Learning Complex Control Laws for Nonlinear Systems Under Uncertainty Using Deep Neural Networks

能量系统（例如，电力网络、建筑物、电池和风力涡轮机）的实时操作需要对受到各种不确定因素（例如，市场、天气、需求和设备故障）。常规的低级控制器（例如PID控制器）可以容易地部署在真实的操作中，但是通常不能提供令人满意的性能。复杂的方法，如模型预测控制（MPC），提供了一个通用的框架来处理不确定性，特别是当随机变量可以解决在真实的时间，以显式地减轻不确定性。然而，这种方法的高计算延迟阻碍了它们的应用范围（特别是对于具有快速动态的系统）。我们建议使用深度神经网络为具有不确定性的非线性系统离线开发复杂的控制律。我们的工作假设是，深度学习控制律可以模拟高级控制架构（如MPC）的性能，但计算成本与低级控制器相当。我们还注意到，PID控制器可以被视为深度学习控制律的特殊情况，因此我们的方法可以被视为广义控制架构。应用深度学习控制律的在线计算时间和内存需求可以忽略不计，允许部署在嵌入式系统中，用于无人机（UAV）或自动驾驶汽车等应用。这种方法的关键挑战是深度神经网络的训练。传统的方法遵循“优化后训练”的协议，即从（随机）优化中产生状态变量和最优控制动作之间的数据对，然后通过监督学习来训练神经网络。然而，需要大量的样本，并且生成每个样本的计算成本很高。我们提出了一种新的“优化和训练”方法，将数据生成和神经网络训练的步骤结合到一个单一的优化问题中，可以使用并行计算技术有效地解决这个问题。 我们还将探索控制与控制律相关的风险的机制，并在能源系统中进行计算研究，例如风力涡轮机的实时控制。开发的理论和算法将使能源系统的效率和鲁棒性获得前所未有的收益。例如，我们最近的论文表明，随机MPC的实时应用可以提高风力涡轮机的功率输出的25%，与最佳调整的PID控制器相比。对于中型风电场（100台额定容量为5 MW的风力涡轮机），性能提高可达2000万CAD/年。这项工作还将为研究生和本科生提供控制，优化，机器学习和能源接口的多学科培训机会。

The real-time operation of energy systems (e.g. power networks, buildings, batteries, and wind turbines) requires robust control of nonlinear systems that are subject to a variety of uncertain factors (e.g., markets, weather, demands, and equipment failures). Conventional low level controllers (e.g. PID controllers) can be easily deployed in real time operations, but typically do not provide satisfactory performance. Sophisticated approaches such as model predictive control (MPC) provide a general framework to deal with uncertainty, especially when stochastic variants can be solved in real time to explicitly mitigate uncertainty. However, the high computational latency of such approaches hinders their application scope (especially for systems with fast dynamics). We propose to use deep neural networks to develop sophisticated control laws offline for nonlinear systems with uncertainty. Our working hypothesis is that deep learning control laws can mimic the performance of advanced control architectures such as MPC, but at a computational cost that is comparable to that of low level controllers. We also note that PID controllers can be viewed as special cases of deep learning control laws and thus our approach can be viewed as a generalized control architecture. The online computational time and memory requirement to apply deep learning control laws is negligible, allowing for deployment in embedded systems for applications like unmanned aerial vehicles (UAVs) or self-driving cars. The key challenge arising in this approach is the training of deep neural networks. The traditional method follows an "optimize then train" protocol, that is to generate data pairs between state variables and optimal control actions from (stochastic) optimization, and then train the neural networks via supervised learning. However, a large number of samples are needed and the computational cost of generating each sample is high. We propose a new "optimize and train" method that combines the steps of data generation and neural network training into one single optimization problem that can be solved efficiently using parallel computing techniques. We will also explore mechanisms to control the risk associated with the control laws and also perform computational studies in energy systems such as real-time control of the wind turbines. The theory and algorithms developed will enable unprecedented gains in efficiency and robustness of energy systems. For example, our recent paper shows that the realtime application of stochastic MPC can improve the power output of a wind turbine by 25%, compared with an optimally tuned PID controller. For a medium-size wind farm (with 100 wind turbines at rated capacities of 5 MW), the increased performance can reach up to 20 million CAD/year. This work would also provide multidisciplinary training opportunities at the interface of control, optimization, machine learning, and energy for both graduate and undergraduate students.