Controller design and energy analysis for stochastic differential systems with one-sided polynomial growth under finite-time attraction constraint

Abstract

This article presents a novel controller design approach for stochastic nonlinear systems exhibiting one-sided polynomial growth. The objective is to achieve finite-time attractiveness and estimate control energy consumption. By constructing an appropriate controller and employing inequality techniques, sufficient conditions for achieving finite-time attractiveness in stochastic nonlinear systems are established. Moreover, the article introduces the concept of expected energy consumption for stochastic systems and provides upper bounds on control time and energy consumption. A comprehensive trade-off analysis between control time and energy consumption is conducted to identify the optimal control intensity. The proposed approach is validated through numerical examples, demonstrating its effectiveness in practice.