Reference and command governors for systems with slowly time-varying references and time-dependent constraints

We present a reference governor/command governor design for use in systems with slowly time-varying references or for enforcing slowly time-varying constraints. Ordinary governor designs are based on constraint-admissible invariant sets, but we base our design on contractive sets, which are used to ensure that the constraint-admissible set decays quickly enough to guarantee reference tracking or constraint enforcement for references or constraints that vary slowly. The results presented in the paper provide bounds on the rate of change of the reference or of the constraints, which are based on the rate of contraction. Two numerical examples are considered illustrating the capabilities of the new design. The first example is a linearized F-16 model that tracks a slowly-varying reference and the second example is a mass-spring-damper system that enforces a slowly-varying constraint.