Parity-aligned control allocation for stochastic aeroelastic systems with distributed actuation

Atmospheric turbulence generates stochastic aerodynamic loads that excite coupled rigid-body and flexible aeroelastic modes, producing transient rotational disturbances that may affect structural integrity, actuator usage, and passenger comfort. Conventional constrained control-allocation methods distribute actuator commands directly in actuator coordinates and usually treat actuator geometry as a passive constraint rather than an exploitable stabilizing structure. Here, we develop a symmetry-structured control-allocation framework for distributed aeroelastic systems with bilaterally paired actuators. The framework is based on an equivariant control-effectiveness relation, MPg=QgM, where Pg represents reflection symmetry in actuator space and Qg represents the corresponding action on roll, pitch, and yaw moment space. This formulation permits symmetric and antisymmetric actuator modes to generate their physically appropriate even and odd moment components, avoiding the incorrect implication that antisymmetric modes vanish. Under equivariance and compatible actuator constraints, the allocation problem admits a parity-aligned decomposition into convex subproblems; under asymmetric saturation or effectiveness loss, the same structure provides a block-preconditioned allocation with feasibility correction. A covariance-based stochastic analysis shows that, when the symmetry-aligned residual operator satisfies a spectral contraction condition, the maximal eigenvalue of the residual disturbance covariance decreases, yielding sharper Gaussian concentration bounds for extreme residual loads. Numerical experiments using a three-axis reduced-order moment-level allocation model with twenty-four distributed actuators show that, in the nominal exactly equivariant case, parity-aligned allocation reproduces the full-space damped-pseudoinverse response to numerical roundoff, with identical residual loads, covariance metrics, actuator-utilization patterns, and saturation statistics. These results validate the corrected parity formulation while showing that tail-risk reduction should be claimed only in regimes where spectral contraction is empirically observed. An additional controlled nonlinear stress-test with cubic disturbance deformation, quadratic cross-axis coupling, and smooth actuator-effectiveness terms shows that residual scales increase under moderate nonlinear perturbation, while the full-space and parity-aligned responses coincide to numerical roundoff.