arXiv:2610.18361v1 Announce Type: new Abstract: Real-time control systems may experience sporadic computational overloads that cause controller executions to overrun their expected deadlines, affecting the timely update of control inputs. Such overruns are classically handled with static decisions, e.g., by either stopping and discarding the late execution at the deadline instant, or continuing it while skipping the next activations. This paper first demonstrates that such static policies can lead to suboptimal performance when the controlled system undergoes varying operating conditions, and thus proposes a control-driven hybrid overrun strategy that optimally adapts the deadline miss handling at runtime. We model the closed loop as a Markov jump linear system, whose modes encode overrun histories, and we formulate a scenario-tree-based stochastic model predictive control problem that predicts and optimizes over possible sequences of deadline hits and misses. We evaluate our proposal on linear benchmarks including a double integrator and an aircraft pitch system.