Stochastic Time-delay Systems Research Articles

Stochastic Stabilization for Discrete-Time System with Input Delay and Multiplicative Noise in Control Variable

The stabilization problems for time-delay stochastic systems with multiplicative noise in the control variable are investigated in this paper. The innovative contributions are described as follows. Since the past work on stabilization is based on some delay-dependent algebraic Riccati equation (DARE), how to numerically calculate the stabilizing solution remains an unsolved and open problem. On the one hand, an iterative algorithm for computing the unique stabilizing solution of DARE is proposed, while the convergence property is also proved. On the other hand, the concepts of critical stabilization and essential destabilization are proposed as a supplement to stochastic stabilization in terms of spectrum technique. Moreover, the Lyapunov-based necessary and sufficient conditions are developed.

Stability and Stabilization of Stochastic Neutral-type Markovian Jump Time-delay Systems with Two Delays

Stability and Stabilization of Stochastic Neutral-type Markovian Jump Time-delay Systems with Two Delays

The Characteristic Analysis and Application of a Novel Time-Delay Feedback Piecewise Tri-stable Stochastic Resonance System

The Characteristic Analysis and Application of a Novel Time-Delay Feedback Piecewise Tri-stable Stochastic Resonance System

Multi-leader-follower group consensus of stochastic time-delay multi-agent systems subject to Markov switching topology.

The multi-leader-follower group consensus issue of a class of stochastic time-delay multi-agent systems subject to Markov switching topology is investigated. The purpose is to determine a distributed control protocol to make sure that the followers' states converge in mean square to a convex hull generated by the leaders' states. Through a model transformation, the problem is transformed into a mean-square stability issue of a new system. Then, an easy-to-check sufficient condition for the solvability of the multi-leader-follower group consensus issue is proposed by utilizing the Lyapunov stability theory, graph theory, as well as several inequality techniques. It is shown that the required feedback gain can be acquired once the condition is satisfied. Finally, an example is used to illustrate the effectiveness of the control protocol.

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

This paper discusses the feasible region of PI control parameters for first-order nonlinear stochastic time-delay systems. The system can robust asymptotically track a set-point under any PI control parameters within the feasible region. First, the first-order nonlinear stochastic time-delay systems is transformed into a linear stochastic time-delay systems with the uncertainty. Second, for the fixed PI control parameters, the maximal allowable time delay under PI control is obtained by using the genetic algorithm (GA) and the generalized eigenvalue problem. Third, a new algorithm is proposed to compute the feasible region of PI control parameters for a fixed allowable time delay. Moreover, the improved algorithm is also proposed to reduce the time complexity. In particular, the stochastic disturbance and time delay disappear, the feasible region of PI control parameters obtained by the algorithm is consistent with the previous work. Finally, two simulation examples show the feasibility and effectiveness of the proposed two algorithms, respectively.

Delay‐dependent stability analysis and stabilization of stochastic time‐delay systems governed by the Poisson process and Brownian motion

AbstractThis article investigates the delay‐dependent stability and stabilization problems for stochastic time‐delay systems (STDSs) governed by the Poisson process and Brownian motion. First, this article exploits the decomposition of semimartingale to transform STDSs governed by the Poisson process and Brownian motion into STDSs governed by martingales, and then one can use effective properties and tools of martingale theory to investigate the stability and stabilization problems. Second, the expectations of stochastic crossterms involving stochastic integrals with respect to (w.r.t.) càdlàg martingale have been studied by martingale theory, and this article proves that the expectations of some particular stochastic crossterms are zero. Third, on the basis of above results on the expectations of stochastic crossterms and the equivalent Itô formula derived, this article uses the free weighting matrix method to give a delay‐dependent stability condition without using bounding techniques. Thus, the conservatism induced by bounding techniques is eliminated, and this method leads to a less conservative condition by a linear matrix inequality. Then, this article designs a state‐feedback controller which can stabilize the STDS governed by the Poisson process and Brownian motion. Finally, the effectiveness of derived results are illustrated by numerical examples.

