Uncertain System Model Research Articles

On Atangana–Baleanu fractional granular calculus and its applications to fuzzy economic models in market equilibrium

Based on relative-distance-measure fuzzy interval arithmetic (RDM-FIA), this paper presents several new concepts for fuzzy functions in fractional granular calculus with Mittag-Leffler (ML) kernels, such as Atangana–Baleanu (AB) fractional granular integrals, AB fractional granular derivatives, and AB Caputo fractional granular derivatives. Then, we present formulas for the fuzzy granular Laplace transform on Caputo fractional granular derivatives, AB fractional granular derivatives, and AB Caputo fractional granular derivatives. In addition to the relationship between AB fractional granular derivatives and AB Caputo fractional granular derivatives established using the granular Laplace transform, new fractional Newton–Leibniz-type formulas for both derivatives and integrals are proved. As applications, we obtain the fundamental solutions for the fuzzy economic models in the framework of Caputo fractional granular derivatives and AB Caputo fractional granular derivatives by utilizing the fuzzy granular Laplace transform. Several graphical explanations are given to show the dynamic behavior of the fundamental solutions. Moreover, we illustrate the advantages of using RDM-FIA to study the mathematical models of uncertain dynamical systems. The results of this study are illustrated using several numerical examples.

Distributed auto disturbances rejection resilient control of permanent magnetic maglev trains based on the optimized deep deterministic policy gradient algorithm

AbstractDue to time‐varying external disturbances and uncertain system models, distributed cooperative controllers with poor adaptability are unable to meet the cooperative control requirements of multiple permanent magnetic maglev trains in virtual coupling mode. In this work, a new effective distributed auto disturbance rejection resilient controller based on the optimized deep deterministic policy gradient algorithm (DDPG) is proposed. The DDPG algorithm is used to improve the adaptability of the controller against the time‐varying disturbances. An adaptive particle swarm optimization method (APSO) is also proposed to optimize the hyperparameters of DDPG in the search space. The simulation results show that, compared to the particle swarm optimization (PSO)‐actor‐critic (AC), PSO‐policy gradient (PG), and PSO‐DDPG algorithms, the proposed APSO‐DDPG algorithm performs better during training and verification. The proposed method achieves adaptive online adjustment of the controller parameters effectively and greatly improves the stability of cooperative control.

Neuro-adaptive non-singular terminal sliding mode control for distributed fixed-time synchronization of higher-order uncertain multi-agent nonlinear systems

This paper presents a novel design for a distributed fixed-time synchronization controller based on neuro-adaptive non-singular terminal sliding mode control for higher-order multi-agent nonlinear systems. In this study, a distributed control strategy is employed in which networked nonlinear systems, referred to as nodes, communicate through a predefined network topology. Within this framework, a leader-follower configuration is adopted, designating one node as the leader and the others as follower agents. Notably, the dynamics of the agents are assumed to be unknown, leading to the development of a generalized uncertain higher-order nonlinear dynamical system model that accounts for the disturbed dynamics of all agents, including the matched bounded uncertainty with an upper algebraic bound. The control design leverages radial basis function neural networks for approximation, effectively addressing unknown nonlinear terms, such as drift terms and input channels. Importantly, the proposed technique successfully mitigated matched-type uncertainty, resulting in rapid sliding-mode enforcement with reduced chattering and stress. This innovative approach establishes fixed-time synchronization by creating a sliding mode with respect to the sliding surface of networked synchronization mismatches. To underscore the effectiveness of this approach, a simulation example that vividly illustrates its captivating properties and contributions is presented.

Improving Tracking Accuracy for Repetitive Learning Systems by High-Order Extended State Observers.

