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) ϵ 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.