Compute-Constrained Safety Filters with Neuromorphic Event Triggering

Safety filters that rely on control barrier function (CBF) quadratic programs (QPs) are typically analyzed under the assumption that the QP is solved instantaneously, although nonzero computation time can render a computed input unsafe by the time it is applied. This paper develops a dual leaky integrate-and-fire (LIF) event-triggered safety filter for linear systems that accounts for this delay. Two LIF states monitor a shifted CBF residual and the deviation of the held input from the nominal feedback law. A computation is initiated when either LIF state reaches its threshold; the previous input remains applied until the prescribed application time, and any solution returned earlier is stored until then. A closed-form charging profile relates the safety-LIF threshold to residual-growth bounds, ensuring sufficient residual margin over the application delay. Under the stated assumptions, the resulting hybrid system guarantees forward invariance, completeness, and non-Zeno execution, with positive lower bounds on computation-initiation and input-application times. A spacecraft terminal-approach simulation demonstrates safety with fewer optimizer calls than a delay-tightened periodic filter.