For systems executing repetitive tasks, how to realize the perfect tracking objective is generally desirable, for which an effective method called "iterative learning control (ILC)" emerges thanks to the incorporation of the repetitive execution of systems into an ILC design framework. However, nonrepetitive (iteration-varying) uncertainties are often inevitable in practice and greatly degrade the tracking accuracy of ILC, which has not been treated well, regardless of considerable robust ILC results. This motivates this article to develop a new design method to improve the tracking accuracy of ILC by adopting a high-order extended state observer (ESO) to address ill effects of nonrepetitive uncertainties and uncertain system models. With the designed ESO-based ILC, the robust tracking of any desired trajectory can be achieved such that the tracking error can be decreased to vary in a small bound depending continuously on the bounds of high-order variations of nonrepetitive uncertainties with respect to the iteration. It makes the tracking accuracy of ILC possible to be regulated through the design of ESO, of which the validity is demonstrated by including a simulation example.

Sampled-Data Output Feedback Control for Nonlinear Uncertain Systems Using Predictor-Based Continuous-Discrete Observer.

In this article, we investigate the problem of sampled-data robust output feedback control for a class of nonlinear uncertain systems with time-varying disturbance and measurement delay based on continuous-discrete observer. An augmented system that includes the nonlinear uncertain system and disturbance model is first found, and by using the delayed sampled-data output, we then propose a novel predictor-based continuous-discrete observer to estimate the unknown state and disturbance information. After that, in order to attenuate the undesirable influences of nonlinear uncertainties and disturbance, a sampled-data robust output feedback controller is developed based on disturbance/uncertainty estimation and attenuation technique. It shows that under the proposed control method, the states of overall hybrid nonlinear system can converge to a bounded region centered at the origin. The main benefit of the proposed control method is that in the presence of measurement delay, the influences of time-varying disturbance and nonlinear uncertainties can be effectively attenuated with the help of feedback domination method and prediction technique. Finally, the effectiveness of the proposed control method is demonstrated via the simulation results of a numerical example and a practical example.

Modeling and Verification of Uncertain Cyber-Physical System Based on Decision Processes

Currently, there is uncertainty in the modeling techniques of cyber-physical systems (CPS) when faced with the multiple possibilities and distributions of complex system behavior. This uncertainty leads to the system’s inability to handle uncertain data correctly, resulting in lower reliability of the system model. Additionally, existing technologies struggle to verify the activity and safety of CPS after modeling, lacking a dynamic verification and analysis approach for uncertain CPS properties.This paper introduces a generalized possibility decision process as a system model. Firstly, the syntax and semantics of generalized possibility temporal logic with decision processes are defined. Uncertain CPS is extended by modeling it based on time-based differential equations and uncertainty hybrid time automaton. After that, model checking is performed on the properties of activity and safety using fuzzy linear time properties. Finally, a cold–hot hybrid constant-temperature system model is used for simulation experiments. By combining theory and experiments, this paper provides a new approach to the verification of uncertain CPS, effectively addressing the state explosion problem. It plays a crucial role in the design of uncertain CPS and offers a key solution for model checking in the presence of uncertainty.

Reliability Optimization of Uncertain Random Systems Combined With Burn-In and Preventive Maintenance

It is well-known that uncertain random systems suffered from a competing failure process have been applied in industrial applications. Extending previous studies, we optimize system cost combined with burn-in and preventive maintenance strategies. A system in burn-in process is only subject to uncertain continuous stationary degradation process while it experiences competitive degradation and shock processes simultaneously in the period of operation. The dependence assumes that shocks can accelerate the degradation by uncertain additional degradation shifts. A reliability optimization model for uncertain random systems is proposed where the reliability index is defined as a chance measure, and the optimal burn-in parameters and maintenance observation time are derived by the genetic algorithm. Finally, we conclude with a numerical example to illustrate the application of burn-in and maintenance methods.

Robust Model Predictive Control for Two-DOF Flexible-Joint Manipulator System

This paper presents a practical study on how to improve the ℋ∞ performance and meet the input–output constraints of the two-degrees-of-freedom (DOF) flexible-joint manipulator system (FJMS) with parameter uncertainties and external disturbances. For this reason, a robust constrained moving-horizon ℋ∞ controller is designed to improve the system ℋ∞ performance while still satisfying the input–output constraints of the uncertain system. First, the uncertain controlled system model of the two-DOF FJMS is established via the Lagrange equation method, Spong’s assumption, and the linear fractional transformation (LFT) technique. Then, the control requirements and input–output constraints of the uncertain system are transformed into the linear matrix inequality (LMI) via the theory of ℋ∞ control and the full-block multiplier technique. Next, the LMI optimization problem refreshed by the current state is addressed at each sample moment with the idea of the moving-horizon control of the model predictive control (MPC), and the calculated gain is implemented to the nonlinear closed-loop system under the state feedback structure. The validity and feasibility of the designed control scheme is finally verified via the results of simulation experiments.

