Abstract
We contrast biostatistical methods for optimal treatment determination with optimal control methodology, originally developed in the engineering literature but now used more widely. We describe non-minimal state space (NMSS) control methods for biological systems, with a particular focus on the use of state-dependent parameter models to represent system nonlinearities. Three examples are considered, namely the control of (i) a nonlinear forced logistic function implemented with a time delay; (ii) athletic horse heart rate with potential application for training improvement; and (iii) a physically-based simulation model for the uptake of CO2 by plant leaves in response to light intensity, with application to closed-environment grow cells. Although all three examples have been extensively studied in the literature, the novelty of the present article is in the NMSS formulation and in the application of a recently developed state-dependent (nonlinear) control algorithm. In the case of the leaf photosynthesis simulation, however, the linear NMSS algorithm yields satisfactory results, illustrating the inherent robustness of feedback.
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Notes
A doctoral studentship on this subject has recently been awarded at Lancaster University (http://www.lancs.ac.uk/staff/taylorcj/projects/grow.htm), and the associated practical results will be reported in future publications.
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The statistical tools for this analysis have been assembled as the CAPTAIN Toolbox [28] for Matlab® (http://www.engineering.lancs.ac.uk/tdc).
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Taylor, C.J., Aerts, JM. Control of Nonlinear Biological Systems by Non-minimal State Variable Feedback. Stat Biosci 6, 290–313 (2014). https://doi.org/10.1007/s12561-013-9098-5
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DOI: https://doi.org/10.1007/s12561-013-9098-5