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Stability Analysis to Parametric multiobjective optimal control Problems

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2025年第1期204卷 1-32页

作者： Anh, Lam Quoc Tai, Vo Thanh Tam, Tran Ngoc Can Tho Univ Teacher Coll Dept Math Can Tho Vietnam An Giang Univ Fac Educ Dept Math Long Xuyen Vietnam Vietnam Natl Univ Ho Chi Minh City Vietnam Can Tho Univ Coll Nat Sci Dept Math Can Tho Vietnam

In this paper, we investigate continuity properties of the efficient solution map of a parametric nonlinear multiobjective optimal control problem. First, by using the equimeasurability condition of the admissible control set, we obtain the compactness and arcwise connectedness of the feasible solution set. Next, we suggest new concepts of the quasi-arcwise connected integrand and employ them to study the semicontinuity of the efficient solution map of this problem. When the multiobjective function does not satisfy these conditions, we propose an estimation hypothesis for approximate efficient solutions to address lower semicontinuity conditions of the efficient solution map of the reference problem. To illustrate the applicability, we apply the obtained results to two practical models, including Glucose model and Epidemic model.

关键词： multiobjective optimal control Glucose and epidemic models Stability analysis Arcwise connected integrand Epi-convergence

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Data-Knowledge-Driven multiobjective Adaptive optimal control for Wastewater Treatment Processes Under Multiple Operating Conditions

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第3期55卷 1056-1069页

作者： Han, Hong-Gui Zhang, Yue Sun, Hao-Yuan Liu, Zheng Qiao, Junfei Beijing Univ Technol Sch Informat Sci & Technol Beijing 100124 Peoples R China Beijing Univ Technol Beijing Key Lab Computat Intelligence & Intelligen Beijing 100124 Peoples R China

Wastewater treatment processes (WWTPs) are operated under multiple operating conditions. Designing an appropriate optimal control strategy based on the identification of operating conditions is crucial for ensuring the safe operation of WWTPs. To effectively deal with the problem of multiple operating conditions in WWTPs, a data-knowledge-driven multiobjective adaptive optimal control (DK-MAOC) strategy is proposed. First, a fuzzy neural network (FNN) is employed as the prediction model to obtain the concentrations of nitrate and total nitrogen. Then, the operating conditions of WWTPs can be determined. Second, an adaptive objective function (AOF) is proposed to dynamically adjust the weights of operating indices to meet the operational requirements of each operating condition. In particular, the AOF integrates operating requirements and tracking errors to simultaneously consider the feasibility of the controller when solving setpoints. Third, due to the differences in data distribution under each operating condition, real-time data during condition changing is insufficient to accurately predict. A data-knowledge-driven model, incorporating operational knowledge into the FNN-based predictive model, is established to predict the future dynamics of WWTPs. Finally, a collaborative gradient descent algorithm is proposed to simultaneously solve for setpoints and control laws. The effectiveness of the proposed DK-MAOC is tested on the Benchmark Simulation Model No. 1. The experimental results indicate that DK-MAOC can effectively avoid the situation of effluent nitrate nitrogen and total nitrogen exceeding the standards while reducing energy consumption of WWTPs. Therefore, the proposed DK-MAOC can guarantee optimal operation of WWTPs.

关键词： optimal control Linear programming Predictive models Process control Data models Nitrogen Standards Fuzzy neural networks Fuzzy control Optimization Data-knowledge-driven multiobjective optimal control multiple operating conditions wastewater treatment process (WWTP)

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multiobjective optimal control With Safety as a Priority

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IEEE TRANSACTIONS ON control SYSTEMS TECHNOLOGY 2018年第3期26卷 1015-1027页

作者： Lesser, Kendra Abate, Alessandro Verus Res Albuquerque NM 87110 USA Univ Oxford Dept Comp Sci Oxford OX1 3QD England

This paper develops a lexicographic approach to multiobjective optimal control on models for cyber-physical systems, encompassing in particular stochasticity, limited access to model variables (partial observations), and possibly hybrid (continuous and discrete) dynamics (with the finite-state partially observable Markov decision process framework as a known special instance). The technique is showcased in two new case studies in the area of smart buildings. Technically, the main achievements of this paper are as follows: the application of the lexicographic framework to multiobjective optimization including quantitative probabilistic safety requirements, thus leading to a principled and scalable integration of correct-by-design synthesis for safety and optimal synthesis for performance, the novel extension of the lexicographic framework to partially observed stochastic models with continuous (possibly hybrid) dynamics, and the emphasis on computational aspects, including the use of compact and approximate representations of value functions combined with the quantification of error bounds on model abstractions.

