Stochastic Disturbances Research Articles

Hierarchical Fault-Tolerant Coverage Control for an Autonomous Aerial Agent

Fault-tolerant coverage control involves determining a trajectory that enables an autonomous agent to cover specific points of interest, even in the presence of actuation and/or sensing faults. In this work, the agent encounters control inputs that are erroneous; specifically, its nominal controls inputs are perturbed by stochastic disturbances, potentially disrupting its intended operation. Existing techniques have focused on deterministically bounded disturbances or relied on the assumption of Gaussian disturbances, whereas non-Gaussian disturbances have been primarily been tackled via scenario-based stochastic control methods. However, the assumption of Gaussian disturbances is generally limited to linear systems, and scenario-based methods can become computationally prohibitive. To address these limitations, we propose a hierarchical coverage controller that integrates mixed-trigonometric-polynomial moment propagation to propagate non-Gaussian disturbances through the agent’s nonlinear dynamics. Specifically, the first stage generates an ideal reference plan by optimising the agent’s mobility and camera control inputs. The second-stage fault-tolerant controller then aims to follow this reference plan, even in the presence of erroneous control inputs caused by non-Gaussian disturbances. This is achieved by imposing a set of deterministic constraints on the moments of the system’s uncertain states.

Approximate controllability of second-order neutral stochastic differential evolution systems with random impulsive effect and state-dependent delay

<p>In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.</p>

Fixed-Time Attitude Control for QUAV With Stochastic Disturbances: Theory and Experiment

Fixed-Time Attitude Control for QUAV With Stochastic Disturbances: Theory and Experiment

Neural-Network-Based Adaptive Fixed-Time Control for Nonlinear Multiagent Non-Affine Systems.

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

A Non-Sampling Time-Domain Simulation Framework for Transient Stability Assessment under Stochastic Continuous Disturbances

A Non-Sampling Time-Domain Simulation Framework for Transient Stability Assessment under Stochastic Continuous Disturbances

Risk-Aware MPC for Stochastic Systems with Runtime Temporal Logics

This paper concerns the risk-aware control of stochastic systems with temporal logic specifications dynamically assigned during runtime. Conventional risk-aware control typically assumes that all specifications are predefined and remain unchanged during runtime. In this paper, we propose a novel, provably correct model predictive control scheme for linear systems with additive unbounded stochastic disturbances that dynamically evaluates the feasibility of runtime signal temporal logic specifications and automatically reschedules the control inputs accordingly. The control method guarantees the probabilistic satisfaction of newly accepted specifications without sacrificing the satisfaction of the previously accepted ones. The proposed control method is validated by a robotic motion planning case study.

Data-Driven Iterative Learning Model Predictive Control With Self-Modified Prior Knowledge.

Iterative learning model predictive control (ILMPC) has become an excellent data-driven intelligent control strategy for digitized batch manufacturing, featured by the progressive improvement of tracking performance along trials, and the persistent rejection of stochastic disturbance along time. The point-to-point learning mechanism of existing ILMPC generally relies on identical operating conditions along trials to guarantee the integrity and accuracy of historical data. However, the variations of production requirements usually lead to trial-varying operating references and durations, resulting in incomplete and inaccurate historical information for the iterative learning of subsequent trials. To promote the adaptability and flexibility of ILMPCs with unconformable prior information, a data-driven self-modification scheme is originally embedded into ILMPC in this article to transfer the prior knowledge contained in the historical operating data into the form consistent with the condition of each current trial. The control actions are imitated along trials by an adaptive deep neural network (DNN), which is then utilized to generate reference control signals for iterative learning in each trial. For attenuating the influence of the considerable DNN approximation error in early trials with limited data accumulation, the 2-D optimization of ILMPC is performed under a tube control frame to ensure the time-domain bounded stability. Based on the intrinsic recursive feasibility and the guaranteed time-domain stability, the iteration-domain bounded convergence of the developed ILMPC system is theoretically validated. Simulations on the nonlinear injection molding process verify the superiority of the proposed method in adapting to significant changes in operating reference and duration.

A practical approach for transfer function estimation using short, transient process data

Increased productivity in the industrial sector requires optimal closed loop performance. This can be solely achieved through optimal tuning of the controller parameters, which requires reliable and efficient process data, further employed in process estimations or high quality models. Most of the classical identification methods require long input-output data sets. In this paper we propose a technique to extract process information from short transient process data. The method is based on short sine test which can be superimposed on nominal process inputs, and estimates the process impulse response, consequently providing a band limited, but highly accurate, frequency response. This in turn is used to accurately estimate a high order plus dead time model. The method is reliable and requires less effort compared to classical step based methods. The main features of the proposed method are: 1) it uses a short duration test based on a sine input; 2) it produces accurate models in the presence of stochastic disturbances; and 3) it can be executed in open or closed loop. Numerical examples are provided to validate the theoretical approach and demonstrate the accuracy of the estimation.

