Tight Reachability Bounds for Nonlinear Systems Using Nonlinear and Uncertain Solution Invariants

This article continues a recent line of research that uses so-called solution invariants to enhance the accuracy of fast interval methods for bounding the reachable sets of nonlinear ODEs under uncertainty. The term solution invariants refers to algebraic state constraints that are implied by the dynamics. These can either exist naturally in the model (i.e., conservation laws) or they can be deliberately introduced by `lifting' to achieve tighter bounds. While such reachability methods have proven very effective in some cases, they are limited in the types of invariants that can be used. In this article, we first present an important theoretical extension that permits the use of invariants that depend on uncertain model parameters. Next, we develop an extension of existing algorithms that enables the use of general nonlinear invariants for the first time. These extensions are demonstrated on an uncertain dynamic model of an anaerobic digestion process.