Stochastic Time-delay Systems Research Articles

Approximation identification for the stochastic time-delayed dynamical system

This paper addresses the challenges of analyzing stochastic dynamical systems with a single time-delay within a data-driven framework. The presence of time-delay introduces non-Markovian characteristics to the system, complicating the analysis of its dynamic behavior using traditional approaches. Drawing inspiration from the small delay approximation, we apply a sparse identification technique to approximate the non-Markovian process with a Markovian one. This innovative method circumvents limitations associated with the system's dimensionality and the complexity of delayed diffusion terms, offering a versatile tool for investigating the dynamics of stochastic time-delayed systems. Our approach begins by establishing a connection between the system's coefficients and simulated data using the Kramers-Moyal formula, which captures the essential statistical properties of the system. We then leverage sparse identification to extract a concise model of the stochastic dynamical system, effectively eliminating the time-delay from consideration. The practicality and efficacy of our method are substantiated through a series of illustrative examples that showcase its application and validate its performance. By introducing this method, we aim to provide a novel analytical framework for stochastic time-delayed systems, advancing the current capabilities for modeling and understanding such complex dynamics.

Output-mask-based adaptive NN control for stochastic time-delayed multi-agent systems with a unified event-triggered approach

This paper investigates a class of output-mask-based adaptive neural network (NN) tracking control for nonlinear stochastic time-delayed multi-agent systems (STMASs) based on a unified event-triggered approach. The output signal relies on an output mapping acted as a mask, defined as a privacy-protection-like method, so that the internal state of one agent cannot be identified by other distrustful eavesdroppers or attackers. Moreover, the construction of a unified event-triggered control scheme retains the advantages of the saturation threshold triggering strategy, incorporates distributed errors, and increases the flexibility of thresholds. Furthermore, for stochastic time-delay multi-agent systems, the initial value limitation of the conventional first-order filter is removed by a first-order Levant differentiator, and a new estimation term in the fuzzy observer is established to solve the nonlinear fault. The unknown function in pure-feedback form is addressed via combining Butterworth low-pass filter and radial basis function neural networks (RBF NNs). Finally, the boundedness of all signals in the closed-loop systems is demonstrated, and the effectiveness of the proposed algorithm is verified by some simulation results.

Finite-Time H∞ Controllers Design for Stochastic Time-Delay Markovian Jump Systems with Partly Unknown Transition Probabilities.

This paper concentrates on the finite-time H∞ control problem for a type of stochastic discrete-time Markovian jump systems, characterized by time-delay and partly unknown transition probabilities. Initially, a stochastic finite-time (SFT) H∞ state feedback controller and an SFT H∞ observer-based state feedback controller are constructed to realize the closed-loop control of systems. Then, based on the Lyapunov-Krasovskii functional (LKF) method, some sufficient conditions are established to guarantee that closed-loop systems (CLSs) satisfy SFT boundedness and SFT H∞ boundedness. Furthermore, the controller gains are obtained with the use of the linear matrix inequality (LMI) approach. In the end, numerical examples reveal the reasonableness and effectiveness of the proposed designing schemes.

Safe Stabilization for Stochastic Time-Delay Systems

Safe Stabilization for Stochastic Time-Delay Systems

On exponential stability in [formula omitted]th moment of neutral Markov switched stochastic time-delay systems

In this article, the problem of the pth moment exponential stability is be investigated for neutral Markov switched stochastic time-delay systems. By virtue of inequalities based on the state-dependent multiple Lyapunov functions, we propose adequate conditions for the p-ES of Markov switched neutral stochastic differential delay equation applying properties for the stationary distribution of Markov switched process. For a class of neutral Markov switched stochastic time delay systems with impulse, several new criteria for pth moment exponential stability is obtained using the impulse average dwell-time condition, the integral transformation inequality, and stochastic analysis theory. The results extend and improve the related results from the existing literature. Some examples are provided to illustrate the validity of our derived results.

Dynamic event-triggered-based global output feedback control for stochastic nonlinear systems with time-varying delay

The current study addresses the issue of global dynamic event-triggered control based on reduced-order observer for a class of nonstrict-feedback stochastic systems in the presence of time-varying delay. Firstly, a lemma about the variable separation technique is proposed and proved for dealing with nonlinear functions in stochastic time-delay systems, which avoids the restrictive growth assumption that nonlinear functions need to satisfy. Secondly, a reduced-order observer is devised to reconstruct partial unmeasured state variables in systems, which equilibrates the control behavior between output feedback and state feedback. Then, without imposing any constraints on the derivative of time-varying delay, a dynamic event-triggered controller based on the symbol function technique is constructed to reduce the waste of resources in data transmissions and improve the communication efficiency. Furthermore, in the light of the stability theory of stochastic systems and Lyapunov-Razumikhin lemma, it is proved that the designed control algorithm can ensure that the controlled system is globally asymptotically stable in probability. Finally, two simulation examples are provided to verify the effectiveness of the developed approach.

