Structured Neural-PI Control with End-to-End Stability and Output Tracking Guarantees
Structured Neural-PI Control with End-to-End Stability and Output Tracking Guarantees
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DOI：
10.48550/arxiv.2305.17777
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发表时间：
2023-05
期刊：
影响因子：
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通讯作者：
Wenqi Cui;Yan Jiang;Baosen Zhang;Yuanyuan Shi
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文献类型：
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作者：
Wenqi Cui;Yan Jiang;Baosen Zhang;Yuanyuan Shi
通过设计具有稳定性和输出跟踪保证的神经网络控制器，研究了多输入多输出动态系统的最优控制问题。虽然基于神经网络的非线性控制器在各种应用中表现出优异的性能，但它们缺乏可证明的保证，限制了它们在高风险实际应用中的采用。本文弥合了基于神经网络的控制器与需要稳定保证之间的差距。利用平衡无关的无源性，一个广泛存在于物理系统中的特性，我们提出了神经比例积分（PI）控制器，它具有可证明的稳定性保证和零稳态输出跟踪误差。其关键结构是比例项和积分项的严格单调性，并将其参数化为严格凸神经网络的梯度。我们构建了具有可调softplus-$\beta$激活的SCNN，这产生了通用逼近能力，并且在合并通信约束方面也很有用。此外，scnn充当Lyapunov函数，为我们提供端到端的性能保证。在交通和电力网络上的实验表明，该方法可以改善暂态和稳态性能，而非结构化神经网络会导致不稳定行为。
We study the optimal control of multiple-input and multiple-output dynamical systems via the design of neural network-based controllers with stability and output tracking guarantees. While neural network-based nonlinear controllers have shown superior performance in various applications, their lack of provable guarantees has restricted their adoption in high-stake real-world applications. This paper bridges the gap between neural network-based controllers and the need for stabilization guarantees. Using equilibrium-independent passivity, a property present in a wide range of physical systems, we propose neural Proportional-Integral (PI) controllers that have provable guarantees of stability and zero steady-state output tracking error. The key structure is the strict monotonicity on proportional and integral terms, which is parameterized as gradients of strictly convex neural networks (SCNN). We construct SCNN with tunable softplus-$\beta$ activations, which yields universal approximation capability and is also useful in incorporating communication constraints. In addition, the SCNNs serve as Lyapunov functions, giving us end-to-end performance guarantees. Experiments on traffic and power networks demonstrate that the proposed approach improves both transient and steady-state performances, while unstructured neural networks lead to unstable behaviors.