A Class Of Optimal Taking Into Account The Sensitive Factors Of The Economic Model And Calculated

This paper , We consider a class of optimal control problems that depend on a set of scalar parameters which could have some uncertainty as to their exact values .When using optimal control theory to discuss economic problems, get the idealization model owing to having ignored a lot of factor.The general model (P) can be described as followsControlled systemFind a control (?)∈U such thatIs minimized over U .where x: [o, T]â†'Rⁿ,u: [0,T]â†'R^m, a∈R^r is Parameter, x₀ :R^mâ†'Rⁿf:[0,T]×Rⁿ×R^m×R^râ†'Rⁿ,L:[0,T]×Rⁿ×R^mâ†'RAnd U = { u((?))∈R^m | u(t) is piecewise continuation function in[0, T] and |u(t)|≤1}Consider a class optimal control problems involving uncertain coefficient a .For specified values of these coefficient a , let (?) be an optimal control andJ((?);a) the corresponding value of the objective functional .We refer to this u as the base control. In this article, we wish to consider the question regarding the sensitivity of J((?);a) with respect to these uncertain a .More precisely, if we use the same base control (?) , but make a small change in the values of the coefficient a , how will thevalue of J((?);a) change in response? Clearly, it is desirable that this change besmall. The aim of this article is to propose a computational approach for solving this class of optimal control problems in such a way that the control obtained takes intoaccount the dual objective of minimizing the objective functional J((?);a) as well as minimizing the sensitivity of J((?);a) with respect to changes in the coefficient a . New optimum model (P_l)Controlled systemFind a control (?) such thatIs minimized over U .Where x:[0,T]â†'Rⁿ,u:[0,T]â†'R^m a∈R^r is Parameter, f:[0,T]×Rⁿ×R^m×R^râ†'Rⁿ,α∈R is Weight modulus, 0≤α≤1.The gradient formulate of the cost function are obtained, On this basis, a gradient-based computational method is established ,and the optimal control software,MISER3.3.can be applied .For illustration , a numerical example is present...