*Article* **Stochastic Drift Counteraction Optimal Control of a Fuel Cell-Powered Small Unmanned Aerial Vehicle**

**Jiadi Zhang 1, Ilya Kolmanovsky <sup>1</sup> and Mohammad Reza Amini 2,\***


**Abstract:** This paper investigates optimal power management of a fuel cell hybrid small unmanned aerial vehicle (sUAV) from the perspective of endurance (time of flight) maximization in a stochastic environment. Stochastic drift counteraction optimal control is exploited to obtain an optimal policy for power management that coordinates the operation of the fuel cell and battery to maximize the expected flight time while accounting for the limits on the rate of change of fuel cell power output and the orientation dependence of fuel cell efficiency. The proposed power management strategy accounts for known statistics in transitions of propeller power and climb angle during the mission, but does not require the exact preview of their time histories. The optimal control policy is generated offline using value iterations implemented in Cython, demonstrating an order of magnitude speedup as compared to MATLAB. It is also shown that the value iterations can be further sped up using a discount factor, but at the cost of decreased performance. Simulation results for a 1.5 kg sUAV are reported that illustrate the optimal coordination between the fuel cell and the battery during aircraft maneuvers, including a turnpike in the battery state of charge (*SOC*) trajectory. As the fuel cell is not able to support fast changes in power output, the optimal policy is shown to charge the battery to the turnpike value if starting from a low initial *SOC* value. If starting from a high *SOC* value, the battery energy is used till a turnpike value of the *SOC* is reached with further discharge delayed to later in the flight. For the specific scenarios and simulated sUAV parameters considered, the results indicate the capability of up to 2.7 h of flight time.

**Keywords:** air mobility; fuel cell hybrid aircraft; stochastic optimal control; energy management; drift counteraction optimal control
