Open AccessNon‐linear feedback control of the p 53 protein– mdm 2 inhibitor system using the derivative‐free non‐linear Kalman filter
Author(s) -
Rigatos Gerasimos G.
Publication year - 2016
Publication title -
iet systems biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.367
H-Index - 50
eISSN - 1751-8857
pISSN - 1751-8849
DOI - 10.1049/iet-syb.2015.0058
Subject(s) - control theory (sociology) , kalman filter , linear system , mathematics , state vector , state variable , flatness (cosmology) , canonical form , invariant extended kalman filter , extended kalman filter , computer science , physics , mathematical analysis , statistics , control (management) , cosmology , classical mechanics , quantum mechanics , artificial intelligence , pure mathematics , thermodynamics
It is proven that the model of the p 53– mdm 2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p 53 protein at the desirable levels. To estimate the non‐measurable elements of the state vector describing the p 53– mdm 2 system dynamics, the derivative‐free non‐linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p 53– mdm 2 system, the derivative‐free non‐linear Kalman filter is re‐designed as a disturbance observer. The derivative‐free non‐linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non‐linear model. The proposed non‐linear feedback control and perturbations compensation method for the p 53– mdm 2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.