Distributionally Robust Control and Incentives with Safety and Risk Constraints

从物联网和网络物理系统收集的大量数据可以对我们的社会产生变革性影响，从个性化医疗到城市基础设施系统。然而，一些与鲁棒性、安全性、风险和可靠性相关的问题已经被提出，这些问题集中在如何将如此大规模的数据纳入解决关键的决策问题，因为数据和估计的统计模型通常是不准确的。因此，提出的研究将建立一个控制理论基础，通过允许统计模型中的分布误差和通过开发对误差具有鲁棒性的控制策略来解决这个问题。分布式鲁棒控制工具的潜在应用领域包括电池管理系统、电网、食品供应链、制造系统和个性化医疗。随着所提出的控制工具在这些领域的成功实施，我们将能够提高个人安全和生活质量，以及数据驱动控制系统的可靠性，这将建立社会的高度信心。该项目的研究成果也将用于(i)南加州大学雪佛龙能源研究前沿夏令营，这是我们K-12 STEM推广工作之一；（ii）南加州大学女性科学和工程项目，为本科生提供实践研究经验；（iii）维特比工程多样性中心的开放日和研讨会，培训和招募教育上弱势的、代表性不足的学生。我们提出的研究的总体目标是为与有限信息运行的安全关键和/或非合作系统相关的分布式鲁棒控制问题发展理论基础和计算方法。建议的工具可以促进以下三个基本领域：1。随机控制理论：本研究旨在为面对不确定变量的模糊分布信息的非线性随机系统建立分布鲁棒控制方法的博弈论和算法基础。特别是，我们将研究一种基于对偶的动态规划解决方案，以缓解控制问题中的无限维问题，并将其与（深度）神经网络和基于职业度量的方法相结合，系统地调整计算复杂度和求解精度。安全和风险意识控制理论：我们将把随机可达性分析方法扩展到关于扰动概率分布的不完全信息的情况。该分布式鲁棒可达性工具将用于指定系统无法保持在安全范围内的最坏情况概率和系统损失的最坏情况风险。基于安全和风险规范，我们将提出一种系统的方法来综合安全保持和风险感知控制律，该律对干扰分布模糊性具有鲁棒性。3. 激励契约理论：道德风险下的激励契约可以用来协调由局部代理控制的非合作子系统，在这些子系统中，局部控制行为和不确定变量无法被中央协调者监控。为了扩大合同对工程和社会技术问题的适用性，我们将在两个方向上推广该理论：(i)将具有非平凡动力学的工程系统集成到合同中，以及（ii）以分布式鲁棒方式构建激励合同。

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.