Stochastic Control of Multidimensional Systems with Relative Optimization

Xi Ren Cao

doi:10.1109/TAC.2019.2925469

Stochastic Control of Multidimensional Systems with Relative Optimization

Xi Ren Cao^*

^*Corresponding author for this work

Department of Electronic and Computer Engineering

Research output: Contribution to journal › Journal Article › peer-review

2 Citations (Scopus)

Abstract

We derive the Tanaka formula for multidimensional semismooth functions with the local time on the semismooth curve along the gradient direction. With this formula, we extend the relative optimization based approach to stochastic control to multidimensional systems. Optimality conditions are derived for systems with semismooth value functions, and no viscosity solution is involved. This approach provides new insights and motivates the research on stochastic control and stochastic calculus, in particular, for problems with nonsmooth features and degenerate points.

Original language	English
Article number	8747547
Pages (from-to)	1886-1900
Number of pages	15
Journal	IEEE Transactions on Automatic Control
Volume	65
Issue number	5
DOIs	https://doi.org/10.1109/TAC.2019.2925469
Publication status	Published - May 2020

Bibliographical note

Publisher Copyright:
© 2020 IEEE.

Keywords

Ito-Tanaka formula
local time
relative optimization theory
semismooth function
viscosity solution

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10.1109/TAC.2019.2925469

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abstract = "We derive the Tanaka formula for multidimensional semismooth functions with the local time on the semismooth curve along the gradient direction. With this formula, we extend the relative optimization based approach to stochastic control to multidimensional systems. Optimality conditions are derived for systems with semismooth value functions, and no viscosity solution is involved. This approach provides new insights and motivates the research on stochastic control and stochastic calculus, in particular, for problems with nonsmooth features and degenerate points.",

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AB - We derive the Tanaka formula for multidimensional semismooth functions with the local time on the semismooth curve along the gradient direction. With this formula, we extend the relative optimization based approach to stochastic control to multidimensional systems. Optimality conditions are derived for systems with semismooth value functions, and no viscosity solution is involved. This approach provides new insights and motivates the research on stochastic control and stochastic calculus, in particular, for problems with nonsmooth features and degenerate points.

KW - Ito-Tanaka formula

KW - local time

KW - relative optimization theory

KW - semismooth function

KW - viscosity solution

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JF - IEEE Transactions on Automatic Control

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Stochastic Control of Multidimensional Systems with Relative Optimization

Abstract

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Keywords

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