Optimal discharge and recharge control of battery-powered energy-aware systems

Motivated by the increasing dependence of many systems (such as wireless devices) on battery energy, we study 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 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, which motivates seeking ways to prevent such behavior. Numerical results are included to illustrate our analysis.