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Soft Computing
Published in: Soft Computing 4/2024

08-01-2024 | Fuzzy systems and their mathematics

Sufficient conditions for interval-valued optimal control problems in admissible orders

Authors: Lifeng Li, Jianke Zhang

Published in: Soft Computing | Issue 4/2024

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Abstract

This paper addresses the optimal control problems with an interval-valued objective function. We consider a type of total order relationships \(\le _{adm}\) between two intervals. For each total order relationship, Kuhn–Tucker sufficient conditions for the optimal control problems with an interval-valued objective function are obtained. A numerical example is considered and solved. Kuhn–Tucker sufficient conditions provided under the total order relationship \(\le _{adm}\) are sufficient conditions under the partial order relationship \(\preceq _{LU}\) for interval-valued optimal control problems. The results of this paper could help construct evolutionary algorithms to solve interval-valued optimal control problems.
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Literature
Abu Arqub O (2017) Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations. Neural Comput Appl 28:1591–1610CrossRef
Abu Arqub O, Singh J, Maayah B et al (2023a) Reproducing kernel approach for numerical solutions of fuzzy fractional initial value problems under the Mittag–Leffler kernel differential operator. Math Methods Appl Sci 46(7):7965–7986
Abu Arqub O, Singh J, Alhodaly M (2023b) Adaptation of kernel functions-based approach with Atangana–Baleanu–Caputo distributed order derivative for solutions of fuzzy fractional Volterra and Fredholm integrodifferential equations. Math Methods Appl Sci 46(7):7807–7834
Abualigah L, Yousri D, Abd Elaziz M et al (2021a) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250
Abualigah L, Diabat A, Mirjalili S et al (2021b) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609
Abualigah L, Abd Elaziz M, Sumari P et al (2022) Reptile search algorithm (RSA): a nature-inspired meta-heuristic optimizer. Expert Syst Appl 191:116158CrossRef
Agarwal D, Singh P, El Sayed MA (2023) The Karush–Kuhn–Tucker (KKT) optimality conditions for fuzzy-valued fractional optimization problems. Math Comput Simul 205:861–877MathSciNetCrossRef
Alshammari M, Al-Smadi M, Arqub OA et al (2020) Residual series representation algorithm for solving fuzzy duffing oscillator equations. Symmetry 12(4):572ADSCrossRef
Bhunia AK, Samanta SS (2014) A study of interval metric and its application in multi-objective optimization with interval objectives. Comput Ind Eng 74:169–178CrossRef
Bustince H, Fernandez J, Kolesárová A et al (2013a) Generation of linear orders for intervals by means of aggregation functions. Fuzzy Sets Syst 220:69–77
Bustince H, Galar M, Bedregal B et al (2013b) A new approach to interval-valued Choquet integrals and the problem of ordering in interval-valued fuzzy set applications. IEEE Trans Fuzzy Syst 21:1150–1162
Chai R, Savvaris A, Tsourdos A et al (2020) Solving multiobjective constrained trajectory optimization problem by an extended evolutionary algorithm. IEEE Trans Cybern 50(4):1630–1643PubMedCrossRef
Chakraverty S, Mahato NR, Jeswal SK (2022) Sign function and ANN based pole placement for computing interval controls. ISA Trans 119:17–24PubMedCrossRef
Chalco-Cano Y, Lodwick WA, Rufian-Lizana A (2013) Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optim Decis Mak 12:305–322MathSciNetCrossRef
Cheng J, Liu Z, Wu Z et al (2016) Direct optimization of uncertain structures based on degree of interval constraint violation. Comput Struct 164:83–94CrossRef
Chiu C, Hung Y (2020) One wheel vehicle real world control based on interval type 2 fuzzy controller. Mechatronics 70:102387CrossRef
Cui Y, Pang JS (2021) Modern nonconvex nondifferentiable optimization, Society for Industrial and Applied Mathematics
Das S, Mondal R, Shaikh AA et al (2022) An application of control theory for imperfect production problem with carbon emission investment policy in interval environment. J Frankl Inst 359(5):1925–1970MathSciNetCrossRef
Das S, Mandal G, Manna AK et al (2023) Effects of emission reduction and rework policy in a production system of green products: an interval valued optimal control theoretic approach. Comput Ind Eng 179:109212CrossRef
EL Sayed MA, Abo-Sinna MA (2021) A novel approach for full intuitionistic fuzzy multi-objective fractional transportation problem. Alex Eng J 60:1447–1463CrossRef
El Sayed MA, Baky IA, Singh P (2020) A modified TOPSIS approach for solving stochastic fuzzy multi-level multi-objective fractional decision making problem. Opsearch 57:1374–1403MathSciNetCrossRef
El Sayed MA, Farahat FA, Elsisy MA (2022) A novel interactive approach for solving uncertain bi-level multi-objective supply chain model. Comput Ind Eng 169:108225CrossRef
Elsisy MA, Elsaadany AS, El Sayed MA (2020) Using interval operations in the Hungarian method to solve the fuzzy assignment problem and its application in the rehabilitation problem of valuable buildings in Egypt. Complexity 2020:1–11
