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

Chiu, Wei‐Yu

doi:10.1109/tsmc.2016.2571323

Cited by 36 publications

(25 citation statements)

References 58 publications

(100 reference statements)

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“…hold true with at least one strict inequality. A solution is nondominated (also called Pareto optimal or Pareto efficient) if improving one objective value must yield a degradation in the other objective value [82]. A set of Pareto optimal solutions or nondominated solutions is desired.…”

Section: Pareto Optimal Demand Response Programmentioning

confidence: 99%

Pareto Optimal Demand Response Based on Energy Costs and Load Factor in Smart Grid

Chiu

Hsieh

Chen

2020

IEEE Trans. Ind. Inf.

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Demand response for residential users is essential to the realization of modern smart grids. This paper proposes a multiobjective approach to designing a demand response program that considers the energy costs of residential users and the load factor of the underlying grid. A multiobjective optimization problem (MOP) is formulated and Pareto optimality is adopted. Stochastic search methods of generating feasible values for decision variables are proposed. Theoretical analysis is performed to show that the proposed methods can effectively generate and preserve feasible points during the solution process, which comparable methods can hardly achieve. A multiobjective evolutionary algorithm is developed to solve the MOP, producing a Pareto optimal demand response (PODR) program. Simulations reveal that the proposed method outperforms the comparable methods in terms of energy costs while producing a satisfying load factor. The proposed PODR program is able to systematically balance the needs of the grid and residential users.

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Section: Pareto Optimal Demand Response Programmentioning

confidence: 99%

Pareto Optimal Demand Response Based on Energy Costs and Load Factor in Smart Grid

Chiu

Hsieh

Chen

2020

IEEE Trans. Ind. Inf.

Self Cite

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“…In addition, several studies have been carried out on nonlinear SDSP problems 39 . In Reference 40, a numerical solution to reduce variables is presented. The principle of the approach of Reference 40 is dividing the unknown variables into two groups of external and internal variables.…”

Section: Introductionmentioning

confidence: 99%

“…In Reference 40, a numerical solution to reduce variables is presented. The principle of the approach of Reference 40 is dividing the unknown variables into two groups of external and internal variables. As a result, a BMI problem can be transformed into an unconstrained optimization problem with less decision‐making variables.…”

Section: Introductionmentioning

confidence: 99%

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

Javanmardi

Dehghani

Mohammadi

et al. 2020

Intl J Robust & Nonlinear

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This article proposes relaxed sufficient bilinear matrix inequality (BMI) conditions to design a gain-scheduling controller for nonlinear systems described by polytopic-linear parameter varying (LPV) representations. The obtained conditions are derived based on a nonquadratic Lyapunov function and a parallel distributed compensator scheme. The controller design procedure involves some novel null terms and leads to a BMI problem, which hardly has been solved in previous researches. Furthermore, to effectively solve the BMI conditions, a novel sequential approach is proposed which convert the overall BMI problem into linear matrix inequality (LMI) constraints and some simpler BMI conditions with fewer dimensions than the original one. Initially, the LMI conditions are solved as a convex optimization problem. Second, the BMI terms are iteratively linearized near the feasible solutions of the LMIs and each solution candidates for the BMI constraints. Finally, the linearized condition is solved as an eigenvalue problem. To show the merits of the proposed approach, several numerical comparisons and simulations are provided.

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“…Though the approaches based on the generalized Benders decomposition and branch-and-bound algorithms are global methods, it is in general impractical to solve large-scale problems. A solution method of reduction of variables is proposed for BMI problems in system and control designs in [36]. The proposed method consists of a principle of variable classification, a procedure for problem transformation and a hybrid algorithm.…”

Section: Introductionmentioning

confidence: 99%

A Lifting-Penalty Method for Quadratic Programming with a Quadratic Matrix Inequality Constraint

Liu

Yang

2020

Mathematics

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In this paper, a lifting-penalty method for solving the quadratic programming with a quadratic matrix inequality constraint is proposed. Additional variables are introduced to represent the quadratic terms. The quadratic programming is reformulated as a minimization problem having a linear objective function, linear conic constraints and a quadratic equality constraint. A majorization–minimization method is used to solve instead a l 1 penalty reformulation of the minimization problem. The subproblems arising in the method can be solved by using the current semidefinite programming software packages. Global convergence of the method is proven under some suitable assumptions. Some examples and numerical results are given to show that the proposed method is feasible and efficient.

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

Cited by 36 publications

References 58 publications

Pareto Optimal Demand Response Based on Energy Costs and Load Factor in Smart Grid

Pareto Optimal Demand Response Based on Energy Costs and Load Factor in Smart Grid

Bilinear matrix inequality‐based nonquadratic controller design for polytopic‐linear parameter varying systems

A Lifting-Penalty Method for Quadratic Programming with a Quadratic Matrix Inequality Constraint

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