Multiobjective controller design by solving a multiobjective matrix inequality problem

Chiu, Wei‐Yu

doi:10.1049/iet-cta.2014.0026

Cited by 15 publications

(13 citation statements)

References 49 publications

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“…Currently, DE has been successfully applied to solve optimization problems in a considerable number of fields, such as electrical and power systems [24], [25], manufacturing science and operational research [26], [27], automotive design [28], and controller design [13], [14], [15].…”

Section: B Differential Evolution (De)mentioning

confidence: 99%

“…, and x t r 4 from the population; 8 Randomly choose a F value from F pool and a CR value from CR pool ; , and x t r 2 from the population ; 13 Randomly choose a F value from F pool and a CR value from CR pool ;…”

Section: A Motivationmentioning

confidence: 99%

“…Note that no other single algorithm can accomplish this [12]. More importantly, its search ability has been demonstrated in many real-world applications [13], [14], [15].…”

mentioning

confidence: 99%

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Composite Differential Evolution for Constrained Evolutionary Optimization

Wang

et al. 2019

IEEE Trans. Syst. Man Cybern, Syst.

126

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Abstract-When solving constrained optimization problems by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite differential evolution, the feasibility rule and the ε constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated constrained optimization problems. By assembling the above techniques together, a constrained composite differential evolution is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

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Section: B Differential Evolution (De)mentioning

confidence: 99%

Section: A Motivationmentioning

confidence: 99%

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Composite Differential Evolution for Constrained Evolutionary Optimization

Wang

et al. 2019

IEEE Trans. Syst. Man Cybern, Syst.

126

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“…The domain Ω lies in the Euclidean space R M for some positive integer M . The associated terminology is presented as follows [43]- [45].…”

Section: Problem Formulation and Variablementioning

confidence: 99%

Method of Reduction of Variables for Bilinear Matrix Inequality Problems in System and Control Designs

Chiu

2017

IEEE Trans. Syst. Man Cybern, Syst.

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Abstract-Bilinear matrix inequality (BMI) problems in system and control designs are investigated in this paper. A solution method of reduction of variables (MRV) is proposed. This method consists of a principle of variable classification, a procedure for problem transformation, and a hybrid algorithm that combines deterministic and stochastic search engines. The classification principle is used to classify the decision variables of a BMI problem into two categories: external and internal variables. Theoretical analysis is performed to show that when the classification principle is applicable, a BMI problem can be transformed into an unconstrained optimization problem that has fewer decision variables. Stochastic search and deterministic search are then applied to determine the decision variables of the unconstrained problem externally and explore the internal problem structure, respectively. The proposed method can address feasibility, singleobjective, and multiobjective problems constrained by BMIs in a unified manner. A number of numerical examples in system and control designs are provided to validate the proposed methodology. Simulations show that the MRV can outperform existing BMI solution methods in most benchmark problems and achieve similar levels of performance in the remaining problems.Index Terms-Bilinear matrix inequality (BMI), BMI solution methods, method of reduction of variables (MRV), multiobjective BMI problems, spectral abscissa optimization, static output feedback.

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“…The ratio related to index j in (21) can represent the normalized improvement in the jth dimension [41]. The antibody p * selected by (21) can be characterized as follows: it maximizes the minimum improvement in order not to advantage one particular objective.…”

Section: End Whilementioning

confidence: 99%

A Multiobjective Approach to Multimicrogrid System Design

Chiu

Sun

Poor

2015

IEEE Trans. Smart Grid

112

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Abstract-The main goal of this study is to design a market operator (MO) and a distribution network operator (DNO) for a network of microgrids in consideration of multiple objectives. This is a high-level design and only those microgrids with nondispatchable renewable energy sources are considered. For a power grid in the network, the net value derived from providing power to the network must be maximized. For a microgrid, it is desirable to maximize the net gain derived from consuming the received power. Finally, for an independent system operator, stored energy levels at microgrids must be maintained as close as possible to storage capacity to secure network emergency operation. To achieve these objectives, a multiobjective approach is proposed: the price signal generated by the MO and power distributed by the DNO are assigned based on a Pareto optimal solution of a multiobjective optimization problem. By using the proposed approach, a fair scheme that does not advantage one particular objective can be attained. Simulations are provided to validate the proposed methodology.

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Multiobjective controller design by solving a multiobjective matrix inequality problem

Cited by 15 publications

References 49 publications

Composite Differential Evolution for Constrained Evolutionary Optimization

Composite Differential Evolution for Constrained Evolutionary Optimization

Method of Reduction of Variables for Bilinear Matrix Inequality Problems in System and Control Designs

A Multiobjective Approach to Multimicrogrid System Design

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