Energy-Efficient Continuous-Descent Operations

• Energy-efficient continuous-descent operations are defined by smooth, optimized trajectories that minimize fuel consumption, emissions, and noise through reduced thrust usage.
• Cooperative control using V2V and V2I communications enables cluster-wise vehicle coordination, increasing traffic throughput and operational robustness.
• Advanced scheduling and optimization methods, such as Dantzig–Wolfe reformulations and consensus-based control, significantly reduce energy use and computational time in complex traffic scenarios.

Energy-efficient continuous-descent operations (CDOs) are procedures in which vehicles—typically aircraft or connected automated ground vehicles (CAVs)—descend or decelerate smoothly along a trajectory that minimizes or eliminates level-offs and excessive power usage. This operational paradigm is designed to reduce fuel burn, emissions, and noise, while improving system throughput and occupant comfort. CDOs leverage advancements in optimal control, trajectory planning, and cooperative vehicle systems, with increasing integration of real-time communication and scheduling optimization. The following sections detail the principal algorithmic techniques, optimization frameworks, implementation strategies, and real-world impacts associated with energy-efficient CDOs, as substantiated by recent research.

1. Principles and Objectives of Continuous-Descent Operations

CDOs are defined by trajectories that maintain continuous, smooth descent profiles—ideally at or near idle-thrust for aircraft, or at minimum necessary propulsion for ground vehicles—thus precluding the need for level-off segments, full stops, or abrupt acceleration/deceleration. The primary objectives of CDOs are:

• Fuel and energy minimization: Reducing the integral of energy expenditure over the descent by shaping trajectories to exploit gravitational potential or minimize resistive forces.
• Emission and noise abatement: Lower energy consumption corresponds to reduced pollutant and acoustic emissions.
• Traffic flow efficiency: Coordinated descent profiles increase throughput by reducing delays, congestion, and conflict at points of high traffic density.
• Operational robustness: Smoother energy management improves vehicle system health and passenger comfort.

These principles are operationalized in multiple transport domains, notably via Eco-Approach and Departure (EAD) systems for CAVs at intersections (Wang et al., 2018), continuous-descent scheduling of aircraft arrivals in terminal maneuvering areas (TMAs) (Hajizadeh et al., 16 Sep 2025), and optimal powered-descent guidance for atmospheric/aerospace vehicles (Szmuk et al., 2018, Chen et al., 2022).

2. Algorithmic Methods: Cooperative and Cluster-wise Approaches

Significant advances in energy-efficient CDOs arise from shifting optimization from a single-vehicle “ego” perspective to a cooperative, cluster-wise framework. In the context of CAVs at signalized intersections, the cluster-wise cooperative EAD (Coop-EAD) algorithm (Wang et al., 2018) exemplifies this approach:

1. Initial Vehicle Clustering: Vehicles entering a communication range are grouped based on projected arrival times at the intersection, forming clusters whose members can share a contiguous “green window.”
2. Intra-cluster Sequence Optimization: Assigns sequencing to clustered vehicles using a job-scheduling formulation, with constraints on safe headways and unique position assignments.
3. Cluster Formation Control: Via consensus-based longitudinal control, clusters are physically formed with minimal inter-vehicle gaps, synchronizing velocity and position profiles.
4. Cooperative Eco-Approach and Departure: Cluster leaders receive SPaT (Signal Phase and Timing) information via V2I communication and determine the optimal approach/departure trajectory; cluster followers implement these trajectories using V2V synchronization.

Mathematically, the intra-cluster sequence problem is formulated as:

$\min E = \sum_i T_{\text{arr},i}$

subject to assignment and safety constraints.

The consensus-based longitudinal control is modeled as:

$$\dot{x}_i(t) = -a_{ij} [x_i(t)-x_i(t-\tau_i)+l_{if}+l_{jr}+d_{\text{safe}}] - \gamma a_{ij}[x_i(t)-x_j(t-\tau_i)]$$

This cooperative paradigm enables significant reductions in energy consumption, acceleration noise, and emissions compared to traditional ego-centric EAD approaches (see Section 3 for quantitative results).

