Time-optimal control algorithm for two-time-scale discrete system

A linear, shift-invariant discrete system exhibiting two-time-scale (slow and fast) character is addressed. An iterative algorithm based on linear programming for the computation of time-optimal control is presented by decoupling the original system into slow and fast subsystems. It is found that the computation time and storage capacity for the computation of time-optimal control of the slow and fast subsystems is less than that required for the original system. A numerical example is provided to illustrate the proposed algorithm.