An Explicit Reference Governor for Time-Varying Linear Constraints

Abstract

The explicit reference governor (ERG) is an add-on unit that provides constraint handling capabilities to prestabilized systems. The basic idea behind this approach is to translate state and input constraints into an upper-bound on the value of the Lyapunov function, which is then enforced by suitably manipulating the derivative of the auxiliary reference. This paper extends the ERG approach to deal with time-varying linear constraints. In particular, it is shown that under a certain condition on the rate of change of the constraints and the strength of stability of the prestabilized system (i.e., the speed of the dynamics of the prestabilized system), it is possible to deploy the ERG approach to handle time-varying constraints. To do so, components of the ERG approach are redefined, and constraints satisfaction and convergence properties are proven analytically. The effectiveness of the proposed scheme is demonstrated through a simulation study on filming a movie scene with a drone.