Stochastic Disturbances Research Articles

A Novel Hybrid Firefly Algorithm with Double-Level Learning Strategy

The firefly algorithm (FA) is a swarm intelligence algorithm capable of solving global optimization problems exactly; it has been used to solve many practical problems. However, traditional firefly algorithms solve complex optimization problems with a simple update method, which leads to premature stagnation due to the limitation of firefly diversity. To overcome these drawbacks, a novel hybrid firefly algorithm (HFA-DLL) with a double-level learning strategy is proposed. In HFA-DLL, a double-level learning strategy is proposed to avoid premature convergence and enhance the algorithm’s global search capability. At the same time, a competitive elimination mechanism is introduced to increase the accuracy of solving complex optimization problems and improve the convergence rate of the algorithm. Moreover, a stochastic disturbance strategy is designed to help the best solution jump out of the local optimum and minimize the time cost in the wrong direction. To understand the advantages and disadvantages of HFA-DLL, experiments were conducted on the CEC 2017 benchmark suite. Experimental results show that HFA-DLL outperforms other state-of-art algorithms in terms of convergence rate and exploration efficiency.

MDOF stochastic stability analysis and applications to a coupled rotating shaft system

Stochastic stability analysis and generalization of moment Lyapunov exponents of multi-degree-of-freedom (MDOF) systems under white noise excitation were carried out using the transformation method and the perturbation method. Such systems represent coupled dynamic models exposed to stochastic disturbances and they are very common in engineering practice. The analysis of individual parts of a mechanical system does not give a clear picture of its real behavior as a whole, so the consideration of dynamic couplings is of great importance. This study proposes a generalized set of new transformations for MDOF systems that are necessary for obtaining Itô’s equations needed for further consideration of stochastic stability. The eigenvalue problem for moment Lyapunov exponents is derived and then solved by the method of perturbation. The generalized procedure is applied in an example of a rotating coupled shaft system whose dynamic behavior should be analyzed with at least four generalized coordinates. Similar models have so far been analyzed with limitations on SDOF and 2DOF systems that do not fully correspond to realistic models. The methodology demonstrated in the study could be applied more broadly, as it has the potential to analyze the dynamic stability of even more intricate or diverse systems whose dynamics have not been previously studied.

Ternary Implicit Criterion for Robust Exponential Stability of Perturbed Stochastic BAM Systems

This brief presents the sufficient criterion to guarantee the robust exponential stability (RES) of perturbed stochastic nonlinear bidirectional associative memory system with derivative contraction coefficients and piecewise constant arguments (SDPNBAM system). Different from the method of solving multiple transcendental equations, the upper bounds of derivative contraction coefficients, stochastic disturbances and piecewise constant arguments are parsed by the same well-defined ternary transcendental equation and characterized by a feasible geometrical enclosed space, formulating the main ternary implicit criterion. Accordingly, the dynamical interconnection among perturbed ternary variables constrained in the same transcendental equation is formed and to moderate the SDPNBAM system to be stable ultimately. Finally, the numerical simulation shows the effectiveness of main results.

Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.

An analogous carrier‐based implementation of virtual space vector modulation with low common‐mode voltage and neutral‐point voltage oscillation elimination for three‐level NPC inverter

AbstractBalancing control of neutral‐point voltage (NPV) and reducing common‐mode voltage (CMV) are crucial for a three‐level neutral‐point‐clamped (NPC) inverter. NPV oscillation can be inhibited by constructing virtual vectors and adding adjustment factors to eliminate stochastic disturbances that cause unbalanced NPV. However, the adjustment factors significantly increase computational complexity and introduce a dynamic sector split instead of the traditional static one. Moreover, constructing virtual vectors prompts a considerable rise in CMV. Therefore, this paper proposes a virtual space vector modulation strategy for the NPC inverter that eliminates NPV oscillation and reduces CMV. The study applies the idea of carrier‐based modulation (CBM), which reduces calculation time caused by the novel strategy of adding adjustment factors. A method to determine the maximum adjustment voltage is designed to evaluate NPV regulation ability, which is analysed. The novel method and the basic VSVM are theoretically compared, and it is proved that the novel method has better NPV regulation capability than the basic VSVM under high modulation ratio and high power factors, such as in motors systems.

Segment-Weighted Information-Based Event-Triggered Mechanism for Networked Control Systems.

