Time optimal feedback control of discrete systems with bounded inputs

Deadbeat control theory gives a feedback solution to the time optimal control of discrete time systems. Experience has shown the results to be impractical because they ignore bounds on the actuator strength. This paper develops two algorithms for generating time optimal control in feedback form for discrete systems with bounded controls. The results are also applicable for generating recovery regions and the set of reachable states. For multiple control problems a method of generating sublayers is developed which decreases off-line and on-line computational effort. Two algorithms are presented with somewhat different computational and storage requirements. The algorithms are practical within certain dimension constraints, and are natural for implementation with parallel processing.