Approximate Optimal Control Governed by some Parabolic Equations via Laguerre Polynomials Collocation Approach

The present paper proposes a novel numerical approach for approximating solutions to optimal control problems with parabolic constraints. Utilizing Laguerre polynomials as a novel basis set, a method was developed to address a class of this problem. The employment of these basis functions in conjunction with the collocation method facilitates the transformation of optimal control problems governed by parabolic constraints into a system of nonlinear algebraic equations. The present study proposes an efficient discretization and transformation of complex optimal control problems governed by parabolic equations into lower-dimensional algebraic systems by leveraging the unique properties of Laguerre polynomials.Convergence analysis has been demonstrated to ascertain the optimal value approximations of the proposed method. In order to provide a comprehensive illustration of the reliability and applicability of the proposed method, two illustrative examples are presented. The findings underscore the efficacy and precision of the implemented methodology. This work makes a significant contribution to the field by offering a robust framework for solving complex parabolic control problems, thereby demonstrating the potential of spectral methods in the context of optimal control theory.‎‎‎‎‎‎‎‎‎‎‎

کلیدواژه ها:

optimal control problems with‎‎ parabolic constraints ، Laguerre polynomials ، Spectral method ، Collocation points ، Convergence analysis‎.‎