Abstract In this paper, we consider the problem of periodic optimal control of nonlinear systems subject to online changing and periodically time-varying economic performance measures using model predictive control (MPC). The proposed economic MPC scheme uses an online optimized artificial periodic orbit to ensure recursive feasibility and constraint satisfaction despite unpredictable changes in the economic performance index. We demonstrate that the direct extension of existing methods to periodic orbits does not necessarily yield the desirable closed-loop economic performance. Instead, we carefully revise the constraints on the artificial trajectory, which ensures that the closed-loop average performance is no worse than a locally optimal periodic orbit. In the special case that the prediction horizon is set to zero, the proposed scheme is a modified version of recent publications using periodicity constraints, with the important difference that the resulting closed loop has more degrees of freedom which are vital to ensure convergence to an optimal periodic orbit. In addition, we detail a tailored offline computation of suitable terminal ingredients, which are both theoretically and practically beneficial for closed-loop performance improvement. Finally, we demonstrate the practicality and performance improvements of the proposed approach on benchmark examples.

中文翻译：

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使用经济模型预测控制的非线性约束系统的周期优化控制

摘要 在本文中，我们使用模型预测控制（MPC）来考虑非线性系统的周期性最优控制问题，该系统受到在线变化和周期性时变经济性能度量的影响。所提出的经济 MPC 方案使用在线优化的人工周期轨道来确保递归可行性和约束满足，尽管经济绩效指标发生了不可预测的变化。我们证明，将现有方法直接扩展到周期轨道不一定会产生理想的闭环经济性能。相反，我们仔细修改了对人工轨迹的约束，以确保闭环平均性能不比局部最优周期轨道差。在预测范围设置为零的特殊情况下，提议的方案是使用周期性约束的最新出版物的修改版本，重要的区别在于所产生的闭环具有更多的自由度，这对于确保收敛到最佳周期轨道至关重要。此外，我们详细介绍了适合终端成分的量身定制的离线计算，这在理论上和实践上都有利于提高闭环性能。最后，我们在基准示例上展示了所提出方法的实用性和性能改进。我们详细介绍了适合终端成分的定制离线计算，这在理论上和实践上都有利于闭环性能的提高。最后，我们在基准示例上展示了所提出方法的实用性和性能改进。我们详细介绍了适合终端成分的定制离线计算，这在理论上和实践上都有利于闭环性能的提高。最后，我们在基准示例上展示了所提出方法的实用性和性能改进。