Optimization-based parameter computation for nonnegative systems to achieve prescribed dynamic behaviour

Abstract

In this paper, an optimization-based approach is proposed for finding parameter values that guarantee a predefined qualitative behavior for a nonlinear nonnegative dynam- ical system. Similarly to a model predictive control setup, we consider the model states and parameters as free decision variables and incorporate the system dynamics as well as the desired behavioral properties into the optimization constraints. To show the feasibility of our idea, we carried out three case studies on models with increasing state dimension: the Brus- sellator, a three-dimensional Lotka-Volterra, and a 4-dimensional epidemic model, where the goal is to induce oscillatory behavior.