Theoretical Foundations for Risk-Averse Control Engineering

风险规避控制工程的理论基础

• 批准号: RGPIN-2022-04140
• 负责人: Chapman, Margaret
• 金额: $ 2.11万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=751573
• 关键词: Theoretical; Foundations; Risk; Averse; Control

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.

我们每天都要决定现在该做什么，而不知道接下来会发生什么。我们经常在效率和安全之间进行权衡。每天影响我们的工程系统，如水和水能源系统，也必须平衡这些权衡。在不确定情况下做决策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性代理，总是导致系统运行效率降低或安全性降低。这种方法已经得到了许多应用，例如在航空航天工业中。另一种方法是假设风险中性的观点。在这里，不确定性表现为随机噪声，并且人们假设系统的性能由平均性能很好地建模。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。一个最坏情况的观点可能过于谨慎，而一个风险中性的观点忽略了罕见的有害结果的可能性。这项研究计划将推进重要的，但欠发达的，连接这两个方面的学科，称为风险规避控制工程。 通常，风险是根据概率或均值-方差近似值进行评估的，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在暴风雨期间可以将未经处理的废水排入自然水道。较大的溢出会将更多的污染引入环境，但评估溢出事件的概率并不能明确地模拟严重程度。此外，以惩罚溢流量的平均值和方差的方式操作水电大坝忽略了低于平均值的偏差比高于平均值的偏差更安全的事实。扩大储存设施以反映当前对本世纪“最严重”风暴的估计是昂贵的，而且没有考虑明年的估计，明年的估计可能会大不相同。 我们将建立理论基础，以更细致入微的方式评估和优化控制系统的风险。由于真实的系统可能有许多维度、不完美的模型和无界的干扰，因此挑战是众多的。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各种想法，以开发具有理论保证的新型风险规避方法，并从城市水和水能源应用中获得灵感。3名博士和2名硕士学生将接受风险分析，控制理论，概率论和算法的高级培训。配备了这些多学科的技能，毕业生将训练有素，在加拿大的工程公司设计创新的解决方案。