Theoretical Foundations for Risk-Averse Control Engineering

我们每天都被要求在不知道下一步会发生什么的情况下决定现在要做什么。通常，我们会在效率和安全之间权衡取舍。影响我们日常生活的工程系统，如水和水能系统，也必须平衡这些权衡。在不确定的情况下做决定的一种方法是假设最坏的情况。也就是说，不确定性表现为对抗因素，这总是导致系统运行效率较低或不太安全。这种方法有很多应用，例如在航空航天工业中。另一种方法是假设风险中立的观点。在这里，不确定性表现为随机噪声，并且假设系统的性能是由平均性能很好地建模的。这被人工智能社区广泛使用，例如，在模拟（摔倒不危险的设置）中教机器人复杂的动作。虽然这两种观点都很有用，但它们都有局限性。最坏情况的观点可能过于谨慎，而风险中立的观点忽略了罕见的有害结果的可能性。这个研究项目将推进一个重要但尚未发展的学科，它将这两个观点联系起来，称为风险规避控制工程。通常，风险是根据概率或平均方差近似值来评估的，这并不广泛适用于今天的挑战。例如，加拿大的联合下水道系统可以在暴雨期间将未经处理的废水排放到自然水道中。更大的溢流会给环境带来更多的污染，但评估溢流事件的概率并不能明确地模拟其严重程度。此外，以一种惩罚溢水量均值和方差的方式运行水电站大坝，忽略了低于均值的偏差比高于均值的偏差更安全的事实。扩大储存设施以反映目前对本世纪“最严重”风暴的估计是昂贵的，而且没有考虑到明年的估计，明年可能会有很大的不同。我们将建立理论基础，以更细致的方式评估和优化控制系统的风险。由于真实的系统可以有很多维度、不完美的模型和无界的干扰，所以挑战是很多的。然而，由于我们的多学科方法，我们在应对这些挑战方面具有独特的优势。我们将综合金融风险分析、随机控制理论、统计学习和计算科学等多种思想，从城市水和水能源应用中获得灵感，开发具有理论保证的新型风险规避方法。3名博士生和2名MASc学生将接受风险分析、控制理论、概率论和算法方面的高级培训。具备这些多学科技能，毕业生将得到良好的训练，在加拿大的工程公司设计创新的解决方案。

We are required to make decisions everyday about what to do now without knowing what will happen next. Often, we balance trade--offs between efficiency and safety. Engineering systems that affect us daily, such as water and water-energy systems, must balance these trade--offs as well. One approach for making decisions under uncertainty is to assume a worst--case perspective. That is, uncertainties behave as adversarial agents, which always cause systems to operate less efficiently or less safely. This approach has found many applications, for example, in the aerospace industry. An alternate approach is to assume a risk--neutral perspective. Here, uncertainties behave as random noise, and one assumes that the performance of a system is well--modeled by the average performance. This is used widely by the artificial intelligence community, for example, to teach robots complex maneuvers in simulation (a setting in which falling down is not dangerous). While both perspectives are useful, they have limitations. A worst--case perspective can be overly cautious, whereas a risk--neutral perspective ignores the possibility of rare harmful outcomes. This research program will advance the important, yet underdeveloped, discipline that connects these two perspectives, called risk--averse control engineering. Typically, risk is assessed in terms of a probability or a mean-variance approximation, which are not broadly applicable to today's challenges. For example, combined sewer systems in Canada can release untreated wastewater into natural waterways during heavy storms. Larger overflows introduce more pollution into the environment, but assessing the probability of an overflow event does not model the severity explicitly. Moreover, operating a hydroelectric dam in a way that penalizes the mean and variance of an overflow volume ignores the fact that deviations below the mean are safer than deviations above. Expanding storage facilities to reflect the current estimate of this century's "worst" storm is expensive and does not consider next year's estimate, which may be quite different. We will build theoretical foundations for assessing and optimizing risk in more nuanced ways for control systems. Since real systems can have many dimensions, imperfect models, and unbounded disturbances, the challenges are numerous. However, we are uniquely positioned to tackle these challenges due to our multi-disciplinary approach. We will synthesize diverse ideas from financial risk analysis, stochastic control theory, statistical learning, and computational science to develop novel risk-averse methods with theoretical guarantees, with inspiration from urban water and water-energy applications. 3 PhD and 2 MASc students will receive advanced training in risk analysis, control theory, probability theory, and algorithms. Equipped with these multi-disciplinary skills, graduates will be well-trained to devise innovative solutions in Canada's engineering companies.