper copes with a joint Location-Allocation-Inventory problem in a three-echelon base-level spare part support system with epistemic uncertainty in uncertain demands of bases. The aim of the paper is to propose an optimization model under the uncertainty theory to minimize the total cost, which integrates crucial characterizations of the inventory control decisions and the location-allocation scheme arrangement under a periodic review order-up-to-S (T, S) policy. Uncertainty theory is introduced in this paper to characterize epistemic uncertainty, where demands are treated as uncertain variables and stockout loss is represented by value-at-risk in uncertain measurement. To solve the original uncertain optimization model, an equivalent deterministic model is derived and addressed by an improved bilevel genetic algorithm. Moreover, the proposed models and algorithm are encoded into numerical examples for supply chain programming. The results highlight the applicability of the model and the algorithm’s effectiveness in approaching the optimal solution compared with traditional genetic algorithm. Sensitivity analyses are further made for the impacts of review time and inventory capacity on different cost components. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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25 pages, 951 KiB

Open AccessArticle

Bargaining-Based Profit Allocation Model for Fixed Return Investment Water-Saving Management Contract

by Shize Liu, Xiaosheng Wang and Wei Li

Axioms 2022, 11(12), 712; https://doi.org/10.3390/axioms11120712 - 9 Dec 2022

Viewed by 1256

Abstract

Fixed Return Investment (FRI) is one of the main operating modes of a Water-Saving Management Contract (WSMC). Aiming at the critical profit allocation of FRI WSMC projects, a new profit allocation model based on bargaining theory is proposed. First, the net present value [...] Read more.

Fixed Return Investment (FRI) is one of the main operating modes of a Water-Saving Management Contract (WSMC). Aiming at the critical profit allocation of FRI WSMC projects, a new profit allocation model based on bargaining theory is proposed. First, the net present value is adopted to determine the profit interval to be allocated. Second, the bargaining process is divided into two levels. The first-level bargaining process is between a water user and an alliance, which consists of a Water Service Company (WSCO) and a financial institution. The second-level bargaining process is between the WSCO and the financial institution. Given the imbalance caused by offering first, the number of bargaining stages and sunk cost are introduced, and the equilibrium offers of the two parties in different bargaining stages are determined by using backward induction and mathematical induction. According to the feature that the number of bargaining stages is an integer in practice, the deterrence discount factors are introduced to redistribute the remaining part, and sixteen situations of profit allocation among participants are given. Third, the model analysis shows that the profit allocation of participants is closely related to the minimum profit requirements, deterrence discount factors, the number of bargaining stages, and sunk cost. Finally, the effectiveness of the model and the influence of various factors on profit allocation are verified by an example. The example shows that in the early stage of FRI WSMC, the water users enjoy more profits. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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17 pages, 454 KiB

Open AccessArticle

Optimal Control for Parabolic Uncertain System Based on Wavelet Transformation

by Yajing Gu and Yuanguo Zhu

Axioms 2022, 11(9), 453; https://doi.org/10.3390/axioms11090453 - 2 Sep 2022

Cited by 3 | Viewed by 1394

Abstract

In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed [...] Read more.

In this paper, we study a new type of optimal control problem subject to a parabolic uncertain partial differential equation where the expected value criterion is adopted in the objective function. The basic idea of Haar wavelet transformation is to transform the proposed problem into an approximate uncertain optimal control problem with arbitrary accuracy because the dimension of Haar basis tends to infinity. The relative convergence theorem is proved. An application to an optimal control problem with an uncertain heat equation is dealt with to illustrate the efficiency of the proposed method. Full article

(This article belongs to the Special Issue Advances in Uncertain Optimization and Applications)

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