In this paper, the optimal control problems (OCPs) are converted into a constrained optimization problem based on state parameterization via the Bspline functions (BSFs). In fact, the state variable can be considered as a series of the BSFs with unknown coefficients, and the OCPs are transformed into a constrained optimization problem. With the proposed method, the control and state variables also the performance index can be obtained approximately. Also, the convergence theorem of the presented approach is proved in details, some illustrative examples are reported. Also, an example, which has analytic noncontinuous state and control variable, is presented to show the efficiency and reliability of the purposed method, compared with other existing methods.
In this study, we use B-spline functions to solve the linear and nonlinear special systems of differential equations associated with the category of obstacle, unilateral, and contact problems. The problem can easily convert to an optimal control problem. Then a convergent approximate solution is constructed such that the exact boundary conditions are satisfied. The numerical examples and computational results illustrate and guarantee a higher accuracy for this technique.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.