In this study, the event-triggered problem of networked control systems (NCSs) is investigated, and a novel information transmission scheme is established. Under this scheme, the segment-weighted information (SWI) in a sliding historical window (SHW) is calculated and then sampled. Compared with the traditional direct sampling method, in this approach, the control input includes historical information in the SHW, thereby leading to less information loss due to sampling. This study also emphasizes on designing an SWI-based event-triggered mechanism (ETM) for scheduling network transmission. Different from most of the existing ETMs, the proposed SWI-based ETM leverages historical information to determine which data are necessary for the whole control system. Our approach can greatly reduce the number of unexpected triggering events of a control system with stochastic disturbances owing to the introduction of the SWI in the ETM. Moreover, Zeno phenomena are prevented thanks to periodic sampling. Sufficient conditions are derived based on the Lyapunov functional approach, and a numerical simulation example is provided to demonstrate the effectiveness of the proposed method.

A Dynamic Behavior Analysis of a Rolling Mill’s Main Drive System with Fractional Derivative and Stochastic Disturbance

Taking the random factors into account, a fractional main drive system of a rolling mill with Gaussian white noise is developed. First, the potential deterministic bifurcation is investigated by a linearized stability analysis. The results indicate that the fractional order changes the system from a stable point to a limit cycle with symmetric phase trajectories. Then, the stochastic response is obtained with the aid of the equivalent transformation of the fractional derivative and stochastic averaging methods. It is found that the joint stationary probability density function appears to have symmetric distribution. Finally, the influence of the fractional order and noise intensity on system dynamics behavior is discussed. The study is beneficial to understand the intrinsic mechanisms of vibration abatement.

Command filtered backstepping control of constrained flexible joint robotic manipulator

AbstractHere, an adaptive radial basis function (RBF) neural network (NN) backstepping controller is proposed for a class of input‐constrained flexible joint robotic manipulators represented by strict‐feedback form with unknown terms, external stochastic disturbance, and output disturbance. The proposed approach is robust against both deterministic and stochastic uncertainties and disturbances and copes with the control input amplitude saturation. Moreover, by deploying the minimal learning parameter method and command filter technique, the computational burden of derivative terms and adaptive terms greatly decreases. Considering the mean‐value theorem assists us to avoid the need for having the input saturation bounds in prior. The suggested tracking control scheme mandates the closed‐loop system states to be semi‐globally bounded‐in‐probability. Also, a quartic Barrier Lyapunov function is utilized to force the tracking error to be confined within a pre‐chosen small region around the origin. Eventually, a numerical simulation of a flexible joint robot manipulator with a single link is performed to show the effectiveness and performance of the developed control method.

Discontinuous control for exponential synchronization of complex-valued stochastic multi-layer networks

This article is concerned with the exponential synchronization issue of complex-valued stochastic multi-layer networks (CVSMLNs) via two discontinuous control approaches. At first, a new network model of complex-valued multi-layer network is built by integrating stochastic disturbances, intra-layer and inter-layer couplings. Different from previous aperiodic intermittent control (APIC) approaches, under the framework of APIC, novel impulsive feedback control (IFC) (IFC is executed at the activation time of APIC) and universal adaptive feedback control (adaptive control gain is different in different layers) are both developed to realize the exponential synchronization of CVSMLNs. Subsequently, some simple sufficient criteria are derived by virtue of Lyapunov method, graph theory and complex generalized Itô’s formula. Ultimately, the theoretical results are used in a practical complex-valued neural network and the availability of the obtained results is verified by giving some numerical examples.

Observability of Boolean control networks with stochastic disturbances

In this paper, the observability problem of Boolean control networks (BCNs) with stochastic disturbances is investigated via two kinds of control schemes: deterministic control and state feedback control. Firstly, based on the proposed indicator matrix, a simplified system of the original augmented Boolean system is constructed. Based on the analysis of the auxiliary system, observability of the original BCN is converted to determine whether an observable set can be reached from another unobservable set. After that, some necessary and sufficient conditions are obtained to judge the observability of BCNs. At the same time, two algorithms are proposed for designing these two types of control sequences. Finally, numerical simulations are also provided to demonstrate feasibility of the theoretical results.

Dynamic analysis of the IFCD rumor propagation model under stochastic disturbance on heterogeneous networks

By taking full consideration of the heterogeneity of network users and stochastic disturbance of network environment, a stochastic IFCD (Ignorants-Forwarders-Collectors-Deleters) rumor propagation model is proposed on heterogeneous networks. This study takes MicroBlog as the research background to investigate the dynamical behaviors of rumor spreading on online social networks, which paves the way for controlling rumors effectively and provides positive guidance for the network public opinion. Firstly, some preparations for building a stochastic model are given, including establishing a deterministic IFCD rumor propagation model and obtaining the rumor-free/spreading equilibrium. Secondly, considering the impact of stochastic disturbance on rumor propagation, the corresponding stochastic rumor propagation model is established. Thirdly, a stopping time is defined, which manifests the existence of the unique global positive solution in the stochastic model. Next, sufficient conditions of the rumor extinction and persistence are obtained by using Itô’s formula and strong law of large numbers. Additionally, simulations are operated to validate the results. Finally, the application of the model is shown to bear out the applicability of the proposed model.

