Kishida Masako, Ford Versypt Ashlee N, Pack Daniel W, Braatz Richard D
University of Illinois at Urbana-Champaign, Urbana IL ; Massachusetts Institute of Technology, Cambridge, MA.
University of Illinois at Urbana-Champaign, Urbana IL.
Optim Control Appl Methods. 2013 Nov;34(6):680-695. doi: 10.1002/oca.2047.
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.
提出并解决了一个由组织工程引发的控制问题，其中对生长因子（信号分子）摄取的控制对于在空间和时间上调节细胞过程以实现组织的理想生长或再生是必要的。比较了四种方法来确定具有反应、扩散和对流的分布参数模型的一维最优边界控制轨迹：（i）基函数展开，（ii）矩量法，（iii）内模控制（IMC），以及（iv）模型预测控制（MPC）。所提出的矩量法在对控制输入施加非负约束的同时计算效率高。虽然比方法（i）-（iii）计算成本更高，但与同时优化整个控制轨迹相比，MPC公式显著降低了计算成本。对这四种方法各自优缺点的比较表明，结合多种方法的算法对于解决多个空间维度的最优控制问题最有前景。
