Stochastic Systems Research Articles

Analyzing the age of information in prioritized status update systems under an interruption-based hybrid discipline

Motivated by real-life applications, a special research-work interest has been recently directed towards the prioritized status update systems, which prioritize the update streams according to their timeliness constraints. The preferential service treatment between priority classes is commonly based on classical disciplines, preemption and non-preemption. However, both disciplines fail to give an even satisfaction between all classes. In our work, an interruption-based hybrid preemptive/non-preemptive discipline is proposed under a single-buffer system modeled as an M/M/1/2 priority queueing system. Each class being served (resp. buffered) can be preempted unless its recorded number of service preemptions reaches the predetermined in-service (resp. in-waiting) threshold. All thresholds between classes are the controlling parameters of the whole system’s performance. Using the stochastic hybrid system approach, the age of information (AoI) performance metric is analyzed in terms of its statistical average along with the higher-order moments, considering a general number of priority classes. Closed-form results are also obtained for some special cases, giving analytical insights about the AoI stability in heavy loading conditions. The average AoI and its dispersion are numerically investigated for the case of a three-class network. The significance of the proposed model is manifested in achieving a compromise satisfaction between all priority classes by a thorough adjustment of its threshold parameters. Two approaches are proposed to clarify the adjustment of these parameters. It turned out that the proposed hybrid discipline compensates for the limited buffer resource, achieving more promising performance with low design complexity and low cost. Moreover, the proposed scheme can operate under a wider span of the total offered load, through which the whole network satisfaction can be optimized under some legitimate constraints on the age-sensitive classes.

Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System

Controllability and Stability of Non-instantaneous Impulsive Stochastic Multiple Delays System

Existence Result for a Stochastic Functional Differential System Driven by G-Brownian Motion with Infinite Delay

Abstract In this article, we are interested in the study of a class of stochastic functional differential systems driven by G-Brownian motion with infinite delay. We prove the existence and uniqueness of the solutions when two basic conditions are met: the linear growth condition and the Lipschitz condition.

Stochastic stabilization based on kinetic-potential energy shaping for stochastic mechanical port-Hamiltonian systems

This paper extends a kinetic-potential energy shaping method to stochastic mechanical port-Hamiltonian systems. The kinetic-potential energy shaping brings a new class of Lyapunov function candidates involving a cross term of the position and the momentum without solving partial differential equations for deterministic port-Hamiltonian systems. However, the conventional kinetic-potential energy shaping does not necessarily work for stochastic port-Hamiltonian systems due to energy increase by stochastic noise. Therefore, we first provide a modification properly compensated by using stochastic generalized canonical transformations. Then, two stochastic stability results are presented. The first result shows a necessary condition for stochastic asymptotic stability for an equilibrium state. The other one shows a necessary condition for stochastic bounded stability for a target state, which is not necessarily an equilibrium point.

Adaptive fuzzy control of stochastic nonlinear systems with predefined time via self-triggered mechanism

Adaptive fuzzy control of stochastic nonlinear systems with predefined time via self-triggered mechanism

Disturbance observer based fixed-time control of stochastic systems

In this paper, the novel fixed-time anti-disturbance control scheme is proposed for a class of stochastic systems subjected to multiple disturbances and faults, and the disturbances consist of derivative-bounded disturbances and multiply noise. Based on the pole placement method, the fixed-time disturbance observer (Fixed-time DO) is devised to estimate derivative-bounded disturbances and an adaptive law is employed to approach the time-varying fault. Then a composite fixed-time controller is constructed to make the system converge to equilibrium position within a pre-specified time. At the same time, simulation examples illustrate that the proposed controller is effective and the convergence time is not related to the initial states of the system.

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.

