Distributionally Robust Control and Incentives with Safety and Risk Constraints

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Massive data collected from the Internet-of-Things and cyber-physical systems can have transformative impacts on our society, spanning from personalized medicine to urban infrastructure systems. However, several concerns related to robustness, safety, risk, and reliability have been raised centered on how to incorporate such large-scale data into solving critical decision-making problems, as the data and the estimated statistical models are often inaccurate. Thus, the proposed research will establish a control-theoretic foundation to resolve this issue by allowing distributional errors in the statistical models and by developing control strategies that are robust against the errors. The potential application domains of the proposed distributionally robust control tools include battery management systems, power grids, food supply chains, manufacturing systems and personalized medicine. With the successful implementations of the proposed control tools in such domains, we will be able to improve individual safety and quality of life, and the reliability of data-driven control systems, which would build high confidence in society. The research outcomes in this project will also be used for (i) the USC Chevron Frontiers in Energy Research Summer Camp which is one of our K-12 STEM outreach efforts; (ii) USC Women in Science and Engineering programs that provide hands-on research experiences to undergraduate and (iii) open house and workshops in Viterbi Center for Engineering Diversity to train and recruit educationally-disadvantaged underrepresented students. The overarching goal of our proposed research is to develop theoretical foundations and computational methods for distributionally robust control problems associated with safety-critical and/or non-cooperative systems that operate with limited information. The proposed tools can contribute to the following three fundamental areas: 1. Stochastic control theory: The proposed research aims to establish a game theoretical and algorithmic foundation of distributionally robust control methods for nonlinear stochastic systems when faced with ambiguous distributional information about uncertain variables. In particular, we will investigate a duality-based dynamic programming solution to alleviate the infinite-dimensionality issue in the control problem and combine it with (deep) neural network- and occupation measure based methods to systematically adjust computational complexity and solution accuracy.2. Safety and risk aware control theory: We will extend stochastic reachability analysis methods to cases with imperfect information about the probability distribution of disturbances. This distributionally robust reachability tool will be used to specify the worst-case probability that the system fails to stay in the safe range and the worst-case risk of system loss. Based on the safety and risk specifications, we will then propose a systematic approach to synthesize a safety preserving and risk-aware control law that is robust against disturbance distributional ambiguity. 3. Incentive contract theory: Incentive contracts under moral hazard can be used to coordinate noncooperative sub-systems controlled by local agents in which local control actions and uncertain variables cannot be monitored by a central coordinator. To broaden the applicability of the contracts to engineering and socio-technical problems, we will generalize the theory in two directions: (i) integrating engineering systems with nontrivial dynamics into contracts, and (ii) constructing incentive contracts in a distributionally robust fashion.