Nonlinear Uncertainties Research Articles

Adaptive finite-time prescribed performance tracking control for hydraulic servo systems with friction compensation

Hydraulic systems present numerous challenges in the development of high-performance tracking controllers due to their highly nonlinear characteristics and heavy modeling uncertainties. Addressing this issue, this paper presents a friction compensation-based finite-time tracking control strategy with prescribed performance constraints. The system model is first derived, taking into consideration the nonlinear behaviors and potential uncertainties encountered in practical scenarios. Then, an adaptive finite-time prescribed performance controller is synthesized based on the backstepping framework. A novel form of finite-time performance function is introduced to constrain the tracking error, which provides the closed-loop system with a less complex guarantee of finite-time convergence and can also deliver the required transient performance and steady-state accuracy. Additionally, given the impact of uncertainty terms and the difficulty in obtaining the virtual command derivative, we employ neural networks (NNs) to estimate unknown dynamics and introduce command filters to acquire the intermediate signals, simplifying the backstepping control design process. Theoretical analysis indicates that the proposed control strategy can achieve the desired tracking performance and ensure the stability of the entire closed-loop system. Comparative numerical simulations are presented to confirm the usefulness of the suggested approach.

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.

Adaptive fractional backstepping intelligent controller for maximum power extraction of a wind turbine system

Controlling wind power plants is a challenging issue, however. This is due to its highly nonlinear dynamics, unknown disturbances, parameter uncertainties, and quick variations in the wind speed profiles. So robust controllers are needed to overcome these challenges. This paper suggests two novel control approaches for doubly fed induction generator-based wind turbines. Its key objective is to regulate the generator speed and rotor currents. A radial basis function (RBF) neural network disturbance observer based fractional order backstepping sliding mode control (SMC) is presented to control the rotor currents. This RBF neural network-based disturbance observer estimates unknown disturbances. Also, a new adaptive fractional order terminal SMC is suggested for the control of the generator speed. This robust chattering-free controller that does not require any information about the bound of uncertainties fractional calculus is adopted in the SMC design to eliminate undesired chattering phenomena. The controller parameters are optimally tuned utilizing the ant colony optimization algorithm. The proposed approach was validated using a simulation study entailing various conditions. Its performance was also compared to that of the conventional backstepping and conventional backstepping sliding mode controller. The simulations results verified the approach's ability to maximize power extraction from the wind and properly regulate the rotor currents. The proposed method has about 20% less tracking error than the other two methods, which means 20% higher efficiency.

Finite-time adaptive super-twisting sliding mode control for autonomous robotic manipulators with actuator faults

This paper proposes a new adaptive super-twisting global integral terminal sliding mode control algorithm for the trajectory tracking of autonomous robotic manipulators with uncertain parameters, unknown disturbances, and actuator faults. Firstly, a novel global integral terminal sliding mode surface is designed to ensure that the tracking errors of autonomous robotic manipulators converge to zero in finite time and the global robustness of the system is also enhanced. Then a new adaptive method is devised to deal with the adverse effect of nonlinear uncertainty. To suppress the chattering phenomenon, the adaptive super-twisting algorithm is used in this paper, which can ensure that the control torque is a continuous input signal. Based on the adaptive mechanism, the adaptive super-twisting global integral terminal sliding mode controller is developed to provide superior control performance. The stability analysis of the system is demonstrated by using the Lyapunov method. Ultimately, the effectiveness of the control scheme is confirmed by a simulation study.

High precision control of direct-drive permanent magnet linear motor with adaptive friction compensation

To improve the control precision and stability of Direct-Drive Permanent Magnet Linear Motor (DPMLM) with frictional nonlinearity and uncertain disturbances at a low speed, an adaptive robust integral sign error control algorithm based on friction compensation of dual nonlinear observer is proposed in this study. An improved LuGre friction model is established to describe the friction phenomena of the system. The dual nonlinear observer is designed to observe the internal frictional state of the model. A parameter adaptive law is designed to perform parameter estimation of structured uncertainty. Robust integral of the sign of the error (RISE) term is designed to overcome the frictional nonlinear disturbances. The friction nonlinearity and parameter uncertainty are compensated by feedforward compensation. The bounded stability of the proposed controller is proved by Lyapunov stability theory. As suggested by the experimental results, RMSE index decreased by 10.8% and the control precision was improved effectively by the proposed control algorithm at a low speed.

