History-Aware Control Barrier Functionals with Nonsingular Fading-Memory Kernels
Safety-critical protection often depends not only on the state and physical limits of the system, but on how that state evolved over time. Here, the safety margin measures the remaining allowance before a physical limit is reached. In this context, the objective is to enforce both physical safety and history-dependent retention of this margin for integer-order control-affine systems. To this end, changes in this margin are converted into memory through fading-memory kernels with finite nonnegative weights. A history-aware control barrier functional (HA-CBFal) is constructed explicitly, with nonnegativity equivalent to retaining a prescribed fraction of this margin's weighted historical value. This condition is enforced by an affine input constraint and proved to imply physical safety under stated kernel, initialization, and feasibility conditions, without finite-dimensional memory realization. In 36 calibration cases on the ADMIRE flight-control benchmark, mean per-case tracking-RMSE reductions of 27.2\% and 7.0\% are obtained relative to calibrated state-only CBF and moving-average control barrier functional (MA-CBFal), respectively, with both constraints preserved to numerical tolerance. In a shorter-recovery maneuver outside calibration with frozen gains, both constraints are preserved to tolerance by HA-CBFal and state-only CBF, but the retention requirement is violated despite MA-CBFal nonnegativity.