Dynamic Event-triggered Control for Nonlinear PDE System with Actuator Dead-zone

A dynamic event-triggered network control scheme is proposed for a class of distributed parameter systems with time delay and nonlinearity. The security control of the PDE system under DOS attack based on dynamic event-triggered is studied. A dynamic event-triggered scheme is adopted to reduce the communication burden, that is, the sampling data will be sent only when the original trigger condition is violated. At the same time, a new model including denial of service attack (DOS) is established to describe the random network attack. When a hacker launches a DoS attack, it prevents the sampling data from reaching the destination by interfering with the network channel. DOS attacks follow no specific pattern and exhibit non-periodic behavior or irregular probability distribution. A mathematical model of a state-dependent uncertain system with an event-triggered scheme was established to study denial of service attacks. By using the Lyapunov-Krasocskii stability theory and linear matrix inequality tools, sufficient conditions were derived to ensure the index mean square stability of the state-dependent uncertain system. Based on this, sufficient conditions for the asymptotic stability of the closed-loop network control system and the expected performance index of the system were obtained. Numerical examples verified the feasibility of the method, and controller design validated the applicability of the theoretical results.

Vision-based particle filtering for quad-copter attitude estimation using multirate delayed measurements.

In this paper, the problem of attitude estimation of a quad-copter system equipped with a multi-rate camera and gyroscope sensors is addressed through extension of a sampling importance re-sampling (SIR) particle filter (PF). Attitude measurement sensors, such as cameras, usually suffer from a slow sampling rate and processing time delay compared to inertial sensors, such as gyroscopes. A discretized attitude kinematics in Euler angles is employed where the gyroscope noisy measurements are considered the model input, leading to a stochastic uncertain system model. Then, a multi-rate delayed PF is proposed so that when no camera measurement is available, the sampling part is performed only. In this case, the delayed camera measurements are used for weight computation and re-sampling. Finally, the efficiency of the proposed method is demonstrated through both numerical simulation and experimental work on the DJI Tello quad-copter system. The images captured by the camera are processed using the ORB feature extraction method and the homography method in Python-OpenCV, which is used to calculate the rotation matrix from the Tello's image frames.

Optimized reduced order ARX modelling and robust control for multivariable uncertain systems

This paper deals with modelling and robust control of linear multivariable uncertain systems based on the new linear multivariable ARX (Auto-Regressive with eXogenous input)-Laguerre model and the loop-shaping design procedure with the relative gain array theory. In fact, to guarantee significant parameter number reduction of the multivariable ARX-Laguerre model compared with the classic multivariable ARX model, we propose the optimization of the Laguerre poles of the model using the genetic algorithm where the Fourier coefficients are identified using the recursive least square method. Later, the optimized multivariable ARX-Laguerre model is exploited to propose a robust control algorithm for linear multivariable uncertain systems. Indeed, we propose to combine the loop-shaping design procedure approach and the relative gain array theory to develop a simplified final robust controller guaranteeing reference tracking and robust stability against parametric uncertainties. This proposition aims for the simplification of the control’s scheme by adjusting the weighting matrix and the final robust controller calculated from the loop-shaping design procedure for a simpler and more experimentally applicable control scheme. The identification of Fourier coefficients and Laguerre poles as well as the robust multivariable control algorithm are experimentally validated on a laboratory coupled two-tank system showing good results in terms of modelling and attending desired control performances.

