Stability analysis for a class of stochastic delay nonlinear systems driven by G-Brownian motion

The 2025 9th International Conference on Mechanics, Mathematics and Applied Physics (ICMMAP 2025) was successfully held on-site at Harbin University of Science and Technology, Harbin, China, from December 12 to 14, 2025. The conference attracted approximately 200 participants, including researchers, engineers, and professionals from academia and industry, reflecting the growing interest and importance of mechanics, mathematics, and applied physics in both theoretical and practical domains. ICMMAP 2025 focused on interdisciplinary advances in mechanics, mathematical modeling, and applied physics. Key topics included optimization theory and algorithms, stochastic nonlinear systems, plasma physics, ionospheric perturbations, numerical methods for partial differential equations, and intelligent detection technologies. The conference provided a platform for sharing the latest research results, innovative methodologies, and practical engineering solutions across these fields. The conference featured keynote speeches delivered by distinguished experts from Uzbekistan, Russia, and China. Speakers included Prof. Bobomurat Ahmedov (Uzbekistan Academy of Sciences), Prof. Anatoly Kudryavtsev (Saint Petersburg State University / Harbin Institute of Technology), Prof. Wei Bian (Harbin Institute of Technology), Prof. Quanxin Zhu (Hunan Normal University), Prof. Chengxun Yuan (Harbin Institute of Technology), Prof. Qiang Zhang (Nanjing University), Assoc. Prof. Xiaozhou Li (University of Electronic Science and Technology of China), Assoc. Prof. Jia Li (Harbin Institute of Technology), and Dr. Fengyu Fu (Harbin University of Science and Technology). Their presentations covered frontier topics such as ionospheric perturbations, plasma-based electromagnetic wave amplification, sparse optimization problems, stabilization of stochastic nonlinear delay systems, plasma detection technologies, advanced numerical methods, and spectral analysis for parallel-in-time solvers. These keynote lectures offered valuable insights into both theoretical foundations and applied innovations. List of Committee Member is available in this PDF.

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

This paper discusses the multi-player non-cooperative game of nonlinear stochastic time-varying systems described by Itô-type differential equations in a finite time interval. Multi-player non-cooperative game problems are represented by multi-objective Pareto (MOP) control problems to describe the fact that each player has their own goals. By applying Hamilton–Jacobi inequalities (HJIs), the criterion of upper bounds of the MOP boundary is obtained for nonlinear stochastic systems, and the corresponding strategies are designed for such games, so the MOP problem is transformed into a HJI-constrained MOP problem. In order to overcome the difficulty of solving HJIs, a global linearization method is proposed to approximate the nonlinear systems. By the proposed global linearization method, multi-player non-cooperative game problems are transformed into Riccati equation-constrained MOP problems, and the approximate solutions of HJI-constrained MOP problems are obtained. Finally, a practical example is given to illustrate the effectiveness of the proposed method.

Backstepping-based decentralized bounded-H∞ adaptive neural control for a class of large-scale stochastic nonlinear systems

Sufficient conditions for the controllability of nonlinear stochastic fractional boundary control systems are established. The equivalent integral equations are derived for both linear and nonlinear systems, and the control function is given in terms of the pseudoinverse operator. The Banach contraction mapping theorem is used to obtain the result. A controllability result for nonlinear stochastic fractional integrodifferential systems is also attained. Examples are included to illustrate the theory.

Exponential stability of non-linear stochastic delay differential system with generalized delay-dependent impulsive points

Adaptive fault tolerant tracking control for a class of stochastic nonlinear systems with output constraint and actuator faults

Fuzzy model-based control of nonlinear stochastic systems with time-delay

In this article, the mean‐square exponential stability of the stochastic nonlinear delay systems with dynamic event‐triggered mechanism under periodically intermittent control scheme is concerned. First, to avoid Zeno behavior, the triggered mechanism contains with a fixed positive lower bound for the inter‐execution time is constructed. Then, an auxiliary system with dynamic event‐triggering mechanism under continuous control is introduced. Combining the Lyapunov theorem with Halanay inequality, the sufficient conditions and the mean‐square exponential stability of the auxiliary system are obtained. In addition, by using the comparison theorem, the exponential stability of the system under intermittent control is also proved. Meanwhile, the lower bound of the duty cycle for a fixed period under intermittent controller is obtained. Furthermore, we apply the theoretical results to the consensus of stochastic nonlinear delay networked multi‐agent systems (MASs) with dynamic event‐triggered mechanism. Finally, numerical examples are given to verify the effectiveness of the proposed methods.