Non-fragile [formula omitted] finite-time sliding mode control for stochastic Markovian jump systems with time delay

This article mainly discusses the realization of H∞ finite-time control for a class of uncertain stochastic time-delay systems with unmeasured states through sliding mode control (SMC). The purpose of this paper is to design a suitable SMC controller to suppress the influence of factors such as model switching and time delay on the system performance, so that the system state can be stabilized within a limited time interval. First, the state of the system is reconstructed through the H∞ state observer, and the SMC law based on the state observer is designed so that the state trajectory reaches the specified sliding surface (s.s.s) in a given finite time. Next, by introducing the concept of time-partitioning strategy, the finite-time boundedness (FTBs) of the reaching phase and the sliding motion phase are realized respectively. Then, according to the linear matrix inequality(LMI), the asymptotic stochastic stability of the system and sufficient conditions for sliding mode dynamics with a given interference attenuation level are derived. Finally, the numerical example and single-link robot arm model (S-lram) show the effectiveness of the method.

Medium Entropy Reduction and Instability in Stochastic Systems with Distributed Delay.

Many natural and artificial systems are subject to some sort of delay, which can be in the form of a single discrete delay or distributed over a range of times. Here, we discuss the impact of this distribution on (thermo-)dynamical properties of time-delayed stochastic systems. To this end, we study a simple classical model with white and colored noise, and focus on the class of Gamma-distributed delays which includes a variety of distinct delay distributions typical for feedback experiments and biological systems. A physical application is a colloid subject to time-delayed feedback control, which is, in principle, experimentally realizable by co-moving optical traps. We uncover several unexpected phenomena in regard to the system’s linear stability and its thermodynamic properties. First, increasing the mean delay time can destabilize or stabilize the process, depending on the distribution of the delay. Second, for all considered distributions, the heat dissipated by the controlled system (e.g., the colloidal particle) can become negative, which implies that the delay force extracts energy and entropy of the bath. As we show here, this refrigerating effect is particularly pronounced for exponential delay. For a specific non-reciprocal realization of a control device, we find that the entropic costs, measured by the total entropy production of the system plus controller, are the lowest for exponential delay. The exponential delay further yields the largest stable parameter regions. In this sense, exponential delay represents the most effective and robust type of delayed feedback.

Sampled-data resilient [formula omitted] control for networked stochastic systems subject to multiple attacks

In this paper, the sampled-data resilient H∞ control problem is concerned for networked stochastic systems with multiple attacks. Multiple attacks consisting of denial-of-service (DoS) attacks and random deception attacks are first described. Then on the basis of these attacks, a new switched stochastic time-delay closed-loop system is proposed under sampled-data and full state feedback controller. By utilizing piecewise Lyapunov-Krasovskii functional analysis theory, some new criterions are derived to guarantee the mean-square asymptotical stability with an H∞ performance of the resulting closed-loop system. The explicit expression of controller gain is subsequently presented. Finally, two examples are given to show the feasibility of the developed control approach.

Asymptotic behavior analysis of Markovian switching neutral-type stochastic time-delay systems

A new integral inequality method is put forward to analyze the general decay stability for Markovian switching neutral stochastic functional differential systems. At first, in order to get around the dynamic analyses difficulty induced by the coinstantaneous presence of neutral term, Markovian switching and Brownian motion noise, an new integral inequality as a powerful tool is gained. Then, based on the integral inequality, general decay stability in the sense of pth(p>0) moment and the almost sure can be taken out by utilizing the nonnegative semimartingale convergence theorem and Lyapunov stability theory. The obtained results can be especially applied to two special types of neutral stochastic differential systems that have been studied in the literature. Finally, an example has been performed to verify the obtained analytical results.