Observer-based Finite-time Adaptive Robust Tracking Control for Nonlinear Stochastic Time-delay Systems With Full State Constraints and Input Saturation

Observer-based Finite-time Adaptive Robust Tracking Control for Nonlinear Stochastic Time-delay Systems With Full State Constraints and Input Saturation

A natural logarithm sliding mode controller for stochastic time-delay systems

This paper presents a new method for sliding mode control to create a compromise between duration of reaching phase and response rate of the stochastic time-delay systems. A natural logarithm sliding surface is first constructed and then, the asymptotic stability with probability one for the closed-loop system has been analyzed by Lyapunov method. Some practical considerations are uncertain parameter variations, environmental matched disturbances, actuator degradation, stochastic environmental mismatched disturbances, and unmodeled dynamics. Finally, the simulation results show how to adjust the response rate and the sensitivity of the closed-loop system to the variations by regulating a special parameter.

Linear quadratic optimal control for time-delay stochastic system with partial information

ABSTRACT This paper is concerned with the linear quadratic optimal control problem for the time-delay stochastic system with partial information. The main contribution is to derive the equivalent solvability condition and give the explicitly optimal controller under partial information in terms of the Riccati equations. The key is to explicitly solve the forward and backward stochastic difference equations with partial information, which is derived from the stochastic maximum principle.

Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

Stability of stochastic time-delay systems involving delayed impulses

In this paper, the pth moment exponential stability is investigated for impulsive stochastic time-delay systems (STDS) with random impulsive delay. A novel concept of average random delay in impulses is introduced to deal with the pth moment exponential stability of STDS, which provides a new idea for the study of the stochastic delay in impulses from a holistic perspective. Considering the impulsive effect, the destabilizing and stabilizing delayed impulses are studied, respectively. It is revealed that the random delay in impulses plays a significant role on the stability of the system, which may not only destabilize a stable system but also stabilize an unstable system. In particular, our results allow the delays in continuous dynamics and impulsive dynamics to exceed the length of the impulsive interval, which are more general than previous results. Finally, some numerical simulations are presented to illustrate our proposed results.

A new design method to global asymptotic stabilization of strict-feedforward stochastic nonlinear time delay systems

The stabilization problems of stochastic nonlinear systems remain challenging because many new obstacles will be encountered and need to be cautiously handled. This paper discusses the global asymptotic stabilization problem of stochastic nonlinear systems which possess strict-feedforward structure and multiple time delays. In the first place, we are trying to transform the considered system into an equivalent one by constructing the novel parameter-dependent state feedback controller and the suitable coordinate transformation. And then, through using the stochastic time delay system stability criterion and introducing the proper Lyapunov–Krasovskii functional, the global asymptotic stability of stochastic closed-loop system is proved. Finally, simulation results show the effectiveness of the parameter-dependent state feedback controller.

Memoryless parameter-dependent control strategy of stochastic strict-feedback time delay systems

For a class of stochastic strict-feedback nonlinear systems subject to different time delay states, this paper mainly concerns the problem of global asymptotic stabilization. Two new control strategies that the memoryless parameter-dependent state feedback control and the memoryless parameter-dependent output feedback control are taken into consideration, respectively. By skillfully constructing the Lyapunov-Krasovskii (L-K) functional, taking the proper determined parameter and employing the stochastic nonlinear time delay system (SNTDS) stability theory, the global asymptotic stability of the stochastic closed-loop system can be achieved. The proposed output feedback control scheme is finally utilized for the control design of the one-link manipulator system and two-stage chemical reactor system, which can verify the availability of the control approach.

Robust Control for Stochastic Nonlinear Delay Systems with Jumps

The problem of infinite horizon H∞ control for general delayed nonlinear stochastic Markov jump systems with the infinite jumping parameters is considered in this paper, in which the noise is dependent on the state, control, and external disturbance. The coupled Hamilton–Jacobi inequalities (HJIs)‐based sufficient condition is given to ensure the existence of the H∞ controller. As a corollary, infinite horizon H∞ controllers are designed for nonlinear stochastic time‐delay systems without jumps by solving a series of coupled HJIs. Besides, the effectiveness of the proposed method is verified by a numerical example.