Identification of Hammerstein-Wiener models using Hamiltonian Monte Carlo

This paper develops and illustrates a process for the Identification of Hammer-stein–Wiener model structures using Hamiltonian Monte Carlo. A central aspect is that a very general situation is considered wherein multi-variable data, non-invertible Hammerstein and Wiener nonlinearities, and Gaussian stochastic disturbances both before and after the Wiener non-linearity are all catered for. The posterior distribution of the parameters is directly sampled from and these samples can then be used to quantify the uncertainty of the system model estimates, and to calculate expected values of various quantities.

Fixed-Time Adaptive Control With Predefined Tracking Accuracy for Piezoactuators Subject to Stochastic Disturbances

Fixed-Time Adaptive Control With Predefined Tracking Accuracy for Piezoactuators Subject to Stochastic Disturbances

Regarding the Spontaneous Mechanism of Atmospheric Whirlwind Generation in Narrow Mountain Canyons

In a narrow, rather deep mountain canyons, under certain conditions, an irregular thermal mechanism can be activated, leading to the spontaneous convective movement of the air mass. This effect differs from the well-known phenomenon caused by the diurnal variation of the solar heat flux in large, broad valleys, where the regular diurnal variation in the direction of onshore winds is systematically suppressed. A specific hydrodynamic picture corresponds to spontaneous convection. In particular, there is a change of direction (inversion) in the vertical profile of the horizontal movement of air along the slope of the canyon at a certain height. At that time, Ludwig Prandtl developed the theoretical model through which it is possible to analytically determine the level of velocity inversion compared to the base of the valley. At this height, due to the instability of the velocity profile, the formation of atmospheric vortexes of a certain size is likely. It is natural that the dissolution (dissipation) of such vortexes will affect the temperature field.Therefore, the breakup of whirlwinds is related to the violation of thermodynamic equilibrium, meaning that there will be an impulsive change in the meteorological regime in the local area due to the spontaneous turbulence of air masses in the areas of velocity inversion. The characteristic time of this event will depend on the duration of the temperature field disturbance. It is likely that such a location will become a dangerous opportunity for hang gliding or paragliding enthusiasts. It should be noted that this type of sport has become an important component of tourism in Georgia, particularly in the mountainous regions of the country. Therefore, there is a need to focus on ensuring the safe flight conditions of individual aircraft in narrow valleys. Their formation, among other measures, requires an assessment of the probability of the operation of a thermal mechanism causing stochastic atmospheric disturbances in narrow canyons. This task can be carried out only as a result of a special investigation, based on the monitoring of seasonal and short-term hourly indicators of the mentioned physical event in a specially selected canyon, which can be considered typical for the mountainous regions of Georgia.

On the convergence of tracking differentiator with multiple stochastic disturbances

On the convergence of tracking differentiator with multiple stochastic disturbances

Transient dynamics mask the resilience of coral reefs

Coral reefs are model systems for studies of ecological resilience, with communities generally exhibiting multiple stable states and more resilient regions trending towards a single, coral-dominated, regime. We expand the theory of ecological resilience beyond the concepts of distinct stable states to integrate emerging ideas from transient dynamics as long-term intermediate states with no pronounced trend towards equilibria. We show that low coral abundance, together with stochastic larval supply and disturbance, can trap otherwise resilient reefs in a persistent intermediate state whose long-term outcome is difficult to predict. Common metrics, such as the ecosystem slowing down before crossing tipping points and using historical coral cover trends, may become unreliable predictors of future behaviour. Helping reefs out of transient states requires agile management that allows for short-term, targeted interventions after which natural ecological feedbacks can take over.

Classification Study of New Power System Stability Considering Stochastic Disturbance Factors

Power system instability causes many local or large-scale power outage accidents. To maintain sustainable development, a new power system construction aimed at maximizing new energy consumption is being put on the agenda. However, with a large increase in stochastic disturbance factors (SDFs), the system gradually shows strong stochasticity, and the stability presents greater complexity. It is necessary to analyze the impact on the system based on different processing methods of SDFs to maintain system stability. This paper delves into the impact of SDFs on system stability by analyzing and summarizing both stochastic variables and processes. Initially, the SDFs in the power system are meticulously analyzed and categorized. When the SDFs are treated as stochastic variables, the probabilistic stability is classified and evaluated based on a probability analysis method, which includes the probabilistic small-disturbance stability, the probabilistic transient stability, and the probabilistic voltage stability. When the SDFs are treated as stochastic processes, the stochastic stability is classified and evaluated by using a stochastic analysis method, including the stochastic small-disturbance stability, the stochastic transient stability, and the stochastic voltage stability. Finally, the research perspectives on SDFs and system stability are discussed and prospected.