Event-triggered [formula omitted] control for networked spar-type floating production platforms with active tuned heave plate mechanisms and deception attacks

The service life of floating production platforms can be substantially shortened due to undesirable excessive vibrations caused by dynamic loads. It is thus necessary to develop effective vibration reduction methods for floating production platforms. This article proposes a network-based active control approach for a spar-type floating production platform (SP) against wave exciting loads and deception attacks. First, a novel active tuned heave plate (ATHP) mechanism based on the concept of the active tuned mass damper is developed for the SP. Second, in the context of networked control of the SP-ATHP system, an event-triggering transmission mechanism is introduced to significantly improve communication efficiency. Meanwhile, a Bernoulli distribution and a nonlinear function are employed to character possible deception attacks in shared communication channels. Then, by modelling the network-based closed-loop SP-ATHP system as a time-delay stochastic system, its stability and H∞ performance analysis is derived. Besides, some criteria are obtained to co-design the triggering mechanism and the H∞ controller. Finally, simulation studies demonstrate that compared with some existing heave plate mechanisms, the designed event-triggered H∞ controllers under this ATHP mechanism are more effective to suppress heave motions of the platform and save network resources and control expenditure. Furthermore, even though there are deception attacks, the proposed scheme can still guarantee satisfactory system performance.

Event-triggered tracking control for multi-agent systems with measurement noises

ABSTRACT This paper considers the mean-square leader-following consensus problem for heterogeneous multi-agent systems (MASs) affected by noises. Because only the output signal of a leader can be measured, a distributed dynamic control driven by an event-triggered mechanism (ETM) is proposed. The proposed ETM can reduce the signal transmission amount from sampler to controller. Using the tine-delay model method, the system under the proposed controller can be modelled as a stochastic time-delay system. Then the time-varying Hanaly inequality is utilised to obtain sufficient conditions that guarantee the consensus of MASs. Further, the quantity-based event-triggered mechanism is proposed to reduce the amount of traffic. Finally, an example is given to illustrate the validity of the obtained results.

Consensus of time-delay stochastic multiagent systems with impulsive behavior and exogenous disturbances

This note investigates the consensus problem of stochastic time-delay dynamical multiagent systems with impulsive behavior. The impulse instants of each agent are not necessarily synchronized with other agents. We provide a compact framework of the overall system then a classical distributed consensus protocol is investigated to guarantee practical exponential consensus of the multiagent system. For each agent, an event-triggered mechanism is used to sample and update the control signals only when its error exceeds the combinational measurements of its neighboring agents. By using the stability theory of stochastic dynamics and the properties of the Laplacian matrix, sufficient condition is presented to guarantee the synchronization among agents. A numerical example is presented to show the effectiveness of the theoretical results.

H ∞ performance for load frequency control systems with random delays

This paper investigates the problem of performance analysis for PI-type load frequency control (LFC) of power systems with random delays. By taking the probability distribution characteristic of communication delays into account in the LFC design, the power systems with a PI controller are modelled as stochastic time-delay systems. Furthermore, a delay-product-type augmented Lyapunov-Krasovskii functional (LKF) is constructed, and a new extended reciprocally convex matrix inequality combining Wirtinger-based integral inequality with convex combination approach is utilized to reduce the conservatism of main results. As a result, less conservative performance criteria are derived, which guarantee the asymptotically stable in the mean-square of the considered systems. Numerical examples are also provided to illustrate the superiority of our proposed methods.

Delay-dependent stability analysis of stochastic time-delay systems involving Poisson process

The delay-dependent (D-D) stability problem is investigated for stochastic time-delay systems (STDSs) involving the Poisson process in this paper. Firstly, semi-martingale theory is conducted to tackle the jump information of Itô formula properly. Secondly, this paper studies the expectations of stochastic cross terms (SCTs) containing Poisson-type stochastic integrals (SIs), and proves that the expectation of the particular SCT is equal to the expectation of a Lebesgue integral. Thirdly, on the basis of the above results, this paper adopts the free weighting matrix (FWM) method to give a D-D stability condition by a linear matrix inequality (LMI). In the derivation, no bounding technique is used, and then the conservatism arising from the common bounding technique is avoided. Finally, an example is presented to show the effectiveness of the derived D-D stability condition.