EFFECTS OF ANTI-PREDATOR BEHAVIOR ON A STOCHASTIC PREDATOR-PREY SYSTEM

An ecosystem with anti-predator behavior is established in both deterministic and stochastic environments. This means that adult prey could attack weak predators. Bifurcation diagrams are used to analyze the deterministic case, while a tool called the most probable trajectory, defined by the spatial extreme point of the probability density function (PDF), is employed to explore the stochastic case. The Fokker-Planck equation is solved using the stochastic averaging method of energy envelope, which provides an analytical expression for the PDF. The results show that in the deterministic case, effective anti-predator behavior can dampen predator-prey oscillations and mitigate negative effects caused by the time delay. Additionally, it can accelerate the transient solution to reach a steady state and reduce the ratio of predator-to-prey densities in coexistence. In the stochastic case, effective anti-predator behavior can raise the noise threshold that leads to population extinction. Furthermore, it can also reduce the randomness of solutions. It’s worth noting that appropriate anti-predator behavior can ensure that the most probable solution in the stochastic system approximates the solution in the deterministic system. Monte Carlo simulations verify the accuracy of these analytical results.

Saddle-Point Equilibrium Strategy for Linear Quadratic Uncertain Stochastic Hybrid Differential Games Based on Subadditive Measures

This paper describes a kind of linear quadratic uncertain stochastic hybrid differential game system grounded in the framework of subadditive measures, in which the system dynamics are described by a hybrid differential equation with Wiener–Liu noise and the performance index function is quadratic. Firstly, we introduce the concept of hybrid differential games and establish the Max–Min Lemma for the two-player zero-sum game scenario. Next, we discuss the analysis of saddle-point equilibrium strategies for linear quadratic hybrid differential games, addressing both finite and infinite time horizons. Through the incorporation of a generalized Riccati differential equation (GRDE) and guided by the principles of the Itô–Liu formula, we prove that that solving the GRDE is crucial and serves as both a sufficient and necessary precondition for identifying equilibrium strategies within a finite horizon. In addition, we also acquire the explicit formulations of equilibrium strategies in closed forms, alongside determining the optimal values of the cost function. Through the adoption of a generalized Riccati equation (GRE) and applying a similar approach to that used for the finite horizon case, we establish that the ability to solve the GRE constitutes a sufficient criterion for the emergence of equilibrium strategies in scenarios extending over an infinite horizon. Moreover, we explore the dynamics of a resource extraction problem within a finite horizon and separately delve into an H∞ control problem applicable to an infinite horizon. Finally, we present the conclusions.

Modeling the dengue control dynamics based on a delay stochastic differential system

Modeling the dengue control dynamics based on a delay stochastic differential system

Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints

Adaptive Fuzzy Tracking Control for Stochastic Nonlinear Systems with Full-State Constraints

Optimal stopping of BSDEs with constrained jumps and related zero-sum games

In this paper, we introduce a non-linear Snell envelope which at each time represents the maximal value that can be achieved by stopping a BSDE with constrained jumps. We establish the existence of the Snell envelope by employing a penalization technique and the primary challenge we encounter is demonstrating the regularity of the limit for the scheme. Additionally, we relate the Snell envelope to a finite horizon, zero-sum stochastic differential game, where one player controls a path-dependent stochastic system by invoking impulses, while the opponent is given the opportunity to stop the game prematurely. Importantly, by developing new techniques within the realm of control randomization, we demonstrate that the value of the game exists and is precisely characterized by our non-linear Snell envelope.

Stability analysis for nonautonomous impulsive hybrid stochastic delay systems

In this paper, the problems on the existence and uniqueness, and the input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are considered. The existence and uniqueness for the global solution of such systems is studied by using the Lyapunov function, the theory of stochastic analysis, and the function of the impulsive density. In order to overcome the difficulty stemming from the simultaneous presence of the indefinite derivative for the Lyapunov function, the bounded external disturbances, and a nonnegative and bounded time-varying delay, one impulsive generalized Halanay inequality of integral version is established. The input-to-state stability, the integral input-to-state stability, the stochastic input-to-state stability and the eλt(λ>0)-weighted input-to-state stability for the global solution of nonlinear nonautonomous impulsive stochastic delay systems with Markovian switching are investigated, respectively. One example is provided to illustrate the effectiveness of the theoretical results obtained.

