Solving optimal control problems of Fredholm constraint optimality via the reproducing kernel Hilbert space method with error estimates and convergence analysis

• Published in: Mathematical methods in the applied sciences Vol. 44; no. 10; pp. 7915 - 7932
• Main Authors: Abu Arqub, Omar, Shawagfeh, Nabil
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 15.07.2021
• Subjects: Algorithms; Calculus of variations; Convergence; Error analysis; Fredholm constraint optimality; Hilbert space; Initial conditions; Kernels; Numerical analysis; Optimal control; optimal control problems; Optimization; reproducing kernel Hilbert space method; symbolic computations
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.5530

Modeling of dynamic systems of optimal control problems (OCPs) is very important issue in applied sciences and engineering. In this analysis, by developed the reproducing kernel Hilbert space (RKHS) method within the calculus of variations, the OCP is solved with respect to initial conditions and Fredholm operator optimality. The solution methodology involves the use of two generalized Hilbert spaces (HSs) for both range and domain spaces. Numerical algorithm and procedure of solution are assembled compatibility with the optimal formulation of the problem. The convergence analysis and error rating of the utilized method are considered under some presumptions, which provide the theoretical structure behind the technique. The optimal profiles show the performance of the numerical solutions and the effect of the Fredholm operator in the optimal results. In this approach, computational simulations are introduced to delineate the suitability, straightforwardness, and relevance of the calculations created.