Solution of optimal control problems with Payoff term and fixed state endpoint by using Bezier polynomials

Abstract

In this paper, a new numerical method for solving the optimal control problems with payoff term or fixed state endpiont by quadratic performance index is presented. The method is based on Bezier polynomial. The properties of Bezier polynomials in any intervel as [a, b] are presented. The operational matrices of integration and derivative are utilized to reduce the solution of the optimal control problems to a nonlinear programming one to which existing well-developed algorithms may be applied. Illustrative examples are included to demonstrate the validity and applicability of the technique.

Direct method for solution variational problems by using Hermite polynomials

“…In [39] operational matrices with respect to Hermite polynomials and their applications is presented for solving linear dfferential equations with variable coeffcients. Investigation of optimal control problems and solving them using Bezier polynomials has been presented [1]. In [2] Solution of optimal control problems with payoff term and fixet state endpoint by using Bezier polynomials has been presented.…”

“…Investigation of optimal control problems and solving them using Bezier polynomials has been presented [1]. In [2] Solution of optimal control problems with payoff term and fixet state endpoint by using Bezier polynomials has been presented. In this paper, we present a computational method for solving variational problems by using Hermite polynomials.…”

“…Example 4. It has been studied by using bezier parameterization [34] and also bezier polynomials [1] for optimal control by differential evolution min Z = where x and u respectively are state and control functions. To solve it by presented method, we reducte optimal control problems to variational problems, therefore let u =ẋ − x. then Eqs.…”

Numerical study of variational problems of moving or fixed boundary conditions by Muntz wavelets

“…Therefore, various direct techniques based on orthogonal functions and polynomial series have been used to solve the VPs. An overall view of these methods can be explored in the research work provided by Schechter (1967), Hwang and Shih (1983), Razzaghi et al (2012), Mashayekhi et al (2012), Haddai et al (2012), Zarebnia and Birjandi (2012), Zarebnia and Sarvari (2014), Jaber (2015), Yari et al (2017), Yari and Mirnia (2021) and Shiri and Baleanu (2019). Also, Baleanu et al (2018) and Shiri et al (2021) introduced the applications of an operational matrix method based on orthogonal polynomials.…”