A control problem motivated by tissue engineering is formulated and solved in which control of the uptake of growth factors (signaling molecules) is necessary to spatially and temporally regulate cellular processes for the desired growth or regeneration of a tissue. Four approaches are compared for determining 1D optimal boundary control trajectories for a distributed parameter model with reaction, diffusion, and convection: (i) basis function expansion, (ii) method of moments, (iii) internal model control (IMC), and (iv) model predictive control (MPC). The proposed method-of-moments approach is computationally efficient while enforcing a non-negativity constraint on the control input. While more computationally expensive than methods (i)-(iii), the MPC formulation significantly reduced the computational cost compared to simultaneous optimization of the entire control trajectory. A comparison of the pros and cons of each of the four approaches suggests that an algorithm that combines multiple approaches is most promising for solving the optimal control problem for multiple spatial dimensions.
In this computational study we consider a generalized minimal model structure for the intravenously infused insulin-blood glucose dynamics, which can represent a wide variety of diabetic patients, and augment this model structure with a glucose rate disturbance signal that captures the aggregate effects of various internal and external factors on blood glucose. Then we develop a model-based, switching controller, which attempts to balance between optimal performance, reduced computational complexity and avoidance of dangerous hypoglycaemic events. We evaluate the proposed algorithm relative to the widely studied proportional-derivative controller for the regulation of blood glucose with continuous insulin infusions. The results show that the proposed switching control strategy can regulate blood glucose much better than the proportional-derivative controller for all the different types of diabetic patients examined. This new algorithm is also shown to be remarkably robust in the event of concurrent, unknown variations in critical parameters of the adopted model.
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