A probabilistic algorithm to test local algebraic observability in polynomial time

Sedoglavic, Alexandre

doi:10.1145/384101.384143

Cited by 47 publications

(80 citation statements)

References 32 publications

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“…To perform nonlinear observability analysis of the models, we apply an observability test algorithm described in [171,172] by A. Sedoglavic. The algorithm is implemented in Maple.…”

Section: Nonlinear Algebraic Methods For Observability Testmentioning

confidence: 99%

Modeling Verticality Estimation During Locomotion

Farkhatdinov

Michalska

Berthoz

et al. 2013

Romansy 19 – Robot Design, Dynamics and Control

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In this thesis, a nonlinear model of the vestibular system is proposed, with special reference to humans and other locomoting animals. The vestibular system is essential for stable locomotion since it provides idiothetic measurements of spatial orientation that are needed for postural control. The model was constructed from general considerations regarding the Newton-Euler dynamics governing the three-dimensional movements of bodies constrained to oscillate in non-inertial frames, such as the otoliths, which were modeled as spherical damped pendula. Two configurations were considered. The medial model considered only one inner ear located in the center of a head. The lateral model considered two inner ears located laterally with respect to the center of rotation of the head. The differences between these two models were analyzed and the importance of having two vestibular organs discussed. To this end, a nonlinear algebraic observability test was used to verify whether the reconstruction of the head orientation with respect to the gravitational vertical was possible from otoliths measurements only. It could be shown that in order for the head vertical orientation to be observable, the head had to be stabilized during locomotion. Moreover, it was shown that the gravitoinertial ambiguity inherent to inertial idiothetic sensing could be resolved if the head was horizontally stabilized. These results were applied to solve the head vertical orientation estimation problem in the linearized case (Luenberger observer, Kalman filter) as well as in the nonlinear case (Extended Kalman filter, Newton method based observation). These observers were designed and tested in simulations. The simulations indicated that the estimation errors were smaller and the observers converged faster when head was stabilized during locomotion, leading to a nonlinear, combined observation-control system that could be stabilized with respect to the gravitational vertical based on no other information than the prior knowledge of the Newton-Euler dynamics. The results were further tested with a specifically designed experimental setup that comprised an actuated gimbal mechanism to represent the head-neck articulation and a liquid-based inclinometer that represented the otoliths organs. The findings derived from this research would be helpful for analyzing spatial perception in humans and animals, and for improving the perceptual capabilities of robotic systems, such as humanoid robots, rough terrain vehicles, or free-moving drones.Keywords: vestibular system, head-neck system, nonlinear system, observation, estimation, verticality, spatial perception, locomotion, humanoid robot. 3 RésuméDans cette thèse, nous proposons un modèle non-linéaire du système vestibulaire, en particulier chez l'humain et autres animaux mobiles. Le système vestibulaire est essentiel pour une locomotion stable dans la mesure où il fournit des mesures idiothétiques d'orientation spatiale nécessairesà la stabilité posturale. Le développement du modèle est basé sur l...

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“…To perform nonlinear observability analysis of the models, we apply an observability test algorithm described in [171,172] by A. Sedoglavic. The algorithm is implemented in Maple.…”

Section: Nonlinear Algebraic Methods For Observability Testmentioning

confidence: 99%

Modeling Verticality Estimation During Locomotion

Farkhatdinov

Michalska

Berthoz

et al. 2013

Romansy 19 – Robot Design, Dynamics and Control

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“…Identifiability analysis can be formulated as a nonlinear observability problem [9,19]. To do so, let us augment the state variable vector so as to include also the model parameters:…”

Section: Structural Identifiability As Observabilitymentioning

confidence: 99%

Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions

Villaverde

Banga

2017

Processes

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Dynamic modelling is a powerful tool for studying biological networks. Reachability (controllability), observability, and structural identifiability are classical system-theoretic properties of dynamical models. A model is structurally identifiable if the values of its parameters can in principle be determined from observations of its outputs. If model parameters are considered as constant state variables, structural identifiability can be studied as a generalization of observability. Thus, it is possible to assess the identifiability of a nonlinear model by checking the rank of its augmented observability matrix. When such rank test is performed symbolically, the result is of general validity for almost all numerical values of the variables. However, for special cases, such as specific values of the initial conditions, the result of such test can be misleading-that is, a structurally unidentifiable model may be classified as identifiable. An augmented observability rank test that specializes the symbolic states to particular numerical values can give hints of the existence of this problem. Sometimes it is possible to find such problematic values analytically, or via optimization. This manuscript proposes procedures for performing these tasks and discusses the relation between loss of identifiability and loss of reachability, using several case studies of biochemical networks.

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“…Moderately complex nonlinear ode systems can be handled by methods of differential algebra (Saccomani [2004]) but large scale systems still remain intractable. As an alternative for larger systems, a local method has been proposed that only assigns a probability of non-identifiability (Sedoglavic [2002]). To overcome the limitations in system size the original ode system (Eq.…”

Section: Structural Identifiabilitymentioning

confidence: 99%

Qualitative and Quantitative Optimal Experimental Design for Parameter Identification of a MAP Kinase Model

Schenkendorf

Mangold

2011

IFAC Proceedings Volumes

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Mathematical models ensuring a highly predictive power are of inestimable value in systems biology. Their application ranges from investigations of basic processes in living organisms up to model based drug design in the field of pharmacology. For this purpose simulation results have to be consistent with the real process, i.e, suitable model parameters have to be identified minimizing the difference between the model outcome and measurement data. In this work graph based methods are used to figure out if conditions of parameter identifiability are fulfilled. In combination with network centralities, the structural representation of the underlying mathematical model provides a first guess of informative output configurations. As at least the most influential parameters should be identifiable and to reduce the complexity of the parameter identification process further a parameter ranking is done by Sobol' indices. The calculation of these indices goes along with a highly computational effort, hence monomial cubature rules are used as an efficient approach of numerical integration. All methods are demonstrated for a well known motif in signaling pathways, the MAP kinase cascade.

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A probabilistic algorithm to test local algebraic observability in polynomial time

Cited by 47 publications

References 32 publications

Modeling Verticality Estimation During Locomotion

Modeling Verticality Estimation During Locomotion

Structural Properties of Dynamic Systems Biology Models: Identifiability, Reachability, and Initial Conditions

Qualitative and Quantitative Optimal Experimental Design for Parameter Identification of a MAP Kinase Model

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