Quantized Feedback Stabilization for Nonlinear Hybrid Stochastic Time-Delay Systems With Discrete-Time Observation.

The quantized feedback stabilization problem is investigated for nonlinear hybrid stochastic time-delay systems with discrete-time observation in this article. A quantized discrete-time observation feedback controller is designed. The designed controller can make the H∞ stability and mean-square sense of the controlled system. Particularly, this note is the first to develop the stability criteria, which is not only related to the duration between two successive observations but also links to time lag of the system. By utilizing the Lyapunov method and inequality scaling techniques, the estimates for the duration and the time delay of the system are gained, respectively. Some case simulations are also provided to testify the proposed method and demonstrate its power.

Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations

Nonlinear time delay systems produce inherently delay-induced periodic oscillations, which are, however, too idealistic compared to observations. We exhibit a unified stochastic framework to systematically rectify such oscillations into oscillatory patterns with enriched temporal variabilities through generic, nonlinear responses to stochastic perturbations. Two paradigms of noise-driven chaos in high dimension are identified, fundamentally different from chaos triggered by parameter-space noise. Noteworthy is a low-dimensional stretch-and-fold mechanism, leading to stochastic strange attractors exhibiting horseshoe-like structures mirroring turbulent transport of passive tracers. The other is high-dimensional , with noise acting along the critical eigendirection and transmitted to "deeper" stable modes through nonlinearity, leading to stochastic attractors exhibiting swarm-like behaviors with power-law and scale break properties. The theory is applied to cloud delay models to parameterize missing physics such as intermittent rain and Lagrangian turbulent effects. The stochastically rectified model reproduces with fidelity complex temporal variabilities of open-cell oscillations exhibited by high-end cloud simulations.

A Precise Stabilization Method for Linear Stochastic Time-Delay Systems

Based on ensuring the steady-state performance of the system, some dynamic performance indicators that have not yet been realized in linear stochastic systems with time-delay are discussed in this paper. First, in view of the relationship between system eigenvalues and system performances, the region stability is provided, which can reflect the dynamic performance of the systems. Second, the design scheme of the region stabilization controller is given based on the region stability, so that the closed-loop system has the corresponding dynamic performance. Third, this paper also designs an algorithm to deal with the situation in which the eigenvalues are located in the non-connected region in order to obtain more accurate control system dynamic performance. Finally, an example shows how the precise control method dominates the dynamic performance of the system.

Protocol-Based Stability Analysis of Stochastic Hybrid Systems Under DoS Attacks

The stability issue of stochastic hybrid systems against energy-constrained denial-of-service (DoS) attacks is investigated in this article. A sampled-data-based Round-Robin protocol, which sends measurement data cyclically according to the predetermined transmission sequence, is introduced to avoid communication network congestion. Additionally, a new switched time-delay stochastic closed-loop system with an unstable subsystem is established by discussing the effect of DoS attacks. Then, the stability of the closed-loop system is discussed in light of the piecewise Lyapunov–Krasovskii functional method and stochastic analysis technique. Finally, two examples are included to illustrate the correctness and applicability of the proposed method.

Closed-loop intermittent sensor fault detection for linear stochastic time-delay systems with unknown disturbances

In this paper, the problem of closed-loop intermittent sensor fault (ISF) detection is investigated for a class of linear stochastic time-delay systems with unknown disturbances. A modified unknown input observer (UIO) is proposed to eliminate the influence of delayed errors caused by the discrete-time proportional-integral controller and constant time delay. In order to detect the appearing time and disappearing time of the ISF, a truncated residual is designed by introducing a sliding-time window. Moreover, two hypothesis tests are utilised to set the ISF detection thresholds, and the detectability, false alarm rates as well as missing alarm rates of the ISF are analysed in the framework of statistical analysis. Finally, the effectiveness of the proposed method is validated via a simulation example of a simplified radial flight control system.

Existence of Solutions and Relative Controllability of a Stochastic System with Nonpermutable Matrix Coefficients

In this study, time-delayed stochastic dynamical systems of linear and nonlinear equations are discussed. The existence and uniqueness of the stochastic semilinear time-delay system in finite dimensional space is investigated. Introducing the delay Gramian matrix, we establish some sufficient and necessary conditions for the relative approximate controllability of time-delayed linear stochastic dynamical systems. In addition, by applying the Banach fixed point theorem, we establish some sufficient relative approximate controllability conditions for semilinear time-delayed stochastic differential systems. Finally, concrete examples are given to illustrate the main results.