Neural message-passing for objective-based uncertainty quantification and optimal experimental design

Various real-world scientific applications involve the mathematical modeling of complex uncertain systems with numerous unknown parameters. Accurate parameter estimation is often practically infeasible in such systems, as the available training data may be insufficient and the cost of acquiring additional data may be high. In such cases, based on a Bayesian paradigm, we can design robust operators retaining the best overall performance across all possible models and design optimal experiments that can effectively reduce uncertainty to enhance the performance of such operators maximally. While objective-based uncertainty quantification (objective-UQ) based on MOCU (mean objective cost of uncertainty) provides an effective means for quantifying uncertainty in complex systems, the high computational cost of estimating MOCU has been a challenge in applying it to real-world scientific/engineering problems. In this work, we propose a novel scheme to reduce the computational cost for objective-UQ via MOCU based on a data-driven approach. We adopt a neural message-passing model for surrogate modeling, incorporating a novel axiomatic constraint loss that penalizes an increase in the estimated system uncertainty. As an illustrative example, we consider the optimal experimental design (OED) problem for uncertain Kuramoto models, where the goal is to predict the experiments that can most effectively enhance robust synchronization performance through uncertainty reduction. We show that our proposed approach can accelerate MOCU-based OED by four to five orders of magnitude, without any visible performance loss compared to the state-of-the-art. The proposed approach applies to general OED tasks, beyond the Kuramoto model.

Hurwicz criterion based optimal control model for uncertain descriptor systems with an application to industrial management

In this work, optimal control models subject to discrete and continuous uncertain descriptor systems are both investigated under Hurwicz criterion. At first, by employing dynamic programming method, a recurrence equation is obtained to simplify the discrete optimal control model, and a bang-bang control problem is settled according to this equation. Then, for the continuous optimal control model, an equation of optimality is proposed and testified with the help of uncertainty theory and the principle of optimality, revealing the internal connection between optimal control and optimal value. Finally, a numerical example and an industrial management model are provided to illustrate the validness of above results.

Improved adaptive backstepping control of MPCVD reactor systems with non-parametric uncertainties

This paper presents an improved adaptive backstepping control strategy for a microwave plasma chemical vapor deposition (MPCVD) reactor system. To describe the dynamics of the reactor system, a non-parametric uncertain nonlinear system model with unknown control direction functions is built up. In order to deal with the non-parametric uncertainties of the system, direct adaptive laws are primarily proposed to estimate such uncertainties, which is superior to traditional adaptive backstepping that can only address parametric uncertainties. Moreover, an equivalence transformation of the system is given to address the system unknown control direction functions. By using Lyapunov stability criterion, it can be proved that the target signals (desired temperature, desired pressure, and desired gas flow rates) are tracked by the reactor system outputs with small errors. Finally, simulation results are given to demonstrate the effectiveness of the proposed control method.

Asymmetric constrained control scheme design with discrete output feedback in unknown robot–environment interaction system

AbstractIn this paper, an overall structure with the asymmetric constrained controller is constructed for human–robot interaction in uncertain environments. The control structure consists of two decoupling loops. In the outer loop, a discrete output feedback adaptive dynamics programing (OPFB ADP) algorithm is proposed to deal with the problems of unknown environment dynamic and unobservable environment position. Besides, a discount factor is added to the discrete OPFB ADP algorithm to improve the convergence speed. In the inner loop, a constrained controller is developed on the basis of asymmetric barrier Lyapunov function, and a neural network method is applied to approximate the dynamic characteristics of the uncertain system model. By utilizing this controller, the robot can track the prescribed trajectory precisely within a security boundary. Simulation and experimental results demonstrate the effectiveness of the proposed controller.