Linear–quadratic optimal control for time-delay stochastic system with recursive utility under full and partial information

This article studies a linear–quadratic (LQ) optimal control problem for time-delay stochastic system with recursive utility under full and partial information. The system is described by an anticipated forward–backward stochastic delayed differential equation (AFBSDDE). We obtain an explicit representation of optimal control in an open-loop form for the time-delay problem by Hamiltonian system, which is an AFBSDDE in double dimensions (D AFBSDDE). Also, we study a partial information counterpart of the above problem, and obtain an optimal control by optimal filtering. As applications of theoretical results, a cash management problem is solved. Analytic optimal controls are given, and some figures are used to illustrate the influence of delay on optimal solution.

L2-L∞ filtering for stochastic delayed systems with randomly occurring nonlinearities and sensor saturation

This work investigates L2-L∞ filtering problem for a class of stochastic systems with time-delay and randomly occurring phenomena. The purpose of the addressed problem is to design a full order filter to ensure the filtering error system is asymptotically mean-square stable with prescribed L2-L∞ performance. A novel stochastic time-delay system model is established, in which randomly occurring nonlinearities and sensor saturation phenomena are considered. Then, a novel functional containing negative definite terms is constructed to relax the constraints on the functional, and a new free-matrix-based stochastic integral inequality is also given. Meanwhile, a novel L2-L∞ performance analysis method making full use of delay information is proposed. As a result, less conservative conditions for the existence of filters are obtained, under which the L2-L∞ performance level can be achieved for the filtering error system. Numerical examples are employed to show the benefits of the proposed approach.

Non‐fragile robust exponential stabilisation and control for uncertain stochastic systems with non‐linearity and mixed delays

This study focuses on the delay-dependent robust exponential stabilisation and H ∞ control for uncertain stochastic time-delay systems with non-linear terms. Uncertain parameters are assumed to be time-varying norm bounded, while time-varying delay terms include both discrete and distributed delays. Firstly, by choosing an appropriate Lyapunov–Krasovskii functional, a sufficient condition for the robust exponential stabilisation is obtained. Secondly, the H ∞ control is also discussed. All criteria are presented in the form of linear matrix inequalities with less conservatism. Finally, an example verifies the validity of the proposed method.

Mixed H2/H∞ Control for Itô-type Stochastic Time-Delay Systems with Applications to Clothing Hanging Device

This paper deals with the problem of mixed H2/H∞ control for Itô-type stochastic time-delay systems. First, the H2/H∞ control problem for stochastic time-delay systems is presented, which considers the mean square stability, H2 control performance index, and the ability of disturbance attenuation of the closed-loop systems. Second, by choosing an appropriate Lyapunov–Krasoviskii functional and using matrix inequality technique, some sufficient conditions for the existence of state feedback H2/H∞ controller for stochastic time-delay systems are obtained in the form of linear matrix inequalities. Third, two convex optimization problems with linear matrix inequality constraints are formulated to design the optimal mixed H2/H∞ controller which minimizes the guaranteed cost of the closed-loop systems with known and unknown initial functions, and the corresponding algorithm is given to optimize H2/H∞ performance index. Finally, a numerical example is employed to show the effectiveness and feasibility of the proposed method.

Neuro-adaptive command filter control of stochastic time-delayed nonstrict-feedback systems with unknown input saturation

This paper addresses the problem of adaptive neural tracking control for a class of nonstrict-feedback stochastic nonlinear time-delayed systems with unknown input saturation and unknown disturbance input. A smooth function is selected to approximate the non-smooth saturation function. By using the command filter method scheme, the well-known problem of the explosion of complexity, which appears in the classical backstepping methods, is avoided. To approximate the unknown nonlinear functions, the radial basis function neural networks (NNs) are deployed. In addition, considering the minimal learning parameter method makes the updating law independent of the number of neural nodes and the order of the system. By using the mean-value theorem, the adaptive NN tracking control law is obtained systematically regardless of pre-known knowledge of input saturation bounds. The proposed control scheme guarantees that the state trajectories of the closed-loop system are semi-global uniformly ultimately bounded in probability and the tracking error finally stays in a small neighborhood around the origin. Eventually, numerical and practical examples show the performance of the proposed controller design.