Asymptotic distribution theory for stochastic control

Xinjia Chen

doi:10.1117/12.3013235

7 June 2024 Asymptotic distribution theory for stochastic control

Xinjia Chen

Proceedings Volume 13055, Unmanned Systems Technology XXVI; 130550H (2024) https://doi.org/10.1117/12.3013235
Event: SPIE Defense + Commercial Sensing, 2024, National Harbor, Maryland, United States

Abstract

The advancement of unmanned systems has set higher standards for making control decisions in the presence of uncertainty. In many unmanned system tasks, stochastic processes influence the stopping time of decision and the control performance index. This paper introduces an asymptotic distribution theory for stochastic processes with independent increments relevant to control systems. We show that, when properly normalized, the stopping time of control decision and the value of the stochastic processes at the stopping time converge asymptotically and independently, with the normalized value of the stochastic processes at the stopping time converging to a Gaussian random variable. Additionally, we derive the limiting distribution for the performance index, which depends on the stopping time and the corresponding value of the stochastic process. To illustrate the practical applications of these asymptotic results, we provide an example related to an integration system, a crucial component in stochastic control systems.

Conference Presentation

(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.

Citation Download Citation

Xinjia Chen "Asymptotic distribution theory for stochastic control", Proc. SPIE 13055, Unmanned Systems Technology XXVI, 130550H (7 June 2024); https://doi.org/10.1117/12.3013235

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