Discrete-time contraction-based control of nonlinear systems with parametric uncertainties using neural networks

In response to the continuously changing feedstock supply and market demand for products with different specifications, industrial processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve their economy, in contrast to traditional process operations around predetermined equilibriums. In this paper, a novel control approach is developed for nonlinear chemical processes to achieve time-varying reference tracking, by combining the universal approximation characteristics of neural networks with the rigor of discrete-time contraction analysis and control. This is a robust approach that can deal with bounded parametric uncertainties in the process model, which are commonly encountered in industrial processes. A new synthesis approach is developed that involves training a neural network representation of a contraction metric and differential feedback gain for a full range of parametric uncertainty. This network is then embedded in a contraction-based control structure. A separate neural network is also incorporated into the control-loop to perform online identification of uncertain system model parameters. The resulting control scheme is capable of achieving efficient offset-free tracking of time-varying references under the parametric uncertainty, without the need for controller redesign as the reference changes. Process stability is also ensured during online simultaneous learning and control. Simulation examples are provided to illustrate the approach.

Reliability modeling of uncertain random fractional differential systems with competitive failures

Typical degradation-shock failure processes have been widely investigated in current researches, and the failures caused by their dependence are described as competitive failure processes. This paper explores competitive failure modes for uncertain random fractional systems involving degradation and shock processes. We develop a wear degradation model explicitly by employing uncertain fractional differential equations in order to demonstrate the potential heredity and memorability of a system. External shocks are then considered to follow a Poisson process. Based on the classification of shock types, three definitions of reliability index for competitive failures are presented. The reliability index formulas are derived for systems with extreme shock, cumulative shock, and δ shock using chance measures. Finally, we introduce a numerical example where the results of the reliability analysis confirm the validity of proposed reliability evaluation methods.

Bounded error modeling using interval neural networks with parameter optimization

Aiming at the issue of interval modeling of uncertain systems, this article proposes a data-based interval neural network (INN) optimization modeling method that combines interval analysis with a neural network and particle swarm optimization (PSO) algorithm, adopts an INN model with interval weights and interval thresholds, and constructs an interval multiobjective PSO (IMOPSO) algorithm to evolve the network, thereby modeling an uncertain system under an unknown-but-bounded error (UBBE) condition. Considering the cases of known and unknown error bounds in UBBE, two optimization objectives, i.e., interval coverage and interval width, are constructed to optimize the parameters of INN, aiming to improve the accuracy and reliability of prediction. The proposed method effectively solves many constraints such as the model structure demanded and error bounds known in UBBE modeling, and provides a new method of data-based interval system modeling. The method was applied to model linear and nonlinear systems, and simulation results showed that the established INN models have good prediction effects and dynamic characteristics, which demonstrate the effectiveness of the method.

Optimal Control of Background-Based Uncertain Systems with Applications in DC Pension Plan.

In this paper, we propose a new optimal control model for uncertain systems with jump. In the model, the background-state variables are incorporated, where the background-state variables are governed by an uncertain differential equation. Meanwhile, the state variables are governed by another uncertain differential equation with jump, in which both the background-state variables and the control variables are involved. Under the optimistic value criterion, using uncertain dynamic programming method, we establish the principle and the equation of optimality. As an application, the optimal investment strategy and optimal payment rate for DC pension plans are given, where the corresponding background-state variables represent the salary process. This application in DC pension plans illustrates the effectiveness of the proposed model.

Optimization of Grid-Connected Photovoltaic Power Generation Technology Based on Nonlinear Back-Stepping Controller

To address the issue of energy scarcity and to use solar photovoltaic energy as a renewable source, a three-phase grid-connected photovoltaic inverter system with uncertain system model parameters is investigated, which converts DC power into AC power, feeds it into the grid, and maintains the grid-connected part’s quality. An enhanced back-stepping approach is proposed to explore the control strategy of three-phase solar grid-connected inverter, which includes adaptive control, dissipative theory, sliding mode control, and rapid terminal sliding mode control, respectively. It is verified that the system is subjected to external interference F = 5 during 0.5 s–0.8 s. As per the simulation results, the improved adaptive terminal sliding mode control method can suppress the interference to a certain extent and has strong robustness to the external interference. When compared with the adaptive sliding mode control approach, the anti-interference ability is better, and the system stability is improved. Then, to improve the above approach, a high speed terminal sliding mode control method is proposed, which can swiftly converge in finite time and the estimated value of uncertain parameters is closer to the actual value, thereby boosting the system’s robustness.