Optimal Control Of Uncertain Time Delay System

Optimal control problems are ubiquitous in engineering. What’s more, time op-timal control is a class of optimal control problem. Due to the variable measurement, transfer of signal and other factors, the phenomena of time-delay in optimal control are ubiquitous. Nowadays, the difficult of optimal control with time-delay is to make the reward value as a function of time and state to be studied in a finite space..Based on the uncertainty theory established by Professor Liu Baoding and an uncertain equation of optimality by Professor Zhu Yuanguo, this paper studies un-certain optimal control problems with time-delay. In this paper, an uncertain control model with time-delay is investigated based on the concept of uncertain process. In this model, the value function is infinite-dimensional in the state. Some conditions are presented to guarantee the model is equivalent to a finite-dimensional one. The latter is solved by the equation of optimality. Then the solution of an uncertain linear quadratic optimal control problem with time-delay is obtained. Finally, examples are given to show how to solve an uncertain optimal control model with time-delay.