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

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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.