In this study, we investigate multi-player noncooperative minmax H∞ target tracking game strategy with conflicting target strategies and cooperative H∞ target tracking game strategy with common target strategy of nonlinear mean-field stochastic jump diffusion (MFSJD) system with external disturbance. Due to the nonlinear terms and mean-field (average) behaviors in the stochastic nonlinear MFSJD system and minmax H∞ payoff function, the multi-player noncooperative and cooperative minmax H∞ mean-field game strategy of nonlinear MFSJD system are more difficult than the linear MFSJD system and conventional nonlinear stochastic system. To avoid solving complex Hamilton Jacobi Isaacs inequalities (HJIIs) of multi-player noncooperative minmax H∞ mean-field target tracking game strategy of nonlinear MFSJD system, the nonlinear MFSJD system is interpolated by a set of local linearized MFSJD system through smoothing functions by the global linearization method. Then the multi-player noncooperative minmax H∞ nonlinear mean-field target tracking game strategy design can be transformed to a linear matrix inequalities (LMIs)-constrained multi-objective optimization problem (MOP). The LMIs-constrained MOP could be efficiently solved by the help of the proposed LMIs-constrained multi-objective evolution algorithm (MOEA). We can prove that the Pareto optimal solution of LMIs-constrained MOP is the Nash equilibrium solution of noncooperative minmax H∞ mean-field target tracking strategy of nonlinear mean-field MFSJD system. Further, the cooperative minmax H∞ mean-field common target tracking strategy of nonlinear mean-field stochastic system is reduced to an LMIs-constrained single-objective optimization problem (SOP). Finally, two simulation examples of cyber-financial mean-field systems are given to illustrate the design procedure and compare the efficacies of the proposed noncooperative and cooperative minmax H∞ mean-field target tracking strategy of nonlinear MFSJD systems.

In this paper, we investigate the pth moment exponential stability of stochastic differential equations driven by G-Brownian motion (G-SDEs) with respect to a part of the variables by means of the G-Lyapunov functions and recently developed Itô's calculus for SDEs driven by G-Brownian motion, as well as Gronwall's inequalities. We establish sufficient conditions to ensure the quasi sure exponential stability of stochastic differential equations perturbed by G-Brownian motion with respect to a part of the variables. Some illustrative examples to show the usefulness of the stability with respect to a part of the variables notion are also provided.

The Markov chain approximation method is an effective and widely used approach for computing optimal values and controls for stochastic systems. It was extended to nonlinear (and possibly reflected) diffusions with delays in a recent book. The path, control, and reflection terms can all be delayed. In models of communications systems, reflection terms correspond to buffer overflows, and to the adjustments needed to keep the buffers and rates nonnegative and bounded. The book concentrated on convergence proofs for general algorithms of promising forms. If the control and/or reflection terms are delayed, the memory requirements can make the problem intractable, since these have little or no regularity. For such models, the problem was recast in terms of a "wave" or "transportation" equation, to get practical algorithms with very much reduced computational needs. The overall approach to getting usable algorithms is outlined. The methods are applied to an ideal model of a communications system with transportation delay. and it is seen that nearly optimal controls for appropriately chosen criteria can improve the performance considerably and be robust in the face of changing operating conditions. The data illustrate the potential usefulness of numerical methods for nonlinear stochastic systems with delays. It opens up new avenues of control for consideration.

Fixed-time adaptive neural self-triggered decentralized control for stochastic nonlinear systems with strong interconnections

In this work, we consider linear and nonlinear fractional stochastic delay systems driven by the Rosenblatt process. With the aid of the delayed Mittag-Leffler matrix functions and the representation of solutions of these systems, we derive the controllability results as an application. By introducing a fractional delayed Gramian matrix, we provide sufficient and necessary criteria for the controllability of linear fractional stochastic delay systems. Furthermore, by employing Krasnoselskii’s fixed point theorem, we establish sufficient conditions for the controllability of nonlinear fractional stochastic delay systems. Finally, an example is given to illustrate the main results.

Feasible Region Optimization of PI Control Parameters for Robust Tracking of First-Order Nonlinear Stochastic Time-Delay Systems