Guaranteed Parameter Set Estimation for Monotone Dynamical Systems Using Hybrid Automata

This paper investigates guaranteed methods for estimating feasible parameter sets when the system under study is modelled with ordinary differential equations (ODE). The issue is to find the set of parameters such that the solution of the ODE remains within specified intervals at known time-data points. These intervals correspond usually to measurement uncertainty. This is a set inversion problem which can be solved in a guaranteed way by using a partitioning algorithm, interval analysis and validated numerical integration methods for IVPs for ODEs. In order to address high dimensional nonlinear continuous-time systems, a guaranteed but tight enclosure of the solution of the ODE is needed. Here, we introduce a new approach which is capable of bracketing any uncertain nonlinear monotone dynamical system between an upper and a lower deterministic hybrid dynamical system. The solution enclosures thus obtained are tighter than the ones given by classical validated numerical integration methods. The methodology is illustrated with simulated data from an actual parameter identification setup.