Backstepping Stabilization of Stochastic Hyperbolic PDE-ODE Systems

TY - GEN

T1 - Backstepping Stabilization of Stochastic Hyperbolic PDE-ODE Systems

AU - Sun, Xuejiao

AU - Wang, Junmin

AU - Lyu, Kaijing

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2026.

PY - 2026

Y1 - 2026

N2 - This paper establishes a constructive boundary control framework for stabilizing coupled hyperbolic PDE-ODE systems subject to stochastic parameter variations. The system under consideration exhibits mixed-directional dynamics, with three positive and one negative characteristic speeds in its PDE subsystem. Building upon nominal backstepping designs for deterministic systems, we develop a parameter-adaptive control law that maintains stabilization capability when system parameters undergo random switching. Through a novel composite Lyapunov analysis, we derive explicit stability conditions relating the controller’s robustness to both the magnitude of parameter variations and their transition statistics. The theoretical results demonstrate that mean-square exponential stability can be preserved when the stochastic parameters remain within probability-dependent neighborhoods of their nominal values. A distinctive feature of our approach lies in the unified treatment of PDE-PDE and PDE-ODE coupling terms under stochastic perturbations, which has not been addressed in existing Markov-jumping PDE literature. The control design is validated through numerical experiments, showing consistent stabilization performance across different parameter switching scenarios.

AB - This paper establishes a constructive boundary control framework for stabilizing coupled hyperbolic PDE-ODE systems subject to stochastic parameter variations. The system under consideration exhibits mixed-directional dynamics, with three positive and one negative characteristic speeds in its PDE subsystem. Building upon nominal backstepping designs for deterministic systems, we develop a parameter-adaptive control law that maintains stabilization capability when system parameters undergo random switching. Through a novel composite Lyapunov analysis, we derive explicit stability conditions relating the controller’s robustness to both the magnitude of parameter variations and their transition statistics. The theoretical results demonstrate that mean-square exponential stability can be preserved when the stochastic parameters remain within probability-dependent neighborhoods of their nominal values. A distinctive feature of our approach lies in the unified treatment of PDE-PDE and PDE-ODE coupling terms under stochastic perturbations, which has not been addressed in existing Markov-jumping PDE literature. The control design is validated through numerical experiments, showing consistent stabilization performance across different parameter switching scenarios.

KW - Boundary control

KW - PDE backstepping

KW - PDE-ODE cascades

KW - Robust stabilization

KW - Stochastic hyperbolic systems

UR - https://www.scopus.com/pages/publications/105030938755

U2 - 10.1007/978-981-95-6730-0_25

DO - 10.1007/978-981-95-6730-0_25

M3 - Conference contribution

AN - SCOPUS:105030938755

SN - 9789819567294

T3 - Communications in Computer and Information Science

SP - 347

EP - 361

BT - Advanced Computational Intelligence and Intelligent Informatics - 9th International Workshop, IWACIII 2025, Proceedings

A2 - Ma, Hongbin

A2 - Xin, Bin

A2 - She, Jinhua

A2 - Dai, Yaping

PB - Springer Science and Business Media Deutschland GmbH

T2 - 9th International Workshop on Advanced Computational Intelligence and Intelligent Informatics, IWACIII 2025

Y2 - 31 October 2025 through 4 November 2025

ER -