Bounding the states of systems with unknown-but-bounded disturbances

Control systems with hard constraints on certain variables are characterized, in an analytical review of recent investigations based on an unknown-but-bounded description of magnitude uncertainties. Hard-constraint problems typically arise in the design of controllers for potentially hazardous systems such as nuclear power plants. Consideration is given to norm bounds based on matrix measures, extensions of Schweppe's (1968) ellipsoid bounds, and set-theoretic regulator design. The performance of these approaches is evaluated by means of numerical simulations involving a third-order nonlinear steam-boiler model; the results are presented in graphs, and it is found that ellipsoid bounds are tightest in the general case, but that box bounds are even tighter for linear systems with Metzler system matrices.