Input convex neural networks (ICNNs) are a family of deep learning models where the outputs are constructed to be convex functions of the inputs. By parameterizing system models using ICNNs, optimization-based control problems can be solved as convex optimization problems, leading to improved performance and robustness. This work proposes a novel framework where the control objective function and constraints are modelled using ICNNs. A case study of optimization-based control with output constraints is conducted on a process with input multiplicity and nonminimum phase behavior. The simulation results demonstrate improved economic yield compared with normal neural networks. Additionally, the input convexity formulation is compared with simple regularization techniques, and unique benefits such as improved data efficiency and robustness of the proposed formulation are shown. By explicitly incorporating prior knowledge about convexity, this framework provides a good balance between the universal approximation power of deep learning and computational feasibility required by control.

输入凸神经网络（ICNN）是一系列深度学习模型，其中输出被构造为输入的凸函数。通过使用ICNNs参数化系统模型，可以将基于优化的控制问题解决为凸优化问题，从而提高性能和鲁棒性。这项工作提出了一个新颖的框架，其中使用ICNN对控制目标功能和约束进行建模。基于具有输出约束的基于优化的控制的案例研究是在具有输入多重性和非最小相行为的过程上进行的。仿真结果表明，与常规神经网络相比，经济收益有所提高。此外，将输入凸度公式与简单的正则化技术进行比较，并显示了独特的好处，例如提高了数据效率和拟议配方的鲁棒性。通过显式合并有关凸性的现有知识，此框架可在深度学习的通用逼近能力与控制所需的计算可行性之间取得良好的平衡。