Self-optimization wavelet-learning method for predicting nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations

In the present work, we propose a self-optimization wavelet-learning method (SO-W-LM) with high accuracy and efficiency to compute the equivalent nonlinear thermal conductivity of highly heterogeneous materials with randomly hierarchical configurations. The randomly structural heterogeneity, temperature-dependent nonlinearity and material property uncertainty of heterogeneous materials are considered within the proposed self-optimization wavelet-learning framework. Firstly, meso- and micro-structural modeling of random heterogeneous materials are achieved by the proposed computer representation method, whose simulated hierarchical configurations have relatively high volume ratio of material inclusions. Moreover, temperature-dependent nonlinearity and material property uncertainties of random heterogeneous materials are modeled by a polynomial nonlinear model and Weibull probabilistic model, which can closely resemble actual material properties of heterogeneous materials. Secondly, an innovative stochastic three-scale homogenized method (STSHM) is developed to compute the macroscopic nonlinear thermal conductivity of random heterogeneous materials. Background meshing and filling techniques are devised to extract geometry and material features of random heterogeneous materials for establishing material databases. Thirdly, high-dimensional and highly nonlinear material features of material databases are preprocessed and reduced by wavelet decomposition technique. The neural networks are further employed to excavate the predictive models from dimension-reduced low-dimensional data. At the same time, advanced intelligent optimization algorithms are utilized to self-search the optimal network structure and learning rate for obtaining the optimal predictive models. Finally, the computational accuracy and efficiency of the presented approach are validated via various numerical experiments on realistic random composites.

Adaptive robust output tracking of uncertain strict-feedback nonlinear systems with full state constraints via control schemes with simple structure

In this paper, the problem of output tracking control is considered for a class of uncertain strict-feedback nonlinear systems with virtual control coefficients and full state constraints. It is assumed only that the nonlinear uncertainties of the systems are some smooth functions enough to guarantee the existence of solutions to the differential equations which describe uncertain systems, and that the virtual control coefficients are unknown. Based on backstepping algorithm, by combining the barrier Lyapunov function with an integral inequality reported in the current control literature, a design method is presented whereby a simple adaptive robust output tracking control scheme can be synthesised. The presented design method can evade the repeated differentiation problem appearing in using backstepping algorithm, and need not know all the nonlinear upper bounds of uncertainties, which are repeatedly employed at each step of backstepping procedure. It is also shown that the output tracking error of the uncertain nonlinear systems with both unknown virtual control coefficients and full state constraints can converge uniformly exponentially towards a ball which can be as small as desired. Finally, a numerical example is given, and the corresponding simulations are also implemented to demonstrate the simplicity of the proposed method and the validity of the theoretical results.

Model-based neuroadaptive event-triggered tracking consensus control for nonlinear multiagent systems with input delay

In this article, a neuroadaptive event-triggered control methodology is proposed to tackle the leader-following tracking consensus issue of uncertain nonlinear multiagent systems (MASs) with input delay and external disturbances. The proposed approach incorporates radial bias function neural networks (RBF NNs) and the integral compensation technique, effectively addressing the issues of nonlinear uncertainty and input delay, respectively. For the sake of reducing the transmission of information, we adopt the strategy that the neural network (NN) weight update law is only changed at the event-triggered instant, and a novel adaptive model and related controller are constructed. Simultaneously, this paper establishes an impulsive dynamic system to analyze the stability of the closed-loop system by extending the Lyapunov theorem to continuous and reset dynamics. Sufficient conditions for achieving leader-following tracking consensus are derived without the Zeno behavior. Finally, a numerical example is presented to illustrate the validity of the proposed method.

Disturbance attenuation for neutral Markovian jump systems with multiple delays

The work explores the study of a neutral Markovian jump system that contains multiple delays, external disturbances, and unknown non-linear uncertainties. To overcome the tracking problem, a modified repetitive controller infused with the higher equivalent-input-disturbance approach and the extended Smith predictor approach is suggested. To guarantee the mean-square asymptotic stability of the system, an appropriate mode-dependent loop-based Lyapunov–Krasovskii functional is used. The proposed controller explicitly forces the system output and accurately follows any supplied periodic reference signal. Subsequently, the efficiency of the recommended technique is demonstrated with the simulations that validate the outcomes by comparing them to the existing results.

