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Stochastic Learning and Optimization with Imperfect Data in Cyber-Physical Systems
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Principal goal of this dissertation is to study stochastic learning and optimization of cyber-physical systems (CPSs) with imperfect data. CPSs are engineered systems that are built from, and depend upon, the seamless integration of computation and physical components. The recent success of data-driven approaches based on the collection of a large amount of data followed by learning and inference will transform the design and operation process into one in which data, models and human designers continuously interact. Therefore, the quality of data plays an important role in the design and operation process, and data imperfections might lead into a CPS with less reliability, adaptability, scalability, resiliency, safety, security, and usability. The degraded quality of data in the context of the cyber-physical energy systems stems from the unique features and requirements of CPSs such as the stochastic nature of communication and measurement infrastructures and privacy measures. To overcome the challenges of the imperfect data, efforts need to revolve around all the constituent problems, and the spectrum of research topics relevant to CPSs is very broad in the energy systems. This dissertation aims to investigate stochastic optimization and learning in CPSs with the focus on data quality issues in user-side demand management programs, and system-side event diagnostic mechanisms.The first part investigates stochastic learning in the incentive-based demand response (DR) programs with perturbed data. A key challenge is how to determine the incentive rates to incentivize users to adapt their loads to supply availability, as users either would show random responses and also perturb their power usage to protect their privacy. Under a stochastic Stackelberg game, we cast the incentive-based DR problem as a learning problem, such that the best incentive strategy can be obtained by learning the users' randomized behaviors. For the non-privacy-preserving users, the DR problem boils down to solve the classical best response problem by converging to an equilibrium point. However, the proposed stochastic game for privacy-preserving users would not converge to a stable mixed strategy equilibrium using the classic best response dynamics since the LSE learns over the users' perturbed behaviours. In this regard, we adopt the notation of the smooth best response as a tool to overcome difficulties in converging to the optimal incentive strategy for the perturbed observations.The second part studies the stochastic optimization for an event diagnosis and control scheme in presence of data imperfections. Three components for the proposed scheme (i.e., data recovery, state estimation, and control) are investigated to not only ensure the system full observability, but also to diagnose the disruptive events and offer the remedial actions in order to have efficient and reliable system operations. First, we focus on the stochastic optimization in the data recovery problem in presence of missing phasor measurement units (PMUs) data. We propose a novel regularized low-rank tensor completion (LRTC) framework to extract the latent structures of PMU data in order for improving the imputation accuracy. Second, we propose a decentralized dynamic system estimation (DSE) scheme by employing an unscented Kalman filter (UKF) to find efficient and unbiased estimates of the system states. Last, we design an intelligent contingency management framework by leveraging a robust deep reinforcement learning (DRL) algorithm to better handle the contingencies in real-time operations while considering the effect of the measurement noise in the design process.