关键词： Correct-by-design control multiobjective optimal control partially observable stochastic systems

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multiobjective optimal control for wastewater treatment process using adaptive MOEA/D

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APPLIED INTELLIGENCE 2019年第3期49卷 1098-1126页

作者： Zhou, Hongbiao Qiao, Junfei Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China Beijing Key Lab Computat Intelligence & Intellige Beijing 100124 Peoples R China Huaiyin Inst Technol Fac Automat Huaian 223003 Peoples R China

Through the analysis of the biological wastewater treatment process (WWTP), a multiobjective optimal control strategy is developed with the usage of energy consumption (EC) and effluent quality (EQ) as objectives to be optimized. To effectively handle the multiobjective optimization problem (MOP) with complex Pareto-optimal front (POF), an adaptive multiobjective evolutionary algorithm based on decomposition (AMOEA/D) is proposed in this paper. Since the efficiency of the multiple reference points and two-phase optimization strategies in solving MOPs with complex POFs has been proved. In the proposed AMOEA/D, an auto-switching strategy based on the aggregation function enhancement is designed to automatically make the algorithm switch from the first phase to the second phase. Besides, an adaptive differential evolution strategy is introduced into AMOEA/D to balance exploration and exploitation during the evolutionary process. Finally, the dynamic optimization, intelligent decision and bottom tracking control of the set-points of the dissolved oxygen and nitrate nitrogen in the WWTP are achieved via the combination of AMOEA/D with the self-organizing fuzzy neural network approximator and the self-organizing fuzzy neural network controller. The international benchmark simulation model No. 1 (BSM1) is utilized for experimental verification. Simulation results demonstrate that the proposed AMOEA/D can effectively reduce the EC of the WWTP under the premise of ensuring effluent parameters to meet the effluent discharge standards.

关键词： Wastewater treatment process multiobjective optimal control MOEA/D Two-phase optimization Auto-switching Adaptive differential evolution strategy

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multiobjective optimal control of the linear wave equation

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AIN SHAMS ENGINEERING JOURNAL 2014年第4期5卷 1299-1305页

作者： Zarei, Hassan Bahrmand, Mehdi Rezai Payame Noor Univ Dept Math Tehran Iran

In this paper, we propose a method for the solution of a multiobjective optimal control problem (MOOCP) in a linear distributed-parameter system governed by a wave equation. An explicit solution for the wave equation is derived and the control problem of this distributedparameter system is reduced to an approximate multiobjective programming problem. The fuzzy goals are incorporated for objectives and the equilibrium problem in terms of maximization of the degree of attainment for the aggregated fuzzy goals is considered. The solution of the equilibrium optimization problem is a Pareto optimal solution with the best satisfaction performance which is achieved by using a metaheuristic algorithm such as the simulated annealing (SA) together with the simplex method of linear programming (LP) problems. An illustrative numerical example is presented to indicate the efficiency of the proposed method and the capability of the SA in finding optimal solution compared with two popular metaheurestics. (C) 2014 Production and hosting by Elsevier B. V. on behalf of Ain Shams University.

关键词： Linear distributed-parameter systems multiobjective optimal control multiobjective programming Fuzzy programming Fuzzy goals Metaheuristic algorithms

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Second-Order Lagrange Multiplier Rules in multiobjective optimal control of Semilinear Parabolic Equations

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SET-VALUED AND VARIATIONAL ANALYSIS 2022年第1期30卷 257-281页

作者： Dinh, Tuan Nguyen Univ Econ Ho Chi Minh City Dept Math & Stat 59C Nguyen Dinh ChieuD-3 Ho Chi Minh City Vietnam Univ Econ Ho Chi Minh City Inst Appl Math 59C Nguyen Dinh ChieuD-3 Ho Chi Minh City Vietnam

We consider multiobjective optimal control problems for semilinear parabolic systems subject to pointwise state constraints, integral state-control constraints and pointwise state-control constraints. In addition, the data of the problems need not be twice Frechet differentiable. Employing the second-order directional derivative (in the sense of Demyanov-Pevnyi) for the involved functions, we establish necessary optimality conditions, via second-order Lagrange multiplier rules of Fritz-John type, for local weak Pareto solutions of the problems.

