The physical and virtual connectivity of systems via flows of energy, material, information, etc., steadily increases. This paper deals with systems of sub-systems that are connected by networks of shared resources that have to be balanced. For the optimal operation of the overall system, the couplings between the sub-systems must be taken into account, and the overall optimum will usually deviate from the local optima of the sub-systems. However, for reasons, such as problem size, confidentiality, resilience to breakdowns, or generally when dealing with autonomous systems, monolithic optimization is often infeasible. In this contribution, iterative distributed optimization methods based on dual decomposition where the values of the objective functions of the different sub-systems do not have to be shared are investigated. We consider connected dynamic systems that share resources. This situation arises for continuous processes in transient conditions between different steady states and in inherently discontinuous processes, such as batch production processes. This problem is challenging since small changes during the iterations towards the satisfaction of the overarching constraints can lead to significant changes in the arc structures of the optimal solutions for the sub-systems. Moreover, meeting endpoint constraints at free final times complicates the problem. We propose a solution strategy for coupled semi-batch processes and compare different numerical approaches, the sub-gradient method, ADMM, and ALADIN, and show that convexification of the sub-systems around feasible points increases the speed of convergence while using second-order information does not necessarily do so. Since sharing of resources has an influence on whether trajectory dependent terminal constraints can be satisfied, we propose a heuristic for the computation of free final times of the sub-systems that allows the dynamic sub-processes to meet the constraints. For the example of several semi-batch reactors which are coupled via a bound on the total feed flow rate, we demonstrate that the distributed methods converge to (local) optima and highlight the strengths and the weaknesses of the different distributed optimization methods.

中文翻译：

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耦合半批量过程的分布式轨迹优化的对偶优化方法比较

通过能量，材料，信息等的流动，系统的物理和虚拟连通性不断增加。本文讨论由必须平衡的共享资源网络连接的子系统系统。为了使整个系统最佳运行，必须考虑子系统之间的耦合，并且总体最佳状态通常会偏离子系统的局部最优值。但是，由于诸如问题大小，机密性，对故障的恢复能力等原因，或者通常在处理自治系统时，整体优化通常是不可行的。在此贡献中，研究了基于双重分解的迭代分布式优化方法，在该方法中不必共享不同子系统的目标函数的值。我们考虑共享资源的连接的动态系统。对于在不同稳态之间的过渡条件下的连续过程以及在固有的不连续过程（例如批生产过程）中出现这种情况。这个问题具有挑战性，因为在迭代过程中朝着总体约束的满足进行小的更改会导致子系统最佳解决方案的弧形结构发生重大更改。而且，在自由的最终时间满足端点约束使问题变得复杂。我们提出了一种用于半批量耦合过程的解决方案策略，并比较了不同的数值方法，次梯度方法ADMM和ALADIN，并表明子系统在可行点附近的凸化可提高收敛速度，而使用二阶信息不一定会收敛。由于资源共享会影响是否满足轨迹相关的终端约束条件，因此我们提出了一种启发式算法，用于计算子系统的自由最终时间，以使动态子过程能够满足约束条件。对于通过总进料流速的界限耦合的几个半间歇式反应器的例子，我们证明了分布式方法收敛于（局部）最优值，并突出了不同分布式优化方法的优缺点。我们提出了一种启发式算法，用于计算子系统的自由最终时间，以使动态子过程能够满足约束条件。对于通过总进料流速的界限耦合的几个半间歇式反应器的例子，我们证明了分布式方法收敛于（局部）最优值，并突出了不同分布式优化方法的优缺点。我们提出了一种启发式算法，用于计算子系统的自由最终时间，以使动态子过程能够满足约束条件。对于通过总进料流速的界限耦合的几个半间歇式反应器的例子，我们证明了分布式方法收敛于（局部）最优值，并突出了不同分布式优化方法的优缺点。