3. Scheduling and Optimization of Arrival Routing

In air traffic management, the problem of sequencing and routing arrivals through a TMA with continuous-descent profiles has traditionally been formulated as a mixed-integer program (MIP) with arc-based or flow-based decision variables. Recent advances have adopted Dantzig–Wolfe (DW) reformulation techniques (Hajizadeh et al., 16 Sep 2025), which bring the following innovations:

• Path-based (column-generation) modeling: Rather than assign aircraft to network arcs, the DW model assigns entire feasible descent paths, each with a fixed speed and energy profile, to an aircraft’s entry point.
• Cost function with explicit energy integration: Each path π bears a cost $c_{b, \pi}$ that combines both path length (proxy for energy/fuel use) and “compactness” (tree structure favoring efficient merges).
• Tighter LP relaxation: The master problem in the DW reformulation selects paths $\rho_{b,\pi}$ for each entry point $b$, with side constraints to guarantee tree consistency and temporal separation at merge fixes, yielding a significantly tighter linear program than traditional arc-based models.

Master problem (abbreviated):

$$\min \sum_{b \in \mathcal{P}} \sum_{\pi \in \Pi_b} c_{b,\pi} \rho_{b,\pi}$$

subject to:

$$\sum_{\pi \in \Pi_b} \rho_{b,\pi} = 1\quad \forall b \in \mathcal{P}$$

and temporal/separation constraints at merge points.

This formulation allows for:

• Direct minimization of energy by selecting CDO paths with minimum fuel cost
• Efficient computational performance (e.g., reducing solution times from 40.9 hours to <1 hour in high-density TMA scenarios)
• Robust enforcement of safety (guaranteed separation between aircraft)

The selection of complete CDO profiles for each aircraft obviates the need for downstream compensatory maneuvers, preserving energy efficiency system-wide.

4. Quantitative Performance and Simulation Outcomes

Cluster-wise cooperative and path-based scheduling models yield demonstrable gains in empirical simulation:

Metric	Ego-EAD	Coop-EAD	% Improvement
Energy Consumption (KJ)	2222.94	1978.15	11% reduction
Pollutant Emissions (PM2.5)	–	–	up to 19.9%
Traffic Throughput (vehicles/period)	–	–	50% increase

(Cooperative EAD simulation, (Wang et al., 2018))

In arrival routing, the DW reformulation enables operationally feasible energy-optimal scheduling for TMA scenarios previously intractable due to computational constraints (Hajizadeh et al., 16 Sep 2025). Solutions for scenarios with up to 33 arrivals are delivered in under an hour, with retained guarantee of continuous-descent speed/fuel profiles and operational safety (wake turbulence separation enforced).

5. Communication Architectures: V2V, V2I, and Information Flow

The efficacy of CDO frameworks such as Coop-EAD is contingent on networked communication:

• Vehicle-to-Infrastructure (V2I): SPaT data for optimal trajectory computation by cluster leaders.
• Vehicle-to-Vehicle (V2V): Real-time broadcast of position, speed, and acceleration among cluster members for consensus-based control.
• Centralized coordination in aviation: CDO schedules in TMAs rely on ground-based or centralized planning systems propagating assignment decisions to aircraft in real time.

The simulation and modeling frameworks assume reliable, low-latency communications and high market penetration (i.e., all vehicles equipped), which remains a limitation for mixed-fleet or degraded infrastructure operations.

6. Operational Integration, Applications, and Limitations

Energy-efficient CDO methodologies offer immediate applicability in high-density, safety-critical domains:

• Urban arterial corridors with CAVs: Improved intersection throughput, emission reductions, and smoother traffic flow contingent on near-universal CAV deployment (Wang et al., 2018).
• Terminal area scheduling: Automated CDO arrival sequencing in busy airspaces, with robust recovery from disturbances and real-time re-optimization capability (Hajizadeh et al., 16 Sep 2025).

Key limitations include the assumption of 100% equipped fleets, fixed or scheduled signalization, and ideal communication. Real-world deployment must address the challenge of incremental adoption, stochastic disruptions, and mixed-traffic conditions. Notably, the intrinsic aerodynamic benefits of close vehicular platooning (expected to further reduce energy use) have not been fully integrated into energy modeling frameworks and represent an area for further research.

7. Future Directions and Research Opportunities

Emerging research seeks to extend CDO optimization by:

• Incorporating aerodynamic drag models and Vehicle-to-Everything (V2X) communication into energy models for more accurate assessment of savings.
• Handling mixed traffic (combination of equipped and non-equipped vehicles/aircraft) via adaptive and multi-level control architectures.
• Increasing robustness against communication delays, packet loss, and real-time traffic signal actuation, requiring predictive and estimation-based enhancements.
• Integrating real-time weather and wake-turbulence prediction for adaptive TMA scheduling.
• Scaling to networked intersections and multi-airport systems for global traffic optimization.

The focus remains on rigorous mathematical modeling, empirical validation, and system integration to realize the operational and environmental benefits of energy-efficient continuous-descent operations across mobility domains.