A Data-Driven Approach for Modeling, Analysis and Control of Stochastic Hybrid Systems using Gaussian Processes

Abstract

The growing advances in information technologies have led to a new generation of systems known as cyber-physical systems (CPS). CPS are multi-discipline engineering systems, which integrate computational and physical processes such as smart buildings, and self-driving urban vehicles. Great opportunities and research challenges arise to enable the development of new CPS technologies that can incorporate complex computational algorithms such as learning with complex physical systems. Moreover, the developments in sensor technologies enable the utilization of data to build robust models of complex physical systems. These robust models are needed to achieve intelligent CPS and to automate their design and control processes. Data availability can potentially support the use of machine learning techniques to develop nonparametric robust models, which can be used for prediction, analysis, and control of CPS. This dissertation presents a data-driven approach to learn, analyze and control many modern CPS based on nonparametric stochastic hybrid systems (SHS). SHS are multi-modal models which represent systems with coupled continuous and discrete dynamics. This dissertation presents an online clustering-based model learning approach, which leverages sensor measurements to learn nonparametric SHS based on Gaussian processes and periodic Markov chains. Essentially, Gaussian processes represent the continuous dynamics of the SHS and periodic Markov chains represent the discrete dynamics of the SHS. The learning approach uses a clustering algorithm such as K-means to identify the latent discrete states of the system, and it runs efficiently in an online fashion so that the system model is updated as new sensor measurements become available. In addition, this dissertation presents a reachability analysis algorithm for a finite-horizon. The reachability analysis algorithm estimates the distribution of the reachable states using mixtures of Gaussian processes and it provides an efficient multi-step prediction for nonparametric SHS. Further, this dissertation presents a scenario-based model predictive control (MPC) to provide an optimal control algorithm for stochastic systems represented by nonparametric SHS. The control algorithm estimates analytically the gradients of the SHS model and the cost function to enhance the accuracy and the efficiency of its optimization routines. Our work considers an in-depth case study of smart buildings and high-fidelity simulation to evaluate and to demonstrate the developed approach.