Parametrized Maximal Admissible Sets With Application to Constraint Management of Systems With Slowly Varying Parameters

Abstract

Real-time constraint management schemes for time-varying or parameter-varying systems often result in conservative (slow) responses or carry a heavy computational burden. This makes some of the existing solutions less suitable for practical applications within these systems. To address this issue, this paper proposes a numerically efficient reference governor (RG) scheme for constraint management of systems with slowly time-varying parameters and constraints. The solution, which we call the adaptive-contractive reference governor (RG-AC), utilizes a contractive, parameterized characterization of the so-called maximal admissible set (MAS). To ensure low computational overhead, this parameter-dependent MAS (PD-MAS) is approximated using a sensitivity-based method that describes the changes in the facets of PD-MAS as a function of the system parameters around a nominal operating point. The computational and theoretical properties of the PD-MAS and RG-AC are presented. The effectiveness and limitations of the proposed method are demonstrated by studying a basic mass–spring–damper system.