Optimal Control Problem For Uncertain Linear Systems With Delays

In engineering practice,a delay is a very common phenomenon.Therefore,the optimal control of time-delay system has become an important issue for scholars now.The key to solving these problems is how to convert the time-delay problem into a non-time-delay problem.Since the objective function of time-delay problem is a function of time and state,the time-delay term makes the objective function become an infinite-dimensional function,which can not be solved in the usual way.We need to deal with the time-delay,so that the problem becomes a conventional control problem and then can be solved by classical method.In this paper,we discuss two types of time-delay models.One is the uncertain multi-input time-delay linear model and the other is the uncertain time-delay quadratic optimistic value model.The two models are analyzed and processed separately,and the models are transformed into non-time-delay models.The optimal value of the objective functions are obtained by combining the uncertain equations of optimality.Then the numerical examples of the multi-input linear uncertain system model and the linear quadratic uncertain system with time-delay are given.Finally,a consumption problem in study as an application of our results.