Decompositional reach-and-stay contract-based control of nonlinear systems with an application to glucose control

Abstract

In this work, we present a novel contract-theoretic framework for controlling large-scale, interconnected, nonlinear systems by decomposing a global specification into local, time-varying assume–guarantee contracts. First, we decompose the system into local components and the global contract into local contracts; then, our main result gives sufficient conditions under which local causal sampled-data controllers — without foreknowledge of future contract changes — ensures satisfaction of the overall piecewise-constant specification, with possible interim violations. When the underlying dynamics are monotone, we further provide an efficient, constructive synthesis procedure. We demonstrate the approach on a glucose–insulin regulatory model with explicit pancreatic beta-cell dynamics, showcasing the potential of the proposed approach.