Theoretical Foundations for Risk-Averse Control Engineering

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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.