Semi-global exponential stabilization of stochastic nonlinear systems with distributed delay under discrete-time state observations and application to circuit systems

This paper is aimed at studying the semi-global exponential stabilization problem for stochastic nonlinear systems with distributed delay under discrete-time state observations. An extended definition of horizontal translation of the segment function along the investigated systems is given, related to the stochastic disturbance and Brownian motion. Basically, the right and upper Dini’s derivative of the constructed functional is presented. Combining this with the global exponential stability of the stochastic nonlinear systems with distributed delay under continuous-time feedback control, the Lyapunov method and Halanay inequality, the maximum observation interval and some stabilization criteria to make the investigated systems under discrete-time state observations reach semi-global exponential stabilization are provided. The results indicate that the semi-global exponential stabilization is dependent upon stochastic disturbance, initial condition range, and maximum observation interval. Finally, an application to the circuit systems is discussed and the involved sufficient conditions for the circuit systems to keep semi-global stabilization are also proposed. Besides, the numerical simulation results confirm the effectiveness of the theoretical results.

Stabilization of nonlinear stochastic systems with input and output delays via event‐triggered predictive control

AbstractThe stabilization of nonlinear stochastic systems with input and output delays is investigated in this article. First, an observer that includes input delay information is designed to estimate the state information after eliminating the effect of input delay. Second, a predictive scheme with delay information is utilized to predict the system state affected by output delay, and an event‐triggered predictive controller is established to eliminate the effects of input and output delays simultaneously. Subsequently, the convergence of the prediction error is analyzed by utilizing a recursive method, and a sufficient condition to ensure the global exponential stability is given by constructing a new closed‐loop system. Finally, numerical simulations of two nonlinear stochastic systems with different delay sizes are utilized to verify the impact of the event‐triggered predictive control in addressing the stabilization of nonlinear stochastic systems with time delays.

Dynamic event-triggered adaptive tracking control for stochastic nonlinear systems with deferred time-varying constraints

This article investigates the problem of adaptive tracking control for stochastic nonlinear systems with deferred state constraints. The novel unified universal barrier function (UUBF) and deferred funnel error transformation are developed to handle various state constraints and adjust the tracking error more precisely, respectively. Multi-dimensional Taylor network (MTN) and dynamic event-triggered mechanism (DETM) are employed to design controller in the backstepping process, which can achieve full-state constraints and the tracking control after the preassigned time while conserving more communication resources. Finally, two simulation examples are presented to verify the effectiveness of the proposed control scheme.

On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

On the Asymptotic Stability of Hilfer Fractional Neutral Stochastic Differential Systems with Infinite Delay

Correction to: A topological framework for identifying phenomenological bifurcations in stochastic dynamical systems

Correction to: A topological framework for identifying phenomenological bifurcations in stochastic dynamical systems

STEWART PLATFORM DYNAMICS MODEL IDENTIFICATION

Context. At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion.
 Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification.
 Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals.
 Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models.
 Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences.

Active fault diagnosis for stochastic systems subject to non-convex input constraints

In this paper, the problem of active fault diagnosis (AFD) is investigated for a class of continuous-time stochastic systems subject to non-convex input constraints. The input is designed to minimize the probability of misdiagnosis. Since the misdiagnosis probability cannot be expressed in the closed form, its Chernoff upper bound likely tighter than its widely used Bhattacharyya upper bound is exploited as an alternative. The closed-form expression of the Chernoff distance under Gaussian distributions is correctly deduced. For calculation simplification and diagnosis performance enhancement purposes, a novel input design criterion is constructed for AFD based on the Chernoff distance. The optimization problem for AFD is formulated as a bilevel optimization, where the outer and inner layers optimize the Chernoff distance parameter and the input respectively. A convex relaxation is proposed to relax non-convex input constraints into convex ones, and the optimal solution to the relaxed inner input design problem is proven to be also optimal for the original inner problem whose objective function and input constraints are both non-convex under certain conditions, which is referred to as lossless relaxation. The relaxed inner input design problem under the constructed design criterion can be solved to global optimums, and the relaxed outer optimization is solved by a grid search method. Given the optimal input, faults are diagnosed based on the minimum misdiagnosis probability decision rule. The effectiveness of the proposed AFD approach is demonstrated by utilizing a planetary landing example.