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Hybrid-electric aircraft represent an important step in the transition from conventional fuel-based propulsion to fully-electric aircraft. For hybrid power systems, overall aircraft performance and efficiency highly depend on the coordination of the fuel and electrical systems and the ability to effectively control state and input trajectories at the limits of safe operation. In such a safety-critical application, the chosen control strategy must ensure the closed-loop system adheres to these operational limits. While hierarchical Model Predictive Control (MPC) has proven to be a computationally efficient approach to coordinated control of complex systems across multiple timescales, most formulations are not supported by theoretical guarantees of actuator and state constraint satisfaction. To provide guaranteed constraint satisfaction, this paper presents set-based hierarchical MPC of a 16 state hybrid-electric aircraft power system. Within the proposed two-level vertical hierarchy, the long-term control decisions of the upper-level controller and the short-term control decisions of the lower-level controller are coordinated through the use of waysets. Simulation results show the benefits of this coordination in the context of hybrid-electric aircraft performance and demonstrate the practicality of applying set-based hierarchical MPC to complex multi-timescale systems. 

In modern high-performance aircraft, the Fuel Thermal Management System (FTMS) plays a critical role in the overall thermal energy management of the aircraft. Actuator and state constraints in the FTMS limit the thermal endurance and capabilities of the aircraft. Thus, an effective control strategy must plan and execute optimized transient fuel mass and temperature trajectories subject to these constraints over the entire course of operation. For the control of linear systems, hierarchical Model Predictive Control (MPC) has shown to be an effective approach to coordinating both short- and long-term system operation with reduced computational complexity. However, for controlling nonlinear systems, common approaches to system linearization may no longer be effective due to the long prediction horizons of upper-level controllers. This paper explores the limitations of using linear models for hierarchical MPC of the nonlinear FTMS found in aircraft. Numerical simulation results show that linearized models work well for lower-level controllers with short prediction horizons but lead to significant reductions in aircraft thermal endurance when used for upper-level controllers with long prediction horizons. Therefore, a mixed-linearity hierarchical MPC formulation is presented with a nonlinear upper-level controller and a linear lower-level controller to achieve both high performance and high computational efficiency. 

The performance of hierarchical Model Predictive Control (MPC) is highly dependent on the mechanisms used to coordinate the decisions made by controllers at different levels of the hierarchy. Conventionally, reference tracking serves as the primary coordination mechanism, where optimal state and input trajectories determined by upper-level controllers are communicated down the hierarchy to be tracked by lower-level controllers. As such, significant tuning is required for each controller in the hierarchy to achieve the desired closed-loop system performance. This paper presents a novel terminal cost coordination mechanism using constrained zonotopes, designed to improve system performance under hierarchical control. These terminal costs allow lower-level controllers to balance both short- and long-term control performance without the need for controller tuning. Unlike terminal costs widely used to guarantee MPC stability, the proposed terminal costs are time-varying and computed on-line based on the optimal state trajectory of the upper-level controllers. A numerical example demonstrates the provable performance benefits achieved using the proposed terminal cost coordination mechanism.