An asymptotic distribution theory with applications to adaptive decision and control

Xinjia Chen

doi:10.1117/12.2618187

31 May 2022 An asymptotic distribution theory with applications to adaptive decision and control

Xinjia Chen

Proceedings Volume 12124, Unmanned Systems Technology XXIV; 121240J (2022) https://doi.org/10.1117/12.2618187
Event: SPIE Defense + Commercial Sensing, 2022, Orlando, Florida, United States

Conference Poster

Abstract

The advancement of modern control systems leads to increasingly high standard on the capability of systems to make decisions and control strategies in an adaptive and efficient way. In many applications, the decision time and performance index of control are determined by stochastic processes. In this paper, we develop a family of new limit theorems on the joint convergence of partial sums of independent random vectors and associated random indexes under general assumptions. We demonstrate that the random index and the partial sum are asymptotically independent under a proper normalization, with the partial sum converges in distribution to a random variable of normal distribution. Moreover, we obtain limit theorems for functions of partial sums, random indexes, and parameters, which include central limit theorems as special cases. We also extend the results to Levy processes. An illustrative example is given on an integration system, which is a building block of control and decision systems.

Conference Presentation

Citation Download Citation

Xinjia Chen "An asymptotic distribution theory with applications to adaptive decision and control", Proc. SPIE 12124, Unmanned Systems Technology XXIV, 121240J (31 May 2022); https://doi.org/10.1117/12.2618187

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