关键词： multiobjective optimal control Semilinear parabolic equation Necessary second-order optimality condition Local weak Pareto solution Second-order directional derivative

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APPROXIMATION OF THE PARETO optimal SET FOR multiobjective optimal control PROBLEMS USING VIABILITY KERNELS

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ESAIM-control OPTIMISATION AND CALCULUS OF VARIATIONS 2014年第1期20卷 95-115页

作者： Guigue, Alexis Univ British Columbia Dept Math Vancouver BC V6T 1Z2 Canada

This paper provides a convergent numerical approximation of the Pareto optimal set for finite-horizon multiobjective optimal control problems in which the objective space is not necessarily convex. Our approach is based on Viability Theory. We first introduce a set-valued return function V and show that the epigraph of V equals the viability kernel of a certain related augmented dynamical system. We then introduce an approximate set-valued return function with finite set-values as the solution of a multiobjective dynamic programming equation. The epigraph of this approximate set-valued return function equals to the finite discrete viability kernel resulting from the convergent numerical approximation of the viability kernel proposed in [P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre. Birkhauser, Boston (1999) 177-247. P. Cardaliaguet, M. Quincampoix and P. Saint-Pierre, Set-Valued Analysis 8 (2000) 111-126]. As a result, the epigraph of the approximate set-valued return function converges to the epigraph of V. The approximate set-valued return function finally provides the proposed numerical approximation of the Pareto optimal set for every initial time and state. Several numerical examples illustrate our approach.

关键词： multiobjective optimal control Pareto optimality viability theory convergent numerical approximation dynamic programming

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Adaptive differential dynamic programming for multiobjective optimal control

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AUTOMATICA 2002年第6期38卷 1003-1015页

作者： Liao, LZ Li, DA Chinese Univ Hong Kong Dept Syst Engn & Engn Management Sha Tin Hong Kong Peoples R China Hong Kong Baptist Univ Dept Math Kowloon Hong Kong Peoples R China

An efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure. For a multiobjective control problem with a general separable structure, the "optimal" weighting coefficients for various performance indices are time-varying as the system evolves along any noninferior trajectory. Recognizing this prominent feature in multiobjective control, the proposed adaptive differential dynamic programming methodology combines a search process to identify an optimal time-varying weighting sequence with the solution concept in the conventional differential dynamic programming. Convergence of the proposed adaptive differential dynamic programming methodology is addressed. (C) 2002 Elsevier Science Ltd. All rights reserved.

关键词： multiobjective optimal control dynamic programming multiobjective dynamic programming differential dynamic programming adaptive differential dynamic programming

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Second-Order Lagrange Multiplier Rules in multiobjective optimal control of Infinite Dimensional Systems Under State Constraints and Mixed Pointwise Constraints

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APPLIED MATHEMATICS AND OPTIMIZATION 2021年第SUPPL 2期84卷 1521-1553页

作者： Tuan Nguyen Dinh Univ Econ Ho Chi Minh City Dept Math & Stat 59C Nguyen Dinh ChieuD3 Ho Chi Minh City Vietnam Univ Econ Ho Chi Minh City Inst Appl Math 59C Nguyen Dinh ChieuD3 Ho Chi Minh City Vietnam

We investigate a multiobjective optimal control problem, governed by a strongly continuous semigroup operator in an infinite dimensional separable Banach space, and with final-state constraints, pointwise pure state constraints and a mixed pointwise control-state constraint. Basing on necessary optimality conditions obtained for an abstract multiobjective optimization framework, we establish a second-order Lagrange multiplier rule, of Fritz-John type, for local weak Pareto solutions of the problem under study. As a consequence of the main result, we also derive a multiplier rule for a multiobjective optimal control model driven by a bilinear system being affine-linear in the control, and with an objective function of continuous quadratic form.

关键词： multiobjective optimal control Necessary second-order optimality condition Local weak Pareto solution Semigroup structure Banach space-valued integration Bilinear control system

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SET-VALUED RETURN FUNCTION AND GENERALIZED SOLUTIONS FOR multiobjective optimal control PROBLEMS (MOC)

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SIAM JOURNAL ON control AND OPTIMIZATION 2013年第3期51卷 2379-2405页

作者： Guigue, A. Univ British Columbia Dept Math Vancouver BC V6T 1Z2 Canada

In this paper, we consider a multiobjective optimal control problem where the preference relation in the objective space is defined in terms of a pointed convex cone containing the origin, which defines generalized Pareto optimality. For this problem, we introduce the set-valued return function V and provide a unique characterization for V in terms of contingent derivative and coderivative for set-valued maps, which extends two previously introduced notions of generalized solution to the Hamilton-Jacobi equation for single objective optimal control problems.

关键词： multiobjective optimal control generalized Pareto optimality dynamic programming set-valued maps contingent derivative coderivative

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