Shahid Chamran University of AhvazJournal of Advanced Mathematical Modeling2251-80881120110522Simultaneously determining the optimal control and state in an vibrating circular surface system by a discretization methodSimultaneously determining the optimal control and state in an vibrating circular surface system by a discretization method274210013FAAlireza FakharzadehjahromiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranParviz ElahiDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranNadimeh JafarpoorDepartment of Mathematics, Shiraz University of Technology, Shiraz, IranJournal Article20130610Presenting a new method for simultaneous determination of the control and trajectory functions in an optimal control problem governed by a vibrating circular surface system, is the main purpose of this paper. First, by identifying the form of the trajectory function, doing discretization and using the properties of measure, the problem is linearized. Then, by doing some approximation steps, the nearly optimal pair of trajectory and control with the optimal value of the objective function are obtained via solving a finite linear programming problem. A numerical example is also presented.Presenting a new method for simultaneous determination of the control and trajectory functions in an optimal control problem governed by a vibrating circular surface system, is the main purpose of this paper. First, by identifying the form of the trajectory function, doing discretization and using the properties of measure, the problem is linearized. Then, by doing some approximation steps, the nearly optimal pair of trajectory and control with the optimal value of the objective function are obtained via solving a finite linear programming problem. A numerical example is also presented.https://jamm.scu.ac.ir/article_10013_798db8826993aac3dc44315bf9c7a433.pdf