We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design. We propose a specific neural network (NN) architecture that yields a hybrid system with piecewise-affine dynamics that is differentiable with respect to the network's parameters, thereby enabling the use of derivative-based training procedures. We show that a careful choice of our NN's weights produces a hybrid system model with structural properties that are highly favourable when used as part of a finite horizon optimal control problem (OCP). Specifically, we show that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming, in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. In addition to being well-suited for optimal control design, numerical simulations illustrate that our NN-based technique enjoys very similar performance to state-of-the-art system identification methodologies for hybrid systems and it is competitive on nonlinear benchmarks.

翻译：我们研究从有限数量的（状态-输入）-后继状态数据点出发，设计基于机器学习的未知动力系统模型的问题，使得所得模型也适用于最优控制设计。我们提出了一种特定的神经网络架构，该架构生成具有分段仿射动力学的混合系统，且该混合系统对网络参数可微，从而能够使用基于导数的训练流程。我们证明，对神经网络权重的精心选择可以产生具有结构特性的混合系统模型，当该模型作为有限时域最优控制问题的一部分时，这些特性非常有利。具体而言，我们证明，与一般混合系统的经典最优控制问题通常需要混合整数优化不同，通过非线性规划可计算出具有强局部最优性保证的最优解。除了非常适合最优控制设计外，数值模拟还表明，我们的神经网络技术在混合系统辨识方面与最先进方法性能非常接近，并且在非线性基准测试中具有竞争力。