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

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.

Observer-based [formula omitted] fuzzy control for nonlinear stochastic systems with multiplicative noise and successive packet dropouts

This article takes a fast finite-time control of stochastic nonlinear systems into account. The presence of unknown stochastic disturbance terms makes the traditional fast finite-time control approaches unavailable. To deal with this difficulty, by establishing an auxiliary function and using Jensen's inequality, in Lemma 6, a new criterion of fast finite-time stability is first established for the uncertain stochastic system. Based on the approximation ability of neural networks (NNs), an innovative fast finite-time strategy is put forward for stochastic nonlinear systems. Furthermore, by adopting the presented fast finite-time stability criterion, the stability of the stochastic systems is confirmed. Finally, two simulations are implemented to validate the feasibility of the presented NN control strategy.

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.

This paper studies the design problem of robust H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter for neutral stochastic uncertain delay systems. Aiming at neutral stochastic delay systems with polytopic uncertainty, we deduce sufficient conditions of the existence of H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</inf> filter, and express them into a form of the linear matrix inequality (LMI), then utilize schur complement lemma transformed them into LMIs which can be solved. At last we utilize standard digital software to get filter parameters. The feasibility of the methods of design filter for neutral stochastic uncertain delay systems is demonstrated by numerical examples.

In this work, we consider dynamical systems of linear and nonlinear stochastic delay-differential equations driven by the Rosenblatt process. With the aid of the delayed matrix functions of these systems, we derive the controllability results as an application. By using a delay Gramian matrix, we provide sufficient and necessary criteria for the controllability of linear stochastic delay systems. In addition, by employing Krasnoselskii’s fixed point theorem, we present some necessary criteria for the controllability of nonlinear stochastic delay systems. Our results improve and extend some existing ones. Finally, an example is given to illustrate the main results.

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

In this work, an adaptive neural network (NN) optimized output-feedback control problem is studied for a class of stochastic nonlinear systems with unknown nonlinear dynamics, input saturation, and state constraints. A nonlinear state observer is designed to estimate the unmeasured states, and the NNs are used to approximate the unknown nonlinear functions. Under the framework of the backstepping technique, the virtual and actual optimal controllers are developed by employing the actor-critic architecture. Meanwhile, the tan-type Barrier optimal performance index functions are developed to prevent the nonlinear systems from the state constraints, and all the states are confined within the preselected compact sets all the time. It is worth mentioning that the proposed optimized control is clearly simple since the reinforcement learning (RL) algorithm is derived based on the negative gradient of a simple positive function. Furthermore, the proposed optimal control strategy ensures that all the signals in the closed-loop system are bounded. Finally, a practical simulation example is carried out to further illustrate the effectiveness of the proposed optimal control method.

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.

This paper focuses on the model of a class of nonlinear stochastic delay systems with Poisson jumps based on Lyapunov stability theory, stochastic analysis, and inequality technique. The existence and uniqueness of the adapted solution to such systems are proved by applying the fixed point theorem. By constructing a Lyapunov function and using Doob’s martingale inequality and Borel-Cantelli lemma, sufficient conditions are given to establish the exponential stability in the mean square of such systems, and we prove that the exponentially stable in the mean square of such systems implies the almost surely exponentially stable. The obtained results show that if stochastic systems is exponentially stable and the time delay is sufficiently small, then the corresponding stochastic delay systems with Poisson jumps will remain exponentially stable, and time delay upper limit is solved by using the obtained results when the system is exponentially stable, and they are more easily verified and applied in practice.

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.

Non-fragile robust stabilization and [formula omitted] control for uncertain stochastic nonlinear time-delay systems

The problem of robust stability and stabilization of stochastic large-scale delay systems has been investigated in recent years. However, the robust exponential stability and stabilization has not been considered. The purpose of this paper is to present delay-dependent criteria for robust decentralized exponential stabilization of the complex systems. The obtained results are based on algebraic Riccati equations and may be extended by using the widely-used LMI techniques.

This paper is concerned with the stabilization problem for nonlinear stochastic delay systems with Markovian switching by feedback control based on discrete-time state and mode observations. By constructing an efficient Lyapunov functionals, we establish the sufficient stabilization criteria not only in the sense of exponential stability (both the mean-square stability and the almost sure stability) but also in other sense – that of stability and asymptotic stability. Meanwhile, the upper bound on the duration τ between two consecutive state and mode observations is obtained. Numerical examples are provided to demonstrate the effectiveness of our theoretical results.

Computing the Density Function for a Nonlinear Stochastic Delay System