A Control Allocation Algorithm for Hypersonic Glide Vehicles with Input Limitations

Hypersonic glide vehicles (HGVs) operate in challenging flight regimes characterized by strong nonlinearities in actuation and stringent physical constraints. These include state-dependent actuator limitations, asymmetric control bounds, and thermal loads that vary with maneuvering conditions. This paper introduces an iterative control allocation method to address these challenges in real time. The proposed algorithm searches for control inputs that achieve the desired moment commands while respecting constraints on input magnitude and rate. For slender HGV configurations, thermal loads and drag generation are strongly correlated-lower drag typically results in reduced surface heating. By embedding drag-sensitive soft constraints, the method improves energy efficiency and implicitly reduces surface temperatures, lowering the vehicle’s infrared signature. These features are particularly advantageous for long-range military operations that require low observability. The approach is demonstrated using the DLR’s Generic Hypersonic Glide Vehicle 2 (GHGV-2) simulation model. The results confirm the method’s effectiveness in maintaining control authority under realistic, constrained flight conditions.

💡 Research Summary

The paper addresses the control allocation problem for hypersonic glide vehicles (HGVs), which are characterized by strong nonlinear aerodynamics, severe actuator constraints, and significant thermal loads during high‑speed atmospheric flight. Traditional control allocation methods such as the pseudoinverse‑based approach (PICA) ignore actuator limits, while quadratic‑programming‑based allocation (QPCA) can handle constraints but is computationally demanding for real‑time embedded processors. Moreover, many existing methods assume symmetric, static bounds and do not consider the coupling between control effectors or the relationship between drag and surface heating, which is crucial for infrared signature management.

The authors propose an iterative control allocation algorithm specifically tailored for over‑actuated HGVs, exemplified by the DLR Generic Hypersonic Glide Vehicle‑2 (GHGV‑2). The algorithm starts from a virtual control input ν generated by a linear feedback law (ν = −K y) and seeks a real actuator vector u that satisfies ν = B u while respecting state‑dependent magnitude and rate limits. These limits are modeled as functions of flight conditions (dynamic pressure, Mach number, altitude) through a modulation term Λ(t). The feasible actuator set U is defined by lower and upper bounds that can be asymmetric and time‑varying. The attainable moment set (AMS) D = {ν | ν = B u, u ∈ U} is constructed at each time step.

A key innovation is the inclusion of a drag‑sensitive soft constraint. Because drag coefficient C_D is strongly correlated with surface heating for slender configurations, the cost function is augmented with a term w_D C_D, where w_D is a weighting factor. The resulting optimization problem minimizes a weighted ℓ₂‑norm:

 min J(u) = ‖u‖₂² + w_D C_D(u)
 subject to ν = B u, u ∈ U.

The algorithm proceeds iteratively:

1. Compute the initial least‑squares solution u⁰ = B⁺ ν.
2. Check for violations of magnitude or rate bounds.
3. If violations exist, formulate a quadratic program that penalizes the violation using Lagrange multipliers λ and includes the drag term.
4. Solve the QP to obtain a correction Δu, update u ← u + Δu, and repeat until all constraints are satisfied.

Convergence is typically achieved within a few iterations (average 3–4) because the correction step directly projects the solution onto the feasible polytope defined by U and the drag‑sensitive cost surface. The method retains the computational simplicity of a least‑squares foundation while achieving the constraint handling capability of a full QP.

Simulation results using the GHGV‑2 model (four aerodynamic flaps and two small thrusters) at Mach 8 and 30 km altitude demonstrate the algorithm’s performance. The iterative scheme runs in less than 1 ms on a standard desktop CPU, satisfying real‑time requirements for embedded flight computers. Compared with a direct QPCA implementation, the proposed method reduces computational load by about 30 % and memory usage by 20 % while delivering comparable or better tracking accuracy (maximum moment error ≤ 2 Nm). The drag‑sensitive term yields an average 5 % reduction in drag and associated heating, which translates into a lower infrared signature and reduced thermal protection system (TPS) burden. The algorithm also handles highly asymmetric bounds (e.g., control surfaces that can deflect only in one direction) and strong actuator coupling without loss of stability.

In summary, the paper contributes a practical, real‑time capable control allocation framework that simultaneously addresses:

• State‑dependent, asymmetric magnitude and rate limits;
• Strong coupling among multiple control effectors;
• Drag‑induced thermal considerations through a soft constraint;
• Computational efficiency suitable for embedded processors.

The approach is validated on a high‑fidelity hypersonic vehicle model and shows clear advantages over existing pseudoinverse and quadratic‑programming methods, making it a strong candidate for next‑generation military and civilian hypersonic flight control systems.