Adaptive neural dynamic surface composite control for path following of underactuated vessels with fixed-time convergence

The article discusses the path following control issue for underactuated marine surface vessels (MSVs) subject to nonlinear uncertainties. Firstly, the tracking goal of MSVs will be changed from the earth-fixed position to the line-of-sight (LOS) angle with the aid of LOS approach. To deal with the nonlinear uncertainties existing in MSVs, radial basis function neural networks (RBFNNs) are utilized. In particular, the fixed-time serial–parallel estimation models are used to boost the approximation of RBFNNs and determine whether RBFNNs really estimate the unknown nonlinearities by using the forecast and the track biases to change the weight of RBFNNs. Then, a fixed-time filter is produced to handle the ‘explosion of complex’ issue and improve the structure of the developed controller. In addition, the function tanh with smooth derivative function is utilized to overcome the singularity issue of the virtual controller derivations caused by fixed-time control. Finally, an adaptive neural fixed-time dynamic surface composite control method is developed for the path following control problem based on the adaptive backstepping control technique. The stability analysis results show the yaw angle ψ converges to the LOS angle ψs when t≥TS where Ts given later is not determined by the system initial variables. The system internal variables also reach a bounded compact set, which indicates the RBFNNs indeed estimate the uncertainties existing in MSVs by using fixed-time serial–parallel estimation models. And comparation simulation results also certificate the utilizability of the developed controller.

ADVANCEMENTS IN MEDICAL DIAGNOSTICS THROUGH FUZZY LOGIC: A COMPREHENSIVE REVIEW

Fuzzy logic has emerged as a groundbreaking tool in medical diagnostics, addressing the complexities and uncertainties inherent in clinical data. Developed by Lotfi Zadeh in the 1960s, fuzzy logic extends classical logic to handle vagueness and imprecision, making it particularly valuable in interpreting diverse and often ambiguous clinical information. Unlike traditional models that rely on precise data, fuzzy logic employs degrees of truth, allowing for a more flexible and realistic analysis of patients' health conditions. Recent studies have demonstrated the effectiveness of fuzzy logic in enhancing diagnostic processes. Ahmadi et al. (2018) conducted a systematic review that highlighted the significance of fuzzy logic in reducing diagnostic ambiguity and uncertainty, offering insights into its impact on various diseases and identifying under-researched areas. Uzoka et al. (2011) compared fuzzy logic with the fuzzy-analytic hierarchy process (fuzzy-AHP), finding that fuzzy logic slightly outperformed AHP in correlating with conventional diagnoses. Alam et al. (2022) explored the integration of fuzzy inference systems (FIS) with the Internet of Things (IoT) for smart disease diagnosis, showing improvements in accuracy and efficiency for diseases like COVID-19 and malaria. Sudha and Girijamma (2017) introduced an enhanced fuzzy logic algorithm for clustering complex medical data, outperforming traditional methods in response time and classification accuracy. Thomas, Goni, and Emeje (2019) reviewed various fuzzy models, emphasizing their ability to manage nonlinear relationships and uncertainties in medical diagnosis. Shetty (2018) proposed a methodology for predicting heart disease using fuzzy logic, incorporating a web app prototype for wider accessibility. Collectively, these studies highlight fuzzy logic’s potential to improve diagnostic accuracy and efficiency by effectively managing uncertainties and integrating diverse data sources. As technology advances, fuzzy logic is expected to play an increasingly crucial role in enhancing medical diagnostics and patient care.

Neural network-based adaptive consensus of second-order multi-agent systems with nonlinear uncertainties and unknown time delay

This paper studies the leader-following adaptive optimal neural network consensus (AONNC) of second-order multi-agent systems (SOMASs) with nonlinear uncertainties and unknown time delay. An objective function involving the squared distance error and control effort is introduced which will be minimized by the AONNC method. The controller consists of two main parts. The first linear part is based on state feedback control idea and it is designed in such a way that the linear part of each agent dynamics is stable and the objective function is minimum. The nonlinear part which is designed based on the neural network (NN) will compensate for the nonlinear uncertainties and the external disturbances. By defining the distance error between each follower and the leader and taking time derivative of it, the error dynamics of each agent is obtained. To estimate the NN gains, appropriate adaptive rules are presented. The Lyapunov stability criterion is employed to prove the asymptotic stability of SOMAS. It is proved that the time derivative of the Lyapunov function for the aforementioned AONNC method and the adaptation laws is negative and therefore, the consensus of SOMAS is achieved. To verify the AONNC protocol, a SOMAS consisting of five agents (one leader and four followers) is considered and the obtained results are discussed.

