Ultimately Exponentially Bounded Estimates for a Class of Nonlinear Discrete-Time Stochastic Systems

Article Automation & Control Systems

Exponential ultimate boundedness and stability of impulsive stochastic functional differential equations

Fang Huang et al.

Summary: This paper mainly studies the globally pth moment exponentially ultimate boundedness and pth moment exponential stability of impulsive stochastic functional differential equations. By using the Lyapunov direct method and principle of comparison, the paper presents some sufficient conditions and obtains the main results using mathematical induction. The contributions of this paper lie in allowing the original system to be unbounded and unstable, and considering the time-varying linear coefficient of the Lyapunov differential operator.

INTERNATIONAL JOURNAL OF CONTROL (2023)

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Article Automation & Control Systems

Security tracking control for discrete-time stochastic systems subject to cyber attacks

Yi Yu et al.

Summary: This paper addresses the security tracking problem for a class of discrete-time stochastic linear networked control systems subject to cyber attacks. The attacks considered include false data injection attacks and a class of DoS attacks. A probabilistic definition of secure trackability is proposed to describe the transient trajectory of the systems under random attacks. An observer-based dynamic output feedback controller is designed to achieve the specified probabilistic secure trackability. The problem is transformed into an input-to-state stability problem in the probabilistic sense, and matrix inequalities are solved to determine the controller parameters and the upper bound of the quadratic cost function.

ISA TRANSACTIONS (2022)

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Article Automation & Control Systems

First-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay

Teng Song et al.

Summary: This paper investigates the first-order and second-order necessary optimality conditions for discrete-time stochastic systems with delay. By utilizing a characteristic method and a discrete-time backward stochastic equation, the linearized discrete-time stochastic maximum principle and Euler-type necessary optimality condition are established. Additionally, by employing a new discrete-time backward stochastic matrix equation, the necessary optimality condition for quasi-singular control and the pointwise second-order optimality condition are derived.

IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION (2022)

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Article Automation & Control Systems

Lyapunov theorems for stability and semistability of discrete-time stochastic systems

Wassim M. Haddad et al.

Summary: This paper develops Lyapunov and converse Lyapunov theorems for discrete-time stochastic semistable nonlinear dynamical systems expressed by Ito-type difference equations possessing a continuum of equilibria. The necessary and sufficient Lyapunov conditions for stochastic semistability are provided, and it is shown that stochastic semistability implies the existence of a continuous Lyapunov function.

AUTOMATICA (2022)

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Article Automation & Control Systems

Exponential bipartite tracking consensus in cooperative-antagonistic nonlinear Multi-Agent Systems with multiple communication time-varying delays

Dario Giuseppe Lui et al.

Summary: This article addresses the problem of bipartite tracking consensus for high-order nonlinear Multi-Agent Systems (MASs) with cooperative-antagonistic agents interacting via a directed non-ideal communication network. A novel distributed delayed bipartite tracking consensus control strategy is proposed to ensure the exponential stability of the networked control system, and the theoretical analysis provides control gains tuning rule and estimation of the maximum admissible delay upper bound. Numerical simulations validate the theoretical derivations.

IFAC JOURNAL OF SYSTEMS AND CONTROL (2022)

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Article Automation & Control Systems

Robust H∞ filtering for nonlinear discrete-time stochastic systems

Tianliang Zhang et al.

Summary: This paper discusses the H-infinity filtering of general nonlinear discrete time-varying stochastic systems, presenting a sufficient condition for its existence via a newly introduced Hamilton-Jacobi inequality (HJI). The suboptimal H-2/H-infinity filtering under worst-case disturbance is also studied, with three examples demonstrating the effectiveness of the main results.

AUTOMATICA (2021)

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Article Automation & Control Systems

Globally Exponentially Stable Tracking Control of Self-Restructuring Nonlinear Systems

Yongduan Song et al.

Summary: This article introduces a neural networks-based tracking control approach for uncertain high-order self-restructuring nonaffine dynamic systems, ensuring globally stable tracking through the cooperation of two control units: safeguard control and NN-based control. The safeguard control forces states into a stable region so that the NN-based control can be activated reliably and safely. This cooperation ensures the tracking error enters the stable region within a specified finite time and then converges to zero exponentially, achieving global zero-error tracking.

IEEE TRANSACTIONS ON CYBERNETICS (2021)

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Article Automation & Control Systems