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首页> 外文期刊>Journal of Optimization Theory and Applications >Gradient descent approach to optimal mode scheduling in hybrid dynamical systems
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Gradient descent approach to optimal mode scheduling in hybrid dynamical systems

机译：混合动力系统最优模式调度的梯度下降方法

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摘要

This paper concerns the problem of optimally scheduling the sequence of dynamic response functions in nonlinear switched-mode hybrid dynamical systems. The control parameter has a discrete component and a continuous component, namely the sequence of modes and the duration of each mode, while the performance criterion consists of a cost functional on the state trajectory. The problem is naturally cast in the framework of optimal control. This framework has established techniques sufficient to address the continuous part of the parameter, but lacks adequate tools to consider the discrete element. To get around this difficulty, the paper proposes a bilevel hierarchical algorithm. At the lower level, the algorithm considers a fixed mode sequence and minimizes the cost functional with respect to the mode durations; at the upper level, it updates the mode sequence by using a gradient technique that is tailored to the special structure of the discrete variable (mode sequencing). The resulting algorithm is not defined on a single parameter space, but rather on a sequence of Euclidean spaces of increasing dimensions, an unusual setting for which there is no established notion of convergence. The paper suggests first a suitable definition of convergence based on the concepts of optimality functions; then, it proves that the proposed algorithm converges in that sense.
机译：本文涉及在非线性开关模式混合动力系统中优化调度动态响应函数序列的问题。控制参数具有离散分量和连续分量，即模式序列和每个模式的持续时间，而性能标准由状态轨迹上的成本函数组成。这个问题自然是在最佳控制的框架中提出的。该框架已经建立了足以解决参数的连续部分的技术，但是缺乏考虑离散元素的足够工具。为了解决这个困难，本文提出了一种双层算法。在较低级别，该算法考虑固定模式序列，并最大程度地降低了与模式持续时间相关的成本函数;在较高级别，它通过使用针对离散变量的特殊结构（模式排序）量身定制的梯度技术来更新模式序列。生成的算法不是在单个参数空间上定义的，而是在维数递增的欧几里德空间的序列上定义的，这是一个不常见的设置，没有确定的收敛概念。本文首先根据最优函数的概念提出了一个合适的收敛定义。然后，证明了该算法在该意义上收敛。

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