Presence Of Random Disturbances Research Articles

Model-Free Adaptive State Feedback Control for a Class of Nonlinear Systems

This paper investigates state feedback control for a class of discrete-time multiple input and multiple output nonlinear systems from the perspective of model-free adaptive control and state observation. The design of a dynamic state feedback control can be efficiently carried out using dynamic linearization and state observation. The stability of the proposed method is guaranteed by theoretical analysis. Numerical simulation tests and experimentation on a continuous stirred tank reactor are carried out to validate the effectiveness of the proposed approach. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —The growth in the scale of factories and the complexity of associated production processes increases the complexity and time involved in associated mathematical modelling. Data driven approaches to control remove the need to model processes. To the best of the authors’ knowledge, existing approaches to model-free adaptive control (MFAC) of general systems are all based on an input-output control paradigm. These methods thus cannot guarantee the stability of the system state. The purpose of this study is to develop a novel Model-Free Adaptive Control (MFAC) approach to achieve control of the system state. In this paper, the assumptions required to achieve model-free adaptive control by state feedback are presented mathematically. A controller design and the associated stability proof are then presented. Numerical simulation and experimentation is conducted to validate the effectiveness of the proposed approach. In future research, state feedback data control in the presence of random disturbances will be investigated.

Robustness Evaluation of LSTM-based Deep Learning Models for Bitcoin Price Prediction in the Presence of Random Disturbances

As Deep Learning (DL) continues to be widely adopted, the growing field of study on the robustness of DL approaches in finance is gaining steam. This paper investigates the robustness of a Recurrent Neural Network (RNN) with Long Short-Term Memory (LSTM) intended for daily closing price predictions of Bitcoin (BTC). The research entails reproducing and adjusting an LSTM design from previous research, with an emphasis on evaluating the robustness of the network. The network is trained using data that has been disturbed by Gaussian noise to assess robustness, and the effect on predictions made outside of the sample is examined. To examine the impact of adding Gaussian noise layers and noisy dense layers on training accuracy and out-of-sample predictions, further robustness tests are conducted. The results show that the LSTM network has remarkable robustness to random disturbances in the data. Nevertheless, the Root Mean Square Error (RMSE) of the prediction increases with the addition of Gaussian noise and noisy dense layers. When random noise is present in the training data, the Autoregressive Integrated Moving Average (ARIMA) model is more vulnerable to it than the LSTM, according to the robustness of the two models. These findings highlight how robustness DL techniques are overall when compared to more conventional linear methods. However, because these models are black-box, the study highlights the significance of comprehensive testing. Although the robustness of the LSTM is impressive, it is important to understand that each network may behave differently depending on the circumstances.

Fuzzy logic-based synchronization control system of generators under conditions of frequency instability

This article focuses on studying and addressing the issue of synchronizing diesel gas generator units (DGGU) in autonomous electric power system (AEPS) in the presence of significant voltage frequency fluctuations. MATLAB models of AEPS are being developed that will enable the study of generator connection procedures while operating under a full load. Fluctuations in the rotation frequency of a diesel gas unit can be simulated by generating a realistic random procedure and adding this random signal to the control circuit. In the present study, the authors simulated the generator synchronization process in the presence of random disturbances. This simulation results indicated that the presence of random voltage frequency fluctuations and a nonzero response time of the circuit breaker (which connects the generator to the bars of the main distribution board) may violate the synchronization conditions and result in significant current surges and voltage sags at the time of synchronization. In the present work, a block diagram of the generator synchronization system is proposed that uses fuzzy logic to control the synchronization process. Software tools were developed using the methods of conceptual simulation to control the generator synchronization process; these tools represent an automated operator working station.

State estimation and optimal control of an inverted pendulum on a cart system with stochastic approximation approach

&lt;abstract&gt; &lt;p&gt;In this paper, optimal control of an inverted pendulum on a cart system is studied. Since the nonlinear structure of the system is complex, and in the presence of random disturbances, optimization and control of the motion of the system become more challenging. For handling this system, a discrete-time stochastic optimal control problem for the system is described, where the external force is considered as the control input. By defining a loss function, namely, the mean squared errors to be minimized, the stochastic approximation (SA) approach is applied to estimate the state dynamics. In addition, the Hamiltonian function is defined, and the first-order necessary conditions are derived. The gradient of the cost function is determined so that the SA approach is employed to update the control sequences. For illustration, considering the values of the related parameters in the system, the discrete-time stochastic optimal control problem is solved iteratively by using the SA algorithm. The simulation results show that the state estimation and the optimal control law design are well performed with the SA algorithm, and the motion of the inverted pendulum cart is addressed satisfactorily. In conclusion, the efficiency of the SA approach for solving the inverted pendulum on a cart system is verified.&lt;/p&gt; &lt;/abstract&gt;

