Plot Differential System Parameters Of The Optimal Control Problem

Optimal control theory is used widely in the application field of engineer technology, economic management and resource allocation etc. However, most practical problems are discussed in infinite - dimensional spaces, so which too complex to obtain analytical solution. Therefore, to find the numerical solution of optimal control problem is very important.This paper devised computational algorithms using concept of the control parametrization for optimal control problems governed by delay integro-differential system on the fixed timeinterval [0,T] .The method partitions the interval [0,T] into several subintervals and controlvariables are approximated by piecewise constant functions with the instants of switching preassigned by the corresponding partition. Then, an optimal control problem is approximated by a series of corresponding optimal parameter selection problems. In order to find the solution of optimal parameter selection problem, we Shift differential constraint to the object function gradient calculation which must use Pontryagin Maximum Principle. In this way, the problem be transformed a standard nonlinear programming problem which only involved equality and inequality constraints. Hence, we can solve it by method of optimization.Therefore, the key to solve the optimal control problem is transforming it into the optimal parameter selection problem, and the key to solve the optimal parameter selection problem is deriving the gradient formula for objective function. Based on this idea, we have been derived the gradient formula for the optimal parameter selection problem governed by integro-differential system first. Then, the optimal control problem was transformed a series of optimal parameter selection problems by method of control parametrization. In this way, we have constructed a new numerical method for optimal control problems governed by delay integro-differential system. Finally, we have proved that the solution of optimal parameter selection in a specified interval converges to the original optimal control problem.And, the gradient formula for the objective function of optimal parameter selection problem governed by a special delay integro-differential system have been derived in the thesis.