Moment propagation of polynomial systems through Carleman linearization for probabilistic safety analysis

We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states and transform it into an infinite-dimensional system with linear deterministic dynamics, which describe the exact evolution of the moments of the original polynomial system. We then truncate this deterministic system to obtain a finite-dimensional linear system, and use it for moment approximation by iteratively propagating the moments along the finite-dimensional linear dynamics across time. We provide efficient online computation methods for this propagation scheme with several error bounds for the approximation. Our results also show that precise values of certain moments at a given time step can be obtained when the truncated system is sufficiently large. Furthermore, we investigate techniques to reduce the offline computation load using reduced Kronecker power. Based on the obtained approximate moments and their errors, we also provide hyperellipsoidal regions that are safe for some given probability bound. Those bounds allow us to conduct probabilistic safety analysis online through convex optimization. We demonstrate our results on a logistic map with stochastic dynamics and a vehicle dynamics subject to stochastic disturbance.

Distributed Economic MPC for Dynamically Coupled Systems With Stochastic Disturbances

Distributed Economic MPC for Dynamically Coupled Systems With Stochastic Disturbances

Practically Predefined-Time Adaptive Fuzzy Tracking Control for Nonlinear Stochastic Systems.

This article addresses the practically predefined-time adaptive fuzzy tracking control problem of strict-feedback nonlinear stochastic systems, where the system under consideration includes stochastic disturbances and uncertain parameters. First, in this study, practically predefined-time stochastic stabilization (PPSS) in the p th moment sense is introduced, and a Lyapunov-type criterion for PPSS is proposed to assure the stabilization of the system considered. With these ideas, based on the backstepping design method, a semiglobally practically predefined-time adaptive fuzzy tracking control algorithm is proposed with a fuzzy system used to approximate the unknown part of the system. Moreover, the settling time of the system response can be arbitrarily adjusted in a mean-value sense, and such freedom can be used to improve the stochastic finite-/fixed-time control results. Finally, a practical example and a numerical example of a comparison are provided to validate the effectiveness of the proposed control strategy.

Distributed Fuzzy Containment Control for Stochastic Nonlinear Multiagent Systems Under Denial-of-Service Attacks

The paper investigates distributed fuzzy adaptive containment control problem of stochastic nonlinear multi-agent systems under an directed communication topology suffering Denial-of-Service (DoS) attacks. Firstly, considering unknown stochastic disturbance and nonlinear characteristics for the followers, the mathematical models are modeled as It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\hat{o}$</tex-math></inline-formula> stochastic nonlinearities terms approximated through fuzzy logic systems (FLS). Secondly, the proposed dynamically adjusted event-triggered condition can effectively avoid inefficient transmission behavior. Moreover, an adaptive compensation protocol for input saturation is constructed to eliminate the effects of nonlinearities caused by input saturation. Finally, instead of the previous uniformly ultimately bounded containment control results, stability and asymptotic performance are guaranteed through valid reasonable adaptive control laws acquired through backstepping control approach despite suffers DoS cyber attacks. Moreover, a simulation is given to verify the feasibility of the proposed method.

Proportional-Integral Observer-Based State Estimation for Singularly Perturbed Complex Networks With Cyberattacks.

This article investigates the asynchronous proportional-integral observer (PIO) design issue for singularly perturbed complex networks (SPCNs) subject to cyberattacks. The switching topology of SPCNs is regulated by a nonhomogeneous Markov switching process, whose time-varying transition probabilities are polytope structured. Besides, the multiple scalar Winner processes are applied to character the stochastic disturbances of the inner linking strengths. Two mutually independent Bernoulli stochastic variables are exploited to characterize the random occurrences of cyberattacks. In a practical viewpoint, by resorting to the hidden nonhomogeneous Markov model, an asynchronous PIO is formulated. Under such a framework, by applying the Lyapunov theory, sufficient conditions are established such that the augmented dynamic is mean-square exponentially ultimately bounded. Finally, the effectiveness of the theoretical results is verified by two numerical simulations.

Response of an Euler–Bernoulli beam subject to a stochastic disturbance

This work concerns the stochastic analysis of the bending of a slender cantilever beam subject to an external force with the inclusion of a stochastic effect characterised by white noise. The beam deflection is governed by the classic dynamic Euler–Bernoulli equation. Its response to the stochastic external load is investigated by learning pattern from the simulation data which are collected from numerical computations of ten thousand numerical experiments, which are achieved using a finite difference method coupled with a Monte Carlo method for the uncertainty quantification. Insightful results are presented with visualisation techniques and discussed in detail. Of note, by performing regression analysis to the data, the solution is shown to follow a centred Gaussian process with a strong numerical evidence. The associated autocovariance matrix is computed using the sample data. Then, a mild solution in the probability sense for the deflection at a fixed position and a fixed time is written explicitly in a simple form. The results obtained by the finite difference scheme were also compared to the finite-element scheme and were found to be in good agreement. Unsurprisingly, the finite-element scheme was found to be much more computationally expensive compared to finite difference scheme. Hence, for such a simple structure, the stochastic analysis using the finite difference scheme is preferred. Analysis of the results also showed that some of the regression parameters converge when the number of simulations reaches five hundred and only vary subject to numerical errors of order 10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-6}$$\\end{document} if the number of simulations is further increased. While others converge when the number of simulations exceeds two thousand showing that depending on the level of precision required fewer than ten thousand simulations might be required.