Optimizing resiliency of train operations in an underground metro: A hybrid discrete-event simulation and response surface methodology

Avoiding the passengers extra waiting time is a vital task for rail planners. The current research focused on minimizing the passenger waiting time on the presence of real frequently random occurred disturbances. Details of the proposed model are on the 1st line of Tehran underground rail rapid transit. All fitness functions are validated using the analysis of variance (ANOVA) by applying the hypothesis testing method. Also, a validated discrete-event computer simulation model is applied to examine the average waiting time per passenger as the key performance measure under different scenarios generated using full factorial design of experiments. The validity of the obtained optimal solution, i.e., train headway times is confirmed at a 95% level of reliability. Also, simulation outcomes indicated that the proposed response surface meta-model could efficiently provide a more reliable train operation plan to ensure a desirable level of system resiliency on the presence of random disturbances. The numerical results indicated that wait time could be reduced by 14.8% for passengers as compared with the baseline train headway plan.

Mathematical Modeling of Working Memory in the Presence of Random Disturbance using Neural Field Equations

In this paper, we describe a neural field model which explains how a population of cortical neurons may encode in its firing pattern simultaneously the nature and time of sequential stimulus events. Moreover, we investigate how noise-induced perturbations may affect the coding process. This is obtained by means of a two-dimensional neural field equation, where one dimension represents the nature of the event (for example, the color of a light signal) and the other represents the moment when the signal has occurred. The additive noise is represented by a Q-Wiener process. Some numerical experiments reported are carried out using a computational algorithm for two-dimensional stochastic neural field equations.

Fixed‐time attitude tracking control for spacecraft based on adding power integrator technique

SummaryIn this article, the fixed‐time attitude tracking problem for rigid spacecraft is investigated based on the adding‐a‐power‐integrator control technique. First, a fixed‐time attitude tracking controller is designed to guarantee fixed‐time convergence of tracking errors. Then, by considering the presence of random disturbance and actuator faults, an adaptive fault‐tolerant attitude tracking controller is designed to guarantee tracking errors converge to a residual set of zero in a fixed time. The complete bounds on settling time are derived independently of initial conditions. The simulation results illustrate the highly precise and robust attitude control performance obtained by using the proposed controllers.

Numerical solution of the neural field equation in the presence of random disturbance

This paper aims at presenting an efficient and accurate numerical method for treating both deterministic- and stochastic-type neural field equations (NFEs) in the presence of external stimuli input (or without it). The devised numerical integration means belongs to the class of Galerkin-type spectral approximations. The particular effort is focused on an efficient practical implementation of the solution technique because of the partial integro-differential fashion of the NFEs in use, which are to be integrated, numerically. Our method is implemented in Matlab. Its practical performance and efficiency are investigated on three variants of an NFE model with external stimuli inputs. We study both the deterministic case of the mentioned model and its stochastic counterpart to observe important differences in the solution behavior. First, we observe only stable one-bump solutions in the deterministic neural field scenario, which, in general, will be preserved in our stochastic NFE scenario if the level of random disturbance is sufficiently small. Second, if the area of the external stimuli is large enough and exceeds the size of the bump, considerably, the stochastic neural field solution’s behavior may change dramatically and expose also two- and three-bump patterns. In addition, we show that strong random disturbances, which may occur in neural fields, fully alter the behavior of the deterministic NFE solution and allow for multi-bump (and even periodic-type) solutions to appear in all variants of the stochastic NFE model studied in this paper.

Vacuum pressure swing adsorption system for N2/CO2 separation in consideration of unstable feed concentration

In this study, an efficient PID control system has been designed for a vacuum pressure swing adsorption (VPSA) process which used silica gel to capture CO2 from dry flue gas. Changes of CO2 composition in feed gas are set as disturbances and vary from 12.0 to 15.0% to make simulation work more closely to reality. Meanwhile, adsorption step time duration was set to change consistently according to the feedback of CO2 purity in product. PID control strategy built in software gPROMS is employed in this paper. The competence of the control system is firstly analyzed by a transient impulse of CO2 content in feed gas (15.0% dropped to 12.0%). Then random pulse is added to test the ability of the control system to reject the unknown disturbances and track the set point. Detailed changes in bed under open and closed-loop are listed and made comparisons. Results demonstrate that the model shows an enhanced performance in the presence of random disturbances under closed-loop control compared with the open-loop operation. And this proves that closed-loop feedback PID control can be used to improve the CO2 capture of VPSA process operations.

