Robust control of uncertain contextsensitive probabilistic Boolean networks
Date
2009Source
IET Systems BiologyVolume
3Issue
4Pages
279295Google Scholar check
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Uncertainty is an intrinsic phenomenon in control of gene regulatory networks (GRNs). The presence of uncertainty is related to impreciseness of GRN models due to: (1) Errors caused by imperfection of measurement devices and (2) Models' inability to fully capture a complex structure of the GRN. Consequently, there is a discrepancy between actual behaviour of the GRN and what is predicted by its mathematical model. This can result in false control signals, which can drive a cell to an undesirable state. To address the problem of control under uncertainties, a risksensitive control paradigm is proposed. Robustness is accomplished by minimisation of the mean exponential cost as opposed to, for instance, minimisation of the mean square cost by riskneutral controllers. The authors derive an optimal risksensitive controller when a GRN is modelled by a contextsensitive probabilistic Boolean network (CSPBN). By using a relation between the relative entropy and freeenergy, a relative stability of the cost achieved by the risksensitive controller is demonstrated when the distribution of the CSPBN attractors is perturbed, as opposed to the cost of the riskneutral controller that exhibits increase. The use of the relation between the relative entropy and freeenergy to analyse the influence of a particular attractor on the robustness of the controller is studied. The efficiency of the risksensitive controller is tested for the CSPBN obtained from the study of malignant melanoma. © The Institution of Engineering and Technology.
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