Observability and Structural Identifiability of Nonlinear Biological Systems

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations, and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.Comment: Accepted for publication in the special issue "Computational Methods for Identification and Modelling of Complex Biological Systems" of Complexit

FRW barotropic zero modes: Dynamical systems observability

The dynamical systems observability properties of barotropic bosonic and fermionic FRW cosmological oscillators are investigated. Nonlinear techniques for dynamical analysis have been recently developed in many engineering areas but their application has not been extended beyond their standard field. This paper is a small contribution to an extension of this type of dynamical systems analysis to FRW barotropic cosmologies. We find that determining the Hubble parameter of barotropic FRW universes does not allow the observability, i.e., the determination of neither the barotropic FRW zero mode nor of its derivative as dynamical cosmological states. Only knowing the latter ones correspond to a rigorous dynamical observability in barotropic cosmologyComment: 10 pages, 0 figure

Proletarsky, A.V., Konstantin, A., Neusypin, K.S., Selezneva, M.S., and Grout, V. (2017) 'Development and Analysis of the Numerical Criterion for the Degree of Observability of State Variables in Nonlinear Systems'. In: Proc. 7th IEEE Int. Conference on Internet Technologies and Applications ITA-17, Wrexham, UK, 12-15 September 2017, pp. 150-154. doi: 10.1109/ITECHA.2017.8101927.

This paper is concerned with the problem of development and analysis of numerical criteria for the degree of observability in nonlinear systems. The disadvantages of existing criteria of observability and controllability were introduced. A numerical criterion for the degree of observability of each state variable was developed in nonlinear systems by utilizing the representation of nonlinear models in the State Dependent Coefficient form. The application of the novel criterion was demonstrated for the analysis of the degree of observability of inertial navigation system errors by the simulation with experimental data

Structural accessibility and structural observability of nonlinear networked systems

The classical notions of structural controllability and structural observability are receiving increasing attention in Network Science, since they provide a mathematical basis to answer how the network structure of a dynamic system affects its controllability and observability properties. However, these two notions are formulated assuming systems with linear dynamics, which significantly limit their applicability. To overcome this limitation, here we introduce and fully characterize the notions "structural accessibility" and "structural observability" for systems with nonlinear dynamics. We show how nonlinearities make easier the problem of controlling and observing networked systems, reducing the number of variables that are necessary to directly control and directly measure. Our results contribute to understanding better the role that the network structure and nonlinearities play in our ability to control and observe complex dynamic systems

Hamiltonian Realizations of Nonlinear Adjoint Operators

This paper addresses state-space realizations for nonlinear adjoint operators. In particular the relationship among nonlinear Hilbert adjoint operators, Hamiltonian extensions and port-controlled Hamiltonian systems are clarified. The characterization of controllability, observability and Hankel operators, and controllability and observability functions will be derived based on it. Furthermore a duality between the controllability and observability functions will be proven. The state-space realizations of such operators provide new insights to nonlinear control systems theory