Fractal variational principle for an optimal control problem
Hongjin Ma
Abstract
The optimal control of a system governed by an elliptic equation has been widely applied in engineering, and it requires twice differentiability. Furthermore, the optimal control cannot effectively deal with unsmooth boundaries. Now, the condition will not be maintained for a long time because this paper suggests a fractal optimal control of a system governed by a fractal variational principle to deal with unsmooth boundaries. The new optimal theory has obvious advantages in low differentiability for an unsmooth boundary problem. The air conditioning in a room is used as an example to show how to maintain maximum comfortableness of the workplace and maximum efficiency of energy saving.
Topics & Concepts
FractalOptimal controlDifferentiable functionMaximum principleMathematicsBoundary (topology)Variational principleControl (management)Applied mathematicsMathematical optimizationMathematical analysisComputer scienceArtificial intelligenceFractional Differential Equations SolutionsAdvanced Mathematical Modeling in EngineeringProbabilistic and Robust Engineering Design