Theoretical Foundations for Risk-Averse Control Engineering

我们被要求每天做出决定，决定现在要做什么，而不知道接下来会发生什么。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，如水和水能源系统，也必须平衡这些权衡。在不确定的情况下做出决定的一种方法是假设最坏的情况。也就是说，不确定性表现为敌对代理，总是导致系统运行效率更低或安全性更差。这种方法已经发现了许多应用，例如，在航空航天行业。另一种方法是采取风险中性的观点。这里，不确定性表现为随机噪声，人们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，在模拟中教机器人复杂的动作(在这种情况下，摔倒并不危险)。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，而风险中性的观点忽略了罕见的有害结果的可能性。这一研究计划将推进连接这两个视角的重要但不发达的学科，称为风险厌恶控制工程。通常，风险是以概率或均值-方差近似来评估的，这并不广泛适用于当今的挑战。例如，加拿大的联合下水道系统可以在暴风雨期间将未经处理的废水排放到自然水道中。更大的溢出会给环境带来更多的污染，但评估溢出事件的可能性并不能明确地模拟严重程度。此外，以惩罚溢流量的均值和方差的方式运行水电站大坝忽略了这样一个事实，即低于均值的偏差比高于均值的偏差更安全。扩大存储设施以反映当前对本世纪“最严重”风暴的估计是昂贵的，而且不考虑明年的估计，后者可能会有很大不同。我们将为以更细微的方式评估和优化控制系统的风险奠定理论基础。由于实际系统可能具有许多维度、不完美的模型和无限的扰动，因此挑战是无数的。然而，由于我们的多学科方法，我们在应对这些挑战方面处于独特的地位。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的不同思想，从城市供水和水能应用中获得灵感，开发具有理论保障的新的风险规避方法。3名博士生和2名硕士研究生将接受风险分析、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的毕业生将接受良好的培训，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.