UC Berkeley

In this thesis we study the optimal control of networked energy systems. Networked energy systems consist of a collection of energy storage nodes and a network of links and inputs which allow energy to be exchanged, injected, or removed from the nodes. The nodes may exchange energy between each other autonomously or via controlled flows between the nodes. Examples of networked systems include building heating, ventilation, and air conditioning (HVAC) systems and networked battery systems. In the building system example, the nodes of the system are rooms which store thermal energy in the air and other elements which have thermal capacity. The rooms transfer energy autonomously through thermal conduction, convection, and radiation. Thermal energy can be injected into or removed from the rooms via conditioned air or slabs. In the case of a networked battery system, the batteries store electrical energy in their chemical cells. The batteries may be electrically linked so that a controller can move electrical charge from one battery to another. Networked energy systems are typically large-scale (contain many states and inputs), affected by uncertain forecasts and disturbances, and require fast computation on cheap embedded platforms.

In this thesis, the optimal control technique we study is model predictive control for networked energy systems. Model predictive or receding horizon control is a time-domain optimization-based control technique which uses predictive models of a system to forecast its behavior and minimize a performance cost subject to system constraints. In this thesis we address two primary issues concerning model predictive control for networked energy systems: robustness to uncertainty in forecasts and reducing the complexity of the large-scale optimization problem for use in embedded platforms. The first half of the thesis deals primarily with the efficient computation of robust controllers for dealing with random and adversarial uncertainties in the forecasts. We show that the exact control policies can be found efficiently for certain types of robust predictive control problems. The second half of the thesis deals with improving computation speed and memory usage through model reduction and exploitation of symmetries in the predictive control problem. We present a model reduction technique tailored for networked systems which preserves sparsity and thus greatly improves computation speed. We also show how to apply symmetry methods for efficient computation of explicit model predictive controllers to systems which are not perfectly symmetric.