Elsisy MA, El Sayed MA, Abo-Elnaga Y (2021) A novel algorithm for generating Pareto frontier of bi-level multi-objective rough nonlinear programming problem. Ain Shams Eng J 12(2):2125–2133CrossRef
Ezugwu AE, Agushaka JO, Abualigah L et al (2022) Prairie dog optimization algorithm. Neural Comput Appl 34:20017–20065CrossRef
Farhadinia B (2014) Pontryagin’s minimum principle for fuzzy optimal control problems. Iran J Fuzzy Syst 11:27–43MathSciNet
Fu C, Cao L (2019) An uncertain optimization method based on interval differential evolution and adaptive subinterval decomposition analysis. Adv Eng Softw 134:1–9CrossRef
Ge X, Zhu Y (2013) A necessary condition of optimality for uncertain optimal control problem. Fuzzy Optim Decis Mak 12:41–51MathSciNetCrossRef
Gong DW, Ji XF, Sun J et al (2014) Interactive evolutionary algorithms with decision-makers preferences for solving interval multi-objective optimization problems. Neurocomputing 137:241–251CrossRef
Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48:219–225CrossRef
Kushner HJ (1972) Necessary conditions for continuous parameter stochastic optimization problems. SIAM J Control 10:550–565MathSciNetCrossRef
Leal U, Lodwick W, Silva G et al (2021) Interval optimal control for uncertain problems. Fuzzy Sets Syst 402:142–154MathSciNetCrossRef
Lian Z, Shi P, Lim C (2021) Hybrid-triggered interval type-2 fuzzy control for networked systems under attacks. Inf Sci 567:332–347MathSciNetCrossRef
Mangasaria OL (1966) Sufficient conditions for the optimal control of nonlinear systems. SIAM J Control 4:139–152MathSciNetCrossRef
Manna AK, Bhunia AK (2022) Investigation of green production inventory problem with selling price and green level sensitive interval-valued demand via different metaheuristic algorithms. Soft Comput 26(19):10409–10421CrossRef
Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. SIAM, PhiladelphiaCrossRef
Neumaier A (1990) Interval methods for systems of equations. Cambridge University Press, Cambridge
Oyelade ON, Ezugwu AE, Mohamed TIA et al (2022) Ebola optimization search algorithm: a new nature-inspired metaheuristic optimization algorithm. IEEE Access 10:16150–16177CrossRef
Ruidas S, Seikh MR, Nayak PK (2021) A production inventory model with interval-valued carbon emission parameters under price-sensitive demand. Comput Ind Eng 154:107154CrossRef
Ruidas S, Seikh MR, Nayak PK et al (2023) An interval-valued green production inventory model under controllable carbon emissions and green subsidy via particle swarm optimization. Soft Comput 27:9709–9733CrossRef
Sahoo L, Bhunia AK, Kapur PK (2012) Genetic algorithm based multi-objective reliability optimization in interval environment. Comput Ind Eng 62:152–160CrossRef
Sampath Dakshina Murthy A, DrS KR, DrK SN et al (2015) Tracking of a manoeuvering target ship using radar measurements. Indian J Sci Technol 8:0974–5645CrossRef
Sampath Dakshina Murthy A, Pavani T, Lakshmi K (2016) An application of firefly hybrid extended Kalman filter tracking a reentry object. Indian J Sci Technol 9:28
Treanţă S (2021) On a new class of interval-valued variational control problems. In: Debnath P, Konwar N, Radenović S (eds) Metric fixed point theory. Forum for interdisciplinary mathematics. Springer, Singapore
Treanţă S (2022) Characterization results of solutions in interval-valued optimization problems with mixed constraints. J Glob Optim 82:951–964MathSciNetCrossRef
Van Su T, Dinh DH (2020) Duality results for interval-valued pseudoconvex optimization problem with equilibrium constraints with applications. Comput Appl Math 39:127MathSciNetCrossRef
Wang L, Liu J, Yang C et al (2021) A novel interval dynamic reliability computation approach for the risk evaluation of vibration active control systems based on PID controllers. Appl Math Model 92:422–446MathSciNetCrossRef
Wu HC (2007) The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function. Eur J Oper Res 176:46–59MathSciNetCrossRef
Xu Z (2020) Stochastic recursive optimal control problem with obstacle constraint involving diffusion type control. Adv Differ Equ 2020:381MathSciNetCrossRef
Xu ZS, Yager RR (2006) Some geometric aggregation operators based on intuitionistic fuzzy sets. Int J Gen Syst 35:417–433MathSciNetCrossRef
Yuan Z, Wang W, He S (2020) Interval-based LQR strategy for optimal control of proton exchange membrane fuel cell system with interval uncertainties. ISA Trans 100:334–345CrossRef
Zhang CL, Huang NJ (2022) On Ekeland’s variational principle for interval-valued functions with applications. Fuzzy Sets Syst 436:152–174MathSciNetCrossRef
Zhou XY (1996) Sufficient conditions of optimality for stochastic systems with controllable diffusions. IEEE Autom Control 41:1176–1179MathSciNetCrossRef
Zhou XY (1998) Stochastic near-optimal controls: necessary and sufficient conditions for near-optimality. SIAM J Control Optim 36:929–947MathSciNetCrossRef
Metadata
Title
Sufficient conditions for interval-valued optimal control problems in admissible orders
Authors
Lifeng Li
Jianke Zhang
Publication date
08-01-2024
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 4/2024
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-023-09563-1

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