Real-Time Learning-Based Model Predictive Control: Online Algorithms and Applications in Energy Systems

Abstract

The increased availability of sensing and computational capabilities in modern cyber-physical systems and networked systems has led to a growing interest in learning and data-driven control techniques. Learning-Based Model Predictive Control (LBMPC), i.e. the integration of learning methods in Model Predictive Control schemes, is one technique with potential applications for the control of dynamical systems under uncertain and stochastic conditions including humans in the control loop. In real-time applications of LBMPC, control solutions must be achieved in limited time, given the computational burden of both the function-learning and control mechanisms. Furthermore, models and functions associated with users must be learned on the fly from possibly parsimonious feedback. In this work, a framework is proposed for a LBMPC scheme in which little or no prior information is known regarding the dynamic state functions of multiple devices and the cost functions modeling satisfaction, comfort or sense of safety of users interacting with these devices. Gaussian Processes are advocated as a non-parametric nonlinear function modeling technique to enable a low sampling rate for black-box dynamic state and dissatisfaction functions. A regularized primal-dual gradient-based optimization algorithm is adapted to the discrete-time case and integrated with the LBMPC framework to facilitate convergence in a real-time setting with a Q-linear tracking error. Considering the rapidly-evolving demands on the power grid as a result of increasing distributed energy resources, the proposed methodology is implemented for a typical Demand Response application, in which the power setpoints of a network of black-box thermostatically-controlled loads in a building are optimized to provide ancillary services to the grid under fluctuating power demands while minimizing costs incurred to the black-box users inhabiting the building. The methodology is also applied to the classic inverted pendulum problem for the purposes of comparing results across true and GP-learned dynamic state and cost functions.