Design of an Online Nonlinear Optimal Tracking Control Method for Unmanned Ground Systems

A nonlinear tracking error model for unmanned ground systems (UGS) was developed, and the constraints and objective function were established; the tracking control problem for UGS was converted to a continuous nonlinear optimal control problem. In order to solve the complex problem, a symplectic pseudospectral method based on the third kind of generation function is proposed. This approach largely reduces the sensitivity of the initial guess for costate variables, and the characteristics of the original system are not lost after discretization, which is not the case for other methods. Subsequently, by considering the influences of random disturbances in the environment, the symplectic pseudospectral method and the receding horizon control principle are combined to solve the nonlinear tracking problem; this method overcomes the problem that a nonlinear optimal control method is difficult to apply for online tracking. Finally, the proposed method is verified using simulation experiments, and it is demonstrated that the proposed method achieves online and real-time tracking control of a standard trajectory in the presence of random disturbances and it provides great maneuverability and feasibility for practical applications.

Robust input-to-state stability of neural networks with Markovian switching in presence of random disturbances or time delays

This paper establishes input-to-state stability (ISS) and robust ISS of neural networks with Markovian switching (NNwMS). The M matrix algebraic condition for stochastic NNwMS is given; the result is then extended to stochastic time varying delays NNwMS. From the ISS condition of stochastic delayed NNwMS, we get robust ISS of NNwMS in two cases: delay perturbation in diffusion and delay perturbation in drift, respectively. These ISS criteria are readily to be checked only from the parameters of the NNwMS and also ensure exponential stability without input term. The results presented here include neural networks without Markovian switching as special cases. Two numerical examples are given to show the effectiveness of theoretical criteria.

Stabilization of stochastic operating modes in the flow reactor

A conceptual multistable model of the flow reactor proposed by Volter and Salnikov is studied in the presence of random disturbances. A stochastic excitability of this system, even in a zone of stable equilibria, is explained by the high stochastic sensitivity. Such high stochastic sensitivity of the equilibrium can be a basic reason of the noise-induced destruction of the operating mode. For the stabilization of the stochastic flow reactor, a theory of the synthesis of the assigned low stochastic sensitivity is suggested. It is shown how to use this control approach and construct an appropriate regulator which suppresses unwanted large-amplitude stochastic oscillations and provide a proper operation of the flow reactor.

Robust Takagi-Sugeno fuzzy control for fractional order hydro-turbine governing system

A robust fuzzy control method for fractional order hydro-turbine governing system (FOHGS) in the presence of random disturbances is investigated in this paper. Firstly, the mathematical model of FOHGS is introduced, and based on Takagi-Sugeno (T-S) fuzzy rules, the generalized T-S fuzzy model of FOHGS is presented. Secondly, based on fractional order Lyapunov stability theory, a novel T-S fuzzy control method is designed for the stability control of FOHGS. Thirdly, the relatively loose sufficient stability condition is acquired, which could be transformed into a group of linear matrix inequalities (LMIs) via Schur complement as well as the strict mathematical derivation is given. Furthermore, the control method could resist random disturbances, which shows the good robustness. Simulation results indicate the designed fractional order T-S fuzzy control scheme works well compared with the existing method.

Method for evaluating the landing aircraft sequence under disturbed conditions with the use of Petri nets

ABSTRACTOne of the important tasks that air traffic management services are faced with today is the task of maximising airport capacity. This can be achieved at the tactical level through proper organisation of air traffic around an airport. In recent years, many methods and algorithms for scheduling aircraft landings have been developed; they take into account various optimisation goals. The aim of this paper was to create a method that would allow one to evaluate landing aircraft sequences resulting from these control algorithms, especially in the presence of random disturbances. This method involves modelling the landing aircraft sequence by using Petri nets. The model and the computer tool that have been developed make it possible to take into account different kinds of disturbances and examine the effectiveness of various control strategies under these conditions. This paper presents two experiments that test disturbances with different characteristics and of different intensities. It has been shown that small but more frequent disturbances lead to the worsening of evaluation scores for a given sequence to a lesser extent than rare but larger disturbances. This is particularly important for control algorithms in which the focus is on high aircraft density. If the type of particular disturbances is properly assessed, then it will be possible to assist the decision-maker (air traffic controller) by providing him/her with quantitative evaluations of possible solutions.

