Optimal Control of Dynamical Biological System: Simplified Model of Balanced Growth and Development

Ilya Ioslovich (September 30, 2010)

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A dynamical biological system containing a vegetable crop and control tools for protected and intensive cultivation is considered. To optimize an economical criterion along the growing season, model based control must be designed. A special simplified biological model was developed for the purpose of determining the control inputs. This model uses the main biological properties of plant growth: the three stage process of growth (vegetative, mixed, and reproductive) resulted from the adaptation to the natural selection ontogeny, and the maintenance of the balanced sink/source ratio in relation to the growth and development processes. The appropriate optimal control problem was investigated by means of the sufficient conditions of optimality and it was found that, independently of weather inputs, the time-invariant parameter, 'optimal control intensity', can be determined analytically. A previously calibrated generic comprehensive multidimensional model of the tomato plant was used as a generator of data for simulation.