Linear Systems with Output Constraints: The Theory and Application of Maximal Output Admissible Sets

An initial state of an unforced linear system is output admissible with respect to a constraint set Y if the resulting output function satisfies the pointwise-in-time condition Y(t) ¿ Y,t ± 0. The set of all such initial states is the maximal output admissible set, O¿. The properties of O¿ and its characterization are investigated. In the discrete-time case it is generally possible to represent O¿, or a close approximation of it, by a finite number of functional inequalities. Practical algorithms for generating the functions are described. O¿ has important applications in the analysis and design of closed loop systems with state and control constraints. An example is given. The discrete-time results are used to obtain an alternative implementation of the error governor control scheme proposed by Kapasouris, Athans and Stein [6]. It works as well as their implementation, but reduces the computational load on the controller. by several orders of magnitude.