Fixed/predefined-time synchronization of coupled memristor-based neural networks with stochastic disturbance

In this paper, with the design of a unified adaptive controller, the fixed-time (FXT) and predefined-time (PDT) synchronization problems of coupled memristor-based neural networks (CMNNs) with stochastic disturbance is studied. The FXT synchronization of CMNNs with stochastic disturbance via adaptive control is investigated, some sufficient conditions for FXT synchronization and a less conservative settling time independent of the initial state are given. By modifying the parameters of the same controller, the synchronization scheme of CMMNs within an arbitrary predefined time, which is not related to the system and controller parameters, is designed. Numerical simulations are finally given to verify the validity of the obtained theoretical results and the feasibility of the secure communication scheme.

Synchronization of Coupled Phase Oscillators with Stochastic Disturbances and the Cycle Space of the Graph

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine the fluctuations of phase differences in the lines between the nodes and to identify the vulnerable lines that may lead to desynchronization. The main result is the derivation of the asymptotic variance matrices of the phase differences which characterizes the severity of the fluctuations. It is found that the cycle space of the graph of the system plays a role in this characterization. With theory of the cycle space, the effect of forming small cycles on the fluctuations is evaluated. It is proven that adding a new line or increasing the coupling strength of a line affects the fluctuations in the lines in any cycle including this line, while it does not affect the fluctuations in the other lines. In particular, if the phase differences at the synchronous state are not changed by these actions, then the affected fluctuations reduce.

Fuzzy Controller Design Approach for a Ship’s Dynamic Path Based on AIS Data with the Takagi–Sugeno Fuzzy Observer Model

A fuzzy controller design approach is developed in this research for the control problem of a ship’s dynamic path based on automatic identification system (AIS) data. Over the past few decades, the equipment of AISs has been widely applied and mandated on ships. Based on the advantages of AIS data, various valuable applications have been proposed to improve safety problems. However, most of the applications depend on the precise control of the ship’s dynamic behavior. Because of this reason, a fuzzy controller design approach is proposed based on the Takagi–Sugeno fuzzy observer model in this research. Firstly, the ship’s dynamic behavior based on the discrete-time AIS data is estimated and represented by the mathematical model of the fuzzy observer. Based on the fuzzy observer model, a fuzzy controller design approach subject to variance constraint is developed to solve the problem of stochastic disturbance in estimation and control. In accordance with the different application aspects, this approach can not only be applied to improve the estimation performance of the fuzzy observer, but it can also be provided as a controller design scheme for the ship’s dynamic path using AISs data. Finally, simulation results of a group of real AIS data from Kaohsiung Port and the assumed Keelung Port AIS data are applied to verify the effectiveness of the designed fuzzy controller.

Process control of mAb production using multi-actor proximal policy optimization

Monoclonal antibodies (mAb) are biopharmaceutical products that improve human immunity. In this work, we propose a multi-actor proximal policy optimization-based reinforcement learning (RL) for the control of mAb production. Here, manipulated variable is flowrate and the control variable is mAb concentration. Based on root mean square error (RMSE) values and convergence performance, it has been observed that multi-actor PPO has performed better as compared to other RL algorithms. It is observed that PPO predicts a 40 % reduction in the number of days to reach the desired concentration. Moreover, the performance of PPO is improved as the number of actors increases. PPO agent shows the best performance with three actors, but on further increasing, its performance deteriorated. These results are verified based on three case studies, namely, (i) for nominal conditions, (ii) in the presence of noise in raw materials and measurements, and (iii) in the presence of stochastic disturbance in temperature and noise in measurements. The results indicate that the proposed approach outperforms the deep deterministic policy gradient (DDPG), twin delayed deep deterministic policy gradient (TD3), and proximal policy optimization (PPO) algorithms for the control of the bioreactor system.

Observer‐based dynamic ETC optimized tracking of nonlinear systems with stochastic disturbances

AbstractThis paper proposes a simple and efficient adaptive event‐triggered optimized control (ETOC) scheme using reinforcement learning (RL) for stochastic nonlinear systems. The scheme includes an online state observer to estimate unmeasured states and a dynamically adjustable event‐triggered mechanism that reduces communication resources. The RL algorithm is based on the negative gradient of a simple positive function and employs the identifier‐actor‐critic architecture. The proposed ETOC approach is in the sensor‐to‐controller channel and directly activates control behavior through triggered states, which saves network resources. The theoretical analysis proves that all closed‐loop signals remain bounded under the proposed output‐feedback ETOC method. Overall, this paper presents a practical and effective ETOC scheme using RL for stochastic nonlinear systems, which has the potential to save communication resources and maintain closed‐loop signal stability. Finally, a simulation example is proposed to validate the presented control algorithm.

