A robust method for optimal control problems governed by system of Fredholm integral equations in mechanics. (English) Zbl 1531.49030
Summary: This essay considers an optimal control problem (OCP) governed by a system of Fredholm integral equations (FIE). In this paper, collocation approach with utilizing Lagrange polynomials is introduced to transform the OCP into a nonlinear programming problem (NLP). An efficient optimization method in Mathematica software is utilized to solve NLP. The convergence analysis is discussed, which show the theoretical structure behind the propounded technique under some assumptions. In this essay, computational outcomes are given to demonstrate the adaptability, forthrightness, and relationship of the calculations manufactured. A practical real-world problem involving hanging chain in classical mechanic is also dissolved utilizing the approach proposed.
MSC:
| 49M25 | Discrete approximations in optimal control |
| 45B05 | Fredholm integral equations |
| 65R20 | Numerical methods for integral equations |
Keywords:
collocation method; Lagrange polynomials; optimal control; system of Fredholm integral equation; convergence analysisReferences:
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