Set-based Hierarchical Control for Multi-timescale Energy Management




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The high-level goal of this PhD dissertation is to develop novel controller formulations and analysis techniques to provide provable closed-loop system behaviors for complex systems. Specifically, this dissertation focuses on the use of novel set-based mechanisms in the development of hierarchical Model Predictive Control (MPC) formulations for multi-timescale energy management systems. Many complex systems such as hybrid-electric vehicle energy systems, smart power grids, water distribution networks, and Heating Ventilation and Air- Conditioned (HVAC) systems are multi-timescaled and have long operation times. A single centralized MPC controller with fast update rates and a long prediction horizon might not be able to solve the control optimization problem within the allocated time and thus, real-time control actuation is not possible. Alternatively, a hierarchical control architecture can be used to distribute control decisions among various controllers connected in a hierarchy where the upper-level controller plans coarse state and input trajectories at slow time steps while the lower-level controllers utilizes this information to plan state and input trajectories at fast time steps. However, existing hierarchical formulations are not well suited to maximize system transient performance subject to state, input, and terminal constraints. The open research challenge is how to provide the flexibility to the lower-level controllers through novel coordination mechanisms to maximize control performance while guaranteeing state, input, and terminal constraint satisfaction. To achieve a computationally efficient hierarchical MPC algorithm for multi-timescale energy management, the following research problems are addressed in this dissertation.

  1. Development of a multi-level vertical hierarchical MPC framework for systems with additive known and unknown bounded disturbances. The proposed hierarchical control algorithm is proven to be recursively feasible and is scalable with increase in prediction horizon and number of states. The sub-optimality index of the hierarchical controller is enhanced through a wayset and terminal cost-based coordination. To facilitate a computationally efficient hierarchical control algorithm, set computations have been developed for zonotopes and constrained zonotopes with a focus on application to systems and control.
  2. Development of a tube-based robust MPC with simultaneous optimization of uncertainty sets using zonotopes. The proposed control formulation guarantees recursive feasibility and constraint satisfaction to bounded additive disturbances from an uncertainty set optimized in real-time. The control formulation is extended to a full hierarchical MPC where the uncertainty is quantified based on difference in control decisions between hierarchical levels and between controllers in the same level. The hierarchical control framework is shown to be recursively feasible and guarantees state and input constraint satisfaction.
  3. Development of a wayset-based Stochastic MPC framework that guarantees Mission- Wide Probability of Safety (MWPS) for systems with long duration. To enable longer missions under greater uncertainty, the wayset-based stochastic MPC allows for the prediction horizon of the MPC to be significantly shorter than the length of the mission. A scenario-based approach is used to approximate the stochastic MPC formulation and recursive feasibility is proven.



Engineering, Mechanical