The closed‐loop optimal control of a linear, time‐invariant, singularly perturbed discrete system is considered. The resulting matrix Riccati difference equation is formulated in the singularly perturbed structure. It is observed that the degeneration affects some of the final conditions of the Riccati equation. A singular perturbation method is developed to obtain approximate solutions in terms of an outer series and a final correction series. The outer series takes advantage of the order reduction associated with degeneration and the correction series takes care of the affected final conditions. Two examples are given to illustrate the proposed method.
- Discrete optimal control system
- Matrix Riccati difference equation
- Order reduction
- Singular perturbation method