Biorthogonal multiwavelets on the interval for solving multidimensional fractional optimal control problems with inequality constraint
Elmira Ashpazzadeh, Mehrdad Lakestani, Ahmet Yıldırım
Abstract
Summary This article proposes a new numerical approach for solving fractional optimal control problems including state and control inequality constraints using new biorthogonal multiwavelets. The properties of biorthogonal multiwavelets are first given. The Riemann‐Liouville fractional integral operator for biorthogonal multiwavelets is utilized to reduce the solution of optimal control problems to a nonlinear programming one, to which existing, well‐developed algorithms may be applied. In order to save the memory requirement and computation time, a threshold procedure is applied to obtain algebraic equations. The method is computationally very attractive and gives very accurate results.
Topics & Concepts
Biorthogonal systemMathematicsFractional calculusConstraint (computer-aided design)Fractional programmingApplied mathematicsOperator (biology)Nonlinear systemOptimal controlMathematical optimizationNonlinear programmingComputer scienceWaveletWavelet transformGeometryArtificial intelligenceChemistryTranscription factorRepressorBiochemistryPhysicsQuantum mechanicsGeneFractional Differential Equations SolutionsProbabilistic and Robust Engineering DesignIterative Methods for Nonlinear Equations