LINEAR-SYSTEMS WITH STATE AND CONTROL CONSTRAINTS - THE THEORY AND APPLICATION OF MAXIMAL OUTPUT ADMISSIBLE-SETS

The 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) element-of Y, t greater-than-or-equal-to 0. The set of all possible such initial conditions is the maximal output admissible set O infinity. The properties of O infinity and its characterization are investigated. In the discrete-time case, it is generally possible to represent O infinity, or a close approximation of it, by a finite number of functional inequalities. Practical algorithms for generating the functions are described. In the continuous-time case simple representations of the maximal output admissible set are not available; however, it is shown that the discrete-time results may be used to obtain approximate representations. Maximal output admissible sets have important applications in the analysis and design of closed-loop systems with state and control constraints. To illustrate this point, a modification of the error governor control scheme proposed by Kapasouris, Athans, and Stein [6] is presented. It works as well as their implementation but reduces the computational load on the controller by several orders of magnitude.