AUTHOR KEYWORDS: Fuzzy derivative and integral; Fuzzy fundamental theorem of calculus; Fuzzy Taylor formula; Zadeh's extension INDEX KEYWORDS: Fuzzy set theory, Fundamental theorem of calculus; Fuzzy derivatives; Fuzzy function; Integral operators; Taylor expansions; Taylor formula; Zadeh's extension; Zadeh's extension principles, Calculations PUBLISHER: Elsevier B.V.
AUTHOR KEYWORDS: Fuzzy linear programming problems (FLP); Fuzzy simplex method; Ranking and selection INDEX KEYWORDS: Fuzzy set theory; Intelligent systems; Linear programming, Fully fuzzy linear programming; Fuzzy environments; Fuzzy linear programming problems; Fuzzy simplex; Gaussian elimination; Linear programming problem; Ranking and selection; Uncertain environments, Problem solving PUBLISHER: Institute of Electrical and Electronics Engineers Inc.
INDEX KEYWORDS: Intelligent systems, Euler-Lagrange; Fractional derivatives; Necessary optimality condition; New results; Riemann-liouville h-differentiability; Riemann-Liouville sense; Variational problems, Variational techniques PUBLISHER: Institute of Electrical and Electronics Engineers Inc.
AUTHOR KEYWORDS: Approximation; Discretization; Haar wavelet; Non-linear time-delay system; Optimal control INDEX KEYWORDS: Mathematical transformations; Nonlinear programming; Numerical methods; Optimal control systems; Time delay, Approximation; Discretizations; Haar wavelets; Non linear; Optimal controls, Delay control systems PUBLISHER: Oxford University Press
This paper presents a hybrid algorithm for solving complex optimal control problems based on decomposition. The general finite-time optimal control problem for a class of hybrid dynamical systems is considered, which has not been solved in a decomposed way by existing methods. The problem is first decomposed into a master problem and a subproblem, and then the two are linked via logic-based Benders decomposition. Computational experiments have been carried out for the considered problem. The results show that the proposed algorithm could substantially reduce the solving time, compared with directly solving by mixed integer solvers.
INDEX KEYWORDS: Benders decomposition; Computational experiment; Finite-time optimal control; Hybrid algorithms; Hybrid dynamical systems; Mixed integer; Optimal control problem; Optimal controls, Algorithms; Control; Hybrid computers; Optimization, Hybrid systems
AUTHOR KEYWORDS: Calculus of variations; Difference equation; Linear programming; Measure theory INDEX KEYWORDS: Approximation algorithms; Linear programming; Measurement theory; Nonlinear equations; Optimization; Problem solving, Approximate solutions; Calculus of variations; Nonlinear difference equations, Difference equations
AUTHOR KEYWORDS: Discrete optimal control; Linear programming; Measure theory INDEX KEYWORDS: Approximation theory; Linear programming; Nonlinear systems, Discrete optimal control; Measure theory, Optimal control systems
AUTHOR KEYWORDS: Fredholm integral equation; Linear programming; Measure theory; Optimal control problem INDEX KEYWORDS: Convergence of numerical methods; Linear programming, Fredholm integral equations; Measure theory; Optimal control problem, Nonlinear equations
AUTHOR KEYWORDS: Approximation theory; Discretization; Linear programming; Measure theory; Nonlinear systems INDEX KEYWORDS: Approximation theory; Linear programming; Linearization; Time varying systems, Discretization; L2-norm; Linear time-varying system; Measure theory, Nonlinear systems
In this paper we present a new method for designing a nozzle. In fact the problem is to find the optimal domain for the solution of a linear or nonlinear boundary value PDE, where the boundary condition is defined over an unspecified domain. By an embedding process, the problem is first transformed to a new shape-measure problem, and then this new problem is replaced by another in which we seek to minimize a linear form over a subset of linear equalities. This minimization is global, and the theory allows us to develop a computational method to find the solution by a finite-dimensional linear programming problem.
AUTHOR KEYWORDS: Approximation theory; Linear programming; Measure theory; Nozzle problem; Optimal control; Optimal shape PUBLISHER: Journal of Applied Mathemathics
In this paper we consider a heat flow in an inhomogeneous body without internal source. There exists special initial and boundary conditions in this system and we intend to find a convenient coefficient of heat conduction for this body so that body cool off as much as possible after definite time. We consider this problem in a general form as an optimal control problem which coefficient of heat conduction is optimal function. Then we replace this problem by another in which we seek to minimize a linear form over a subset of the product of two measures space defined by linear equalities. Then we construct an approximately optimal control.
AUTHOR KEYWORDS: Approximation theory; Heat equation; Linear programming; Measure theory PUBLISHER: Journal of Applied Mathemathics
AUTHOR KEYWORDS: Approximation; Controllability; Heat equation; Linear programming; Measure theory; Moment problem INDEX KEYWORDS: Controllability; Heat transfer; Linear programming; Optimal control systems, Approximation; Finite dimensional linear programming; Heat equation; Linear programming problem; Measure theory; Moment problems; Optimal control function; Positive linear functionals, Partial differential equations PUBLISHER: Springer Verlag
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