Semi-global exponential stability of stochastic nonlinear functional sampling systems by emulation approach

In this paper, the semi-global exponential stability is studied for the stochastic nonlinear functional systems by emulation of sampled-data controller. In consideration of the stochastic factor, a novel definition of the right and upper Dini’s derivative of the constructed functional is given. Based on this novel definition, combining with stochastic analysis techniques and Lyapunov method, some sufficient criteria for the semi-global exponential stability of the stochastic nonlinear functional systems by suitably fast sampling are given. As a special case, a class of stochastic nonlinear functional systems with multiple time delays is studied and two coefficient type theorems that lead to the semi-global exponential stability of the sampling system are derived. Finally, a practical application about parallel active suspension systems with time delay and stochastic disturbance is discussed at length and the corresponding numerical example is given to illustrate the feasibility of the theoretical results.

Stability Analysis of Neutral Fractional Stochastic Differential Equations Driven by Mixed Brownian Motion and Subfractional Brownian Motion With Applications in the I-Cub Robot

Exponential stability is often used to barricade stochastic disturbance in visual trajectory tracking of a robotic system. In this work, a nonlinear mathematical model to deal with the exponential stability of visual trajectory in the I-cub robot is developed. The main contributions of this article are: 1) exponential stability is studied for the first time in the literature for the neutral fractional stochastic differential equations (NFSDEs) driven by mixed Brownian motion (Bm) and subfractional Bm (sub-fBm); 2) existence and stability results are derived based on the Banach contraction principle, semi-group theory, and fractional calculus in stochastic settings; 3) stability results of mixed Bm and sub-fBm are established and applied to avoid dense environment stochastic disturbance in the visual trajectory of the I-cub robot; and 4) stability of sub-fBm is entrusted in the dense environment even in small particles from the shorter length. A weak solution of the proposed result ensures a sufficiently smooth solution of the considered robotic system. The obtained results are new and innovative in the sense that the proposed algorithms have several advantages for gaze shift framed to the I-cub robot, including helping to maintain the fixation of eye movement in the microscopic laboratory. Furthermore, the results are used to enhance the performance of decreasing rendering gaze shift to achieve high-quality visual tracking.

Accelerated recovery of lake macroinvertebrates in the third decade since the reversal of acidification

Chemical reversal from acidification has been progressing in European freshwaters since the late 1980s, responding to successful control of atmospheric pollution by acidifying emissions. However, biological recovery is often delayed after improvements in water composition. We studied macroinvertebrate recovery from acidification in eight glacial lakes in the Bohemian Forest (central Europe) between 1999 and 2019. The chemical composition of these lakes reflects a complex of environmental changes, dominated by a very steep decline in acid deposition and, currently, by elevated nutrient leaching following climate-induced tree dieback within their catchments. Temporal trends in species richness, abundance, species traits and community composition were evaluated with regard to water chemistry, littoral habitat properties and fish colonisation. The results showed accelerated recovery of macroinvertebrates following two decades of gradual improvement in water composition and slowly progressing biological rehabilitation. We observed a significant increase in macroinvertebrate species richness and abundance, coupled with distinct changes in community composition, the extent of changes varying between lakes, reflecting different littoral habitat properties (vegetated vs. stony) and water chemistry. Overall, the communities shifted toward more specialised (grazers, filterers, and phytophilous species) and acid-tolerant taxa at the expense of detritivorous, eurytopic and acid-resistant taxa. Where fish reappeared, open-water taxa declined greatly. Compositional changes were likely driven by the combined effects of water chemistry reversal, rehabilitation of habitat conditions and fish colonisation. Despite favourable trends, communities in recovering lakes still lack several biotic elements, particularly less vagile, acid-sensitive taxa and specialised herbivores known from the regional species pool. It is expected that future progress in lake recovery will be further promoted or inhibited by stochastic colonisation or disturbance events.

Switching threshold‐based event‐triggered adaptive asymptotic tracking control for stochastic nonlinear systems with full‐state constraints

AbstractIn this article, the problem of event‐triggered adaptive asymptotic tracking control (ATC) for stochastic nonlinear systems with unknown control directions (UCDs) and full state constraints is concerned. It must be said that the controller design and system analysis is more complex and difficult since the existence of stochastic disturbances, UCDs and full state constraints simultaneously. By introducing the lower bound of the UCDs into the barrier Lyapunov functions, an event‐triggered adaptive MTN ATC scheme is proposed based on the boundary estimation method and a new event‐triggered control (ETC) strategy, which can achieve satisfactory asymptotic tracking performance and control performance of the system, while reduce the occupation of network resources. The simulation results not only verify the effectiveness of the proposed control scheme, but also present different tracking performances between three ETC strategies for comparison, further confirming the superiority of the proposed ETC strategy in achieving asymptotic tracking performance.