Finite-Time Stability and State-Feedback Stabilization of Output-Constrained Stochastic Nonlinear Systems

The finite-time stabilization and robust control of stochastic nonlinear systems was discussed in this paper. First, by transforming the considered system to its equivalent Hamiltonian system, we showed that the stochastic dissipative Hamiltonian system was finite-time stable in probability if the Hamiltonian function and internal damping matrix possessed some structures. Then, we utilized the energy shaping and damping injection techniques to reformulate the internal structures and Hamiltonian function of the stochastic Hamiltonian system and constructed a finite-time stabilization controller. Finally, a robust finite-time controller was put forward for uncertain stochastic nonlinear systems by using the Hamiltonian function to construct a solution of Hamiltonian-Jacobi Inequality. Numerical simulations results demonstrated the effectiveness of the proposed stabilization and robust stabilization methods.

This paper presents a new Lyapunov theorem on almost surely finite-time stability for stochastic nonlinear systems with Markovian switching. Unlike the work in [3] that consider finite-time stability and stabilisation of conventional stochastic differential equation (SDE) systems, this paper aims to propose a weaker finite-time stability theory for a more general class of SDE systems with Markovian switching. A lemma is presented to discuss conditions that ensure the existence of a unique strong solution for such SDE systems with Markovian switching. Extended Comparison Principle and Bihari's inequality are derived, which relaxes some previous conditions and play an important role in the proof of the new Lyapunov theorem. Weaker conditions are proposed to ensure finite-time stability in probability one with supportive examples. Two simulation examples are given to illustrate the theoretical analysis.

Predefined-time stabilization of stochastic nonlinear systems with application to UAVs

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.

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

The finite-time stabilization for stochastic high-order nonlinear systems is considered in this paper using output feedback. The power orders in the system nonlinearities are relaxed to be rational number greater than one. A new constructive output-feedback, finite-time controller is designed based on a finite-time observer together with the homogeneous domination. The stochastic finite-time stability analysis is given rigorously for the closed-loop stochastic system.

Finite-time stability and stabilization of linear discrete time-varying stochastic systems

This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs) and linear matrix inequalities (LMIs). Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Almost sure exponential stability and stochastic stabilization of stochastic differential systems with impulsive effects

This manuscript considers the finite time adaptive neural tracking control problem for a class of the nonstrict-feedback stochastic nonlinear systems with Bouc-Wen hysteresis input. During the design process, a Bouc-Wen model is first adopted to obtain the input hysteresis phenomenon. By fusion with the backstepping technique and the neural network approximation capability, the unknown nonlinearities are coped with, a constructive finite time adaptive neural network control strategy is proposed. Furthermore, the finite-time mean square stability of stochastic nonlinear systems is proved, and at last the effectiveness of the proposed control strategy is validated by the simulations.

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.

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.

An approximation-based adaptive neural controller is constructed for uncertain stochastic nonlinear systems in nonstrict-feedback form appearing dead-zone and output constraint. Neural networks (NNs) are directly utilized to approximate the unknown nonlinear functions existing in systems. A barrier Lyapunov function is introduced to ensure that the trajectory of output is limited within a predetermined range. By integrating NNs into the backstepping technique, an adaptive neural controller is designed to guarantee all variables existing in the considered closed-loop system are semi-globally uniformly ultimately bounded, and by appropriately tuning several design parameters online, the tracking error can be converged to a small neighborhood of the origin. Simulations on a numerical example are given to demonstrate the effectiveness of the method proposed in this paper.

Finite time stability and stabilization of hybrid dynamic systems

Finite-time stability and stabilization of nonlinear singular time-delay systems via Hamiltonian method