Abstract
Safety evaluation in sampling-based stochastic model predictive control often requires numerical estimation of exit functionals. The approximation of first-exit times and exit indicators is therefore a key numerical bottleneck, and discretization error in these quantities directly affects the resulting controller. This paper studies how existing higher-order methods for strong approximation of exit times can be brought into safe control. Two cases are highlighted. For general noncommutative dynamics, an adaptive order-1 Milstein discretization is used together with Lévy-area simulation via Wiktorsson's method. For commutative dynamics, an adaptive order-1.5 construction achieves a stronger exit-time rate. Under a local anti-concentration condition on the exit-time law, we show that strong exit-time approximation transfers to strong approximation of the failure indicator. The methods are then studied in the context of chance-constrained path integral control, which provides an exact continuous-time representation of safety through exit events. Numerical experiments compare the two cases in terms of strong exit-time error, failure-indicator error, and closed-loop constraint satisfaction, showing improvement over Euler-Maruyama and thereby enabling existing and future techniques whose applicability depends on improved strong approximation.
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Cite this article
APA 7
Modali, S., & Tanaka, T. (2026). Higher-Order Approximation of Exit Functionals in Sampling-Based Stochastic Model Predictive Control. https://omanscience.com/en/articles/higher-order-approximation-of-exit-functionals-in-sampling-based-stochastic-model-predictive-control
MLA 9
Modali, Sashank, and Takashi Tanaka. "Higher-Order Approximation of Exit Functionals in Sampling-Based Stochastic Model Predictive Control." https://omanscience.com/en/articles/higher-order-approximation-of-exit-functionals-in-sampling-based-stochastic-model-predictive-control.
Chicago (author–date)
Modali, Sashank, and Takashi Tanaka. 2026. "Higher-Order Approximation of Exit Functionals in Sampling-Based Stochastic Model Predictive Control." https://omanscience.com/en/articles/higher-order-approximation-of-exit-functionals-in-sampling-based-stochastic-model-predictive-control.
Harvard
Modali, S. and Tanaka, T. (2026) 'Higher-Order Approximation of Exit Functionals in Sampling-Based Stochastic Model Predictive Control', Available at: https://omanscience.com/en/articles/higher-order-approximation-of-exit-functionals-in-sampling-based-stochastic-model-predictive-control.
Vancouver
Modali S, Tanaka T. Higher-Order Approximation of Exit Functionals in Sampling-Based Stochastic Model Predictive Control. https://omanscience.com/en/articles/higher-order-approximation-of-exit-functionals-in-sampling-based-stochastic-model-predictive-control
IEEE
S. Modali, and T. Tanaka, "Higher-Order Approximation of Exit Functionals in Sampling-Based Stochastic Model Predictive Control," https://omanscience.com/en/articles/higher-order-approximation-of-exit-functionals-in-sampling-based-stochastic-model-predictive-control.