Optimal control for multistage uncertain random dynamic systems with multiple time delays

A complex system exhibiting uncertainty as well as randomness is an uncertain random dynamic system. A novel idea of an uncertain random matrix is introduced as an interaction between uncertainty and randomness. Thereby a time-delayed uncertain random dynamic system is formulated. And then the corresponding time-delayed optimal control problem is first presented in this paper. To tackle a problem like that, a method is proposed to translate it into an equivalent optimization problem without time delay. The relevant recursion equations are developed with the dynamic programming technique to solve the converted optimization problem. Solving the related recursion equations yields the answer to such an optimization problem. The presented approach offers a unified framework for tackling the discrete-time uncertain random optimal control problem involving time delays. In this framework, three algorithms are successfully devised in doing with time-delayed optimal control problems for dynamic systems regarding linear, quadratic, and cubic controls. Meanwhile, the optimal solutions for numerical examples are found by the raised algorithms. Finally, a problem of optimal control for a two-spool turbofan engine is investigated as an application of our results.