REGULATORY NETWORKS UNDER ELLIPSOIDAL UNCERTAINTY - OPTIMIZATION THEORY AND DYNAMICAL SYSTEMS

In this paper, we introduce and analyze time-discrete target-environment regulatory systems (TEsystems) under ellipsoidal uncertainty. The uncertain states of clusters of target and environmental items of the regulatory system are represented in terms of ellipsoids and the interactions between the various clusters are defined by affine-linear coupling rules. The parameters of the coupling rules and the time-dependent states of clusters define the regulatory network. Explicit representations of the uncertain multivariate states of the system are determined with ellipsoidal calculus. In addition, we introduce various regression models that allow us to determine the unknown system parameters from uncertain (ellipsoidal) measurement data by applying semidefinite programming and interior point methods. Finally, we turn to rarefications of the regulatory network. We present a corresponding mixed integer regression problem and achieve a further relaxation by means of continuous optimization. We analyze the structure of the optimization problems obtained, especially, in view of their solvability, we discuss the structural frontiers and research challenges, and we conclude with an outlook.

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