Predicting the Formation of Electrodeposition Patterns Caused By Interfacial Instabilities

Electrodeposition is a common process via which metal ions are reduced at a cathode as a thin film. However, the deposited film on the cathode often exhibits a unique interfacial pattern that is dependent on the applied voltage, the concentration, and the distance between electrodes. Although these morphological instabilities have been observed in the past, it still remains difficult to predict the interfacial pattern formed during electrodeposition. These morphological patterns arise in an electrolytic cell because the reduction reaction runs faster than oxidation. Therefore small crests or troughs on the surface of the electrode act as a disturbance that alters the rate and uniformity of metal deposition at these sites, initiating the growth of an interfacial pattern. We first develop a model that describes the electrodeposition instabilities that lead to these interfacial patterns. Transport and kinetic reactions described by Butler-Volmer equations are used to calculate and predict the growth characteristics of the film. It is found that the patterns of the film are periodic and harmonic waves composed of different wavelengths. While each wavelength corresponds to a specific growth rate, many wavelengths have similar growth rates. Changes to surface tension and ionic diffusion can yield narrower distributions of the wavelengths observed. A simple Cu-Cu electrodeposition system is then investigated to observe the instabilities. The pattern on the cathode is observed as a function of deposition time in the presence of random disturbances. By image analysis, the wavelength distribution of the interfacial pattern is detected, which is consistent with the developed model. Due to its inherent instability, the harmonic waves of the pattern are not identical every time under the same experiment condition. Nevertheless, the wavelengths observed during deposition are still located within the predicted range. The results demonstrate that the wavelengths of the pattern are predictable but difficult to control because of inherent disturbances on the surface. Further, the growth of the patterns creates localized flow convection that leads to the formation of dendritic patterns. Now that the model can predict these patterns, the goal will be to find experimental conditions that can either minimize pattern formation or generate a single wavelength.

Stabilization conditions for fuzzy control of uncertain fractional order non‐linear systems with random disturbances

A novel fractional order Takagi–Sugeno (T–S) fuzzy control method for a class of fractional order non-linear systems is proposed in this study. On the basis of the fractional order interval theory, the generalised T–S fuzzy model for a class of uncertain fractional order non-linear systems is presented. By using fractional order Lyapunov stability theorem, the more relaxed and practical sufficient stability conditions which are presented as a new set of linear matrix inequalities are put forward, which are guaranteed by rigorous mathematical derivation. The proposed control scheme is developed for fractional order non-linear systems stabilisation in the presence of random disturbances. Typical instances including the fractional order three-dimensional (3D) non-linear system and the fractional order 4D non-linear Lorenz hyperchaos are implemented. Simulation results indicate the designed fractional order T–S fuzzy control scheme works well compared with the existing method.

Economic MPC of deep cone thickeners in coal beneficiation

The thickener is an important operating unit in a coal handling and preparation plant (CHPP). The optimal control and operation of the thickener is critical for the efficiency and economics of a CHPP. In this work, we apply a computationally efficient economic model predictive controller (EMPC) to a deep cone thickener and compare its performance to a proportional‐integral controller and a regular model predictive controller (MPC). Based on a detailed model of the deep cone thickener that is appropriate for controller design purpose, the three control designs are compared on different aspects, including average water recovery rate and controller execution time, via extensive simulations. The robustness of the EMPC is also investigated in the presence of random disturbances in feed flow rate. The results demonstrate that the EMPC has the potential to significantly improve water recovery rate compared to the proportional‐integral control and the regular MPC.

Diagnosis of Oscillations Between Controller Tuning and Harmonic External Disturbances

This paper studies the properties of linear systems described by discrete-time stochastic dynamic models and the conditions that yield an oscillatory response. Feedback loops that are oscillatory due to the controller tuning fall into this category of systems. Therefore, analyzing linear systems with oscillatory responses reveals the properties of self-oscillatory feedback loops. It is shown that in the presence of random disturbances, the oscillation due to the controller has a varying amplitude and phase even though the oscillation frequency is constant. The autocorrelation function of these types of oscillatory signals has a decay ratio and does not have a deterministic amplitude of oscillation. These properties can be utilized in distinguishing between the controller induced and externally introduced oscillations. Two hypothesis tests are developed to facilitate a solution for the above stated oscillation diagnosis problem.

Triple grouping and period-three oscillations in minority-game dynamics.

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Adaptive management of environmental acidity

This paper proposes a new approach to the determination of doses of some meliorant for stabilizing the environmental acidity in an agricultural field through the application of optimal control methods in the presence of random disturbances. The acidity dynamics process is considered as a partially observable Markov process, and the Bayesian approach is applied.