The Space-Time Transform: Memory-Augmented Control Barrier Functions

What the math gives to ML

The paper offers a constructive replacement for memoryless control-barrier operators with proper space-time kernels that attenuate high-frequency measurement noise while retaining affine dependence on the control input. Its central transferable mechanism is a dynamic barrier state whose invariance condition can still be enforced by a small quadratic program, together with a robust forward-invariance guarantee. The most direct neural-network transfer is a safety layer for learned robot policies: filter the noisy barrier residual rather than filtering the neural action after the fact. This predicts a measurable frequency-dependent reduction in action chattering and a feasibility boundary determined by the filter bandwidth and actuator limits.