可扩展计算用于受约束的级联系统的最优控制
Scalable computation for optimal control of cascade systems with constraints
AI总结：
本文提出了一种解决有限时间最优控制问题的方法，利用级联系统空间和时间维度的分离性，使计算成本与子系统数量线性增长，但时间范围增长呈立方体，适用于子系统数量大的情况。
摘要：
本文提出了一种方法，用于数值求解一类受级联线性离散时间动态约束的有限时间最优控制问题。假设线性状态和输入不等式约束以及二次性能测度均按底层级联子系统的空间维度和动态的时间维度分离。借助这种结构，等价二次规划形式的最优控制问题的内点法计算成本可与子系统数量线性增长。然而，该方法的复杂度随时间范围呈立方体增长。因此，在子系统数量相对较大的情况下具有计算优势。无论如何，该方法适用于分布式计算，具有低通信开销，仅需处理代理与上游邻居共享部分模型数据。一个例子展示了将主要结果应用于自动化灌溉渠道级联动态的模型数据。
英文摘要：
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure of performance, are all separable with respect to the spatial dimension of the underlying cascade of sub-systems, as well as the temporal dimension of the dynamics. By virtue of this structure, the computation cost of an interior-point method for an equivalent quadratic programming formulation of the optimal control problem can be made to scale linearly with the number of sub-systems. However, the complexity of this approach grows cubically with the time horizon. As such, computational advantage becomes apparent in situations where the number of sub-systems is relatively large. In any case, the method is amenable to distributed computation with low communication overhead and only immediate upstream neighbour sharing of partial model data among processing agents. An example is presented to illustrate an application of the main results to model data for the cascade dynamics of an automated irrigation channel.
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