Estimation of consistent parameter sets for continuous-time nonlinear systems using occupation measures and LMI relaxations

Stefan Streif (1) , Philipp Rumschinski (1) , Didier Henrion (2) , Rolf Findeisen (3)

1 OVGU - Otto-von-Guericke-Universität Magdeburg = Otto-von-Guericke University [Magdeburg]
2 LAAS-MAC - Équipe Méthodes et Algorithmes en Commande
3 IFAT - Institute for Automation Engineering

Obtaining initial conditions and parameterizations leading to a model consistent with available measurements or safety specifications is important for many applications. Examples include model (in-)validation, prediction, fault diagnosis, and controller design. We present an approach to determine inner- and outer-approximations of the set containing all consistent initial conditions/parameterizations for nonlinear continuous-time systems. These approximations are found by occupation measures that encode the system dynamics and measurements, and give rise to an infinite-dimensional linear program. We exploit the flexibility and linearity of the decision problem to incorporate uncertain-but-bounded and pointwise-in-time state and output constraints, a feature which was not addressed in previous works. The infinite-dimensional linear program is relaxed by a hierarchy of LMI problems that provide certificates in case no consistent initial condition/parameterization exists. Furthermore, the applied LMI relaxation guarantees that the approximations converge (almost uniformly) to the true consistent set. We illustrate the approach with a biochemical reaction network involving unknown initial conditions and parameters.

Domaines: Optimisation et contrôle [math.OC]

Stefan Streif, Philipp Rumschinski, Didier Henrion, Rolf Findeisen. Estimation of consistent parameter sets for continuous-time nonlinear systems using occupation measures and LMI relaxations. IEEE Conference on Decision and Control ( CDC ), Dec 2013, Florence, Italy. pp. 6379-6384. ⟨hal-00802306⟩