Tao Wang

May 2013
Control and Optimization Approaches for Power Management in Energy-Aware Battery-Powered Systems
Committee Members: Advisor: Christos Cassandras, SE/ECE; Yannis Paschalidis, SE/ECE; Michael Caramanis, SE/ME; Pirooz Vakili, SE/ME

Abstract: Motivated by the increasing dependence of many systems on battery energy, we study the energy-aware performance of battery-powered systems based on non-ideal battery models. First, we investigate the problem of optimally controlling how to discharge and recharge a non-ideal battery so as to maximize the work it can perform over a given time period and still maintain a desired final energy level. Modeling a battery as a dynamic system, we adopt a Kinetic Battery Model (KBM) and formulate an optimal control problem when recharging is always feasible under the constraint that discharging and recharging cannot occur at the same time. The solution is shown to be of bang-bang type with the property that the battery is always in recharging mode during the last part of the interval. When the length of the time interval exceeds a critical value, we also show that the optimal policy includes chattering. We then develop the problem to settings where recharging is only occasionally feasible and show that it can be reduced to a nonlinear optimization problem which can be solved at least numerically. Moreover, inspired by the connection between the KBM and another more elaborate non-ideal battery model, we employ the latter in the same problem framework and compare the corresponding solution with the one based on the KBM. The results show the same solution structure and demonstrate the validity of our solution to the general non-ideal battery systems.

Furthermore, we extend our research to multi-battery systems. First, we study the problem of optimally controlling a set of non-ideal rechargeable batteries that can be shared to perform a given amount of work over some specified time period. We seek to maximize the minimum residual energy among all batteries at the end of this period by optimally controlling the discharging and recharging process at each battery. Still by adopting the KBM, we formulate an optimal control problem under the constraint that discharging and recharging cannot occur at the same time. We show that the optimal solution must result in equal residual energies for all batteries as long as such a policy is feasible, which simplifies the task of subsequently deriving explicit solutions for the problem. Second, we explore the influence of non-ideal battery models on the lifetime maximization in wireless sensor networks (WSN). By replacing the ideal battery model with the KBM in the same lifetime maximization problem framework, we find even though the computational complexity to achieve a solution is increased due to the more complicated battery model, we still preserve the property of solution, i.e., the existence of a static optimal routing policy, which motivates more investigation in future research on battery-powered network systems.