Nonlinear control of discrete-time linear systems with state and control constraints: a reference governor with global convergence properties

Discrete-time, linear control systems with specified pointwise-in-time constraints, such as those imposed by actuator saturation, are considered. The constraints are enforced by the addition of a nonlinear “reference governor” that attenuates, when necessary, the input commands. Because the constraints are enforced, the control system remains linear and undesirable response effects such as instability due to saturation are avoided. The structure of the governor is a modification of the continuous-time reference governor proposed by Kapasouris, Athans and Stein (1990). Its nonlinear action is defined using an appropriate, finitely determined, maximal output admissible set. As a result, the governor can be implemented on-line for systems of significant order. Algorithmic details of the implementation are described. Theorems provide comprehensive results concerning the response of the overall system which are much stronger than those given in the above paper. The main result is global in nature: if the input command converges to a statically admissible input and the initial state of the system belongs to the maximal output admissible set, the eventual action of the reference governor is a unit delay. A tenth-order, helicopter system is considered as an example