Adaptive state-feedback control for low-order stochastic nonlinear systems with an output constraint and SiISS inverse dynamics

Mengmeng Jiang; Qiqi Ni; Mengmeng Jiang; Qiqi Ni

doi:10.3934/math.2025508

AIMS Mathematics

2025, Volume 10, Issue 5: 11208-11233. doi: 10.3934/math.2025508

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Adaptive state-feedback control for low-order stochastic nonlinear systems with an output constraint and SiISS inverse dynamics

Mengmeng Jiang ^,,
Qiqi Ni

School of Mathematics Science, Liaocheng University, Liaocheng, 252059, China

Received: 24 March 2025 Revised: 25 April 2025 Accepted: 13 May 2025 Published: 16 May 2025
MSC : 93C40, 93E15

This paper focuses on state-feedback adaptive control for stochastic low-order nonlinear systems with an output constraint and stochastic integral input-to-state stability (SiISS) inverse dynamics. The system with an output constraint was transformed straightforwardly into the equivalent system without a constraint using important coordinate transformations. SiISS was used to characterize unmeasured stochastic inverse dynamics. By introducing Lyapunov functions and using the stochastic systems stability theorem, we constructed a new adaptive state-feedback controller that assures the closed-loop system's trivial solution is stable in probability while fulfilling the requirements of the output constraint and all closed-loop signals are likely to be almost surely bounded. The validity of the control scheme presented in this paper was demonstrated by using simulation outcomes.
Citation: Mengmeng Jiang, Qiqi Ni. Adaptive state-feedback control for low-order stochastic nonlinear systems with an output constraint and SiISS inverse dynamics[J]. AIMS Mathematics, 2025, 10(5): 11208-11233. doi: 10.3934/math.2025508

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Abstract

This paper focuses on state-feedback adaptive control for stochastic low-order nonlinear systems with an output constraint and stochastic integral input-to-state stability (SiISS) inverse dynamics. The system with an output constraint was transformed straightforwardly into the equivalent system without a constraint using important coordinate transformations. SiISS was used to characterize unmeasured stochastic inverse dynamics. By introducing Lyapunov functions and using the stochastic systems stability theorem, we constructed a new adaptive state-feedback controller that assures the closed-loop system's trivial solution is stable in probability while fulfilling the requirements of the output constraint and all closed-loop signals are likely to be almost surely bounded. The validity of the control scheme presented in this paper was demonstrated by using simulation outcomes.

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