Distributed adaptive finite-time fault-tolerant formation-containment control for networked Euler–Lagrange systems under directed communication interactions

This paper addresses the finite-time formation-containment control problem for multiple Euler–Lagrange systems with actuator faults and input saturations subject to external disturbances and nonlinear uncertainties under directed communication interactions. Systematic procedures on how to synthesize a distributed control scheme are developed based on adaptive backstepping control, fault-tolerant control, dynamic gain control and finite-time control such that leaders form a desired geometric configuration while tracking the virtual leader, and followers converge to the convex hull spanned by the leaders during a finite-time period with sufficient accuracy. Two auxiliary systems are constructed to facilitate the control scheme design. Finite-time convergence and ease of computation burden in the sense of not using fractional powers of cooperative error information are realized by integrating dynamic gain control, finite-time control and one auxiliary system. Actuator faults, control input saturations, external disturbances and nonlinear uncertainties are coupled together and dealt with by adaptive backstepping control, fault-tolerant control and the other auxiliary system. In the end, the effectiveness of the proposed control scheme is verified with simulation results.

Adaptive neural network control of multiple‐sectioned flexible riser with time‐varying output constraint and input nonlinearity

AbstractIn this paper, an adaptive neural network controller is proposed for vibration suppression of a multisectional riser system with unknown boundary disturbance, time‐varying asymmetric output constraint, and input nonlinearity. The considered riser system is composed of a continuous connection of several different pipes, and its dynamic models are represented by a set of multiple continuously connected partial differential equations (PDEs) and an ordinary differential equation (ODE) at the top boundary. Considering input nonlinearity, external disturbance, and system uncertainty, radial basis function (RBF) neural networks are adopted to eliminate the effect of these uncertain terms. Besides, a barrier Lyapunov function is employed to guarantee the restrictions. With the proposed boundary control, the stability of the closed‐loop system is proved and simulations are given to illustrate the well performance of the proposed control strategy.

Automatic Landing System Design for Unmanned Fixed-Wing Vehicles via Multivariable Active Disturbance Rejection Control

Landing control of unmanned aerial vehicles (UAVs) is challenging because of the strong nonlinear dynamics, multivariable, model uncertainties, wind variations, and sensor noise. Motivated by this fact, this paper investigates an automatic landing system (ALS) that includes trajectory generation and guidance law for the first flight test of a turbine-based combined cycle technology demonstrator. Specifically, the control scheme increases the original model’s order to generate a reasonable monotone-decreasing throttle reference flare trajectory by the pseudospectral method. Subsequently, the guidance law based on innovative multivariable active disturbance rejection control is designed to robustly track the reference altitude and velocity simultaneously with high accuracy. The multivariable extended state observer (ESO) incorporated decoupling algorithm enhances the estimation capability and accuracy of potential problem in cross-coupling dynamics compared to the traditional ESO. It is proven that the closed-loop error dynamic has bounded-input bounded-output stability and an explicit upper bound is given. Numerical simulation verifies that the presented approach has better robustness and higher tracking accuracy for external disturbances and parametric uncertainties than the existing benchmark autolanding controller. Finally, flight tests show that the proposed ALS can land the vehicle effectively and safely under severe wind conditions.

Stochastic optimal control for autonomous driving applications via polynomial chaos expansions

AbstractModel‐based methods in autonomous driving and advanced driving assistance gain importance in research and development due to their potential to contribute to higher road safety. Parameters of vehicle models, however, are hard to identify precisely or they can change quickly depending on the driving conditions. In this paper, we address the problem of safe trajectory planning under parametric model uncertainties motivated by automotive applications. We use the generalized polynomial chaos expansions for efficient nonlinear uncertainty propagation and distributionally robust inequalities for chance constraints approximation. Inspired by the tube‐based model predictive control, an ancillary feedback controller is used to control the deviations of stochastic modes from the nominal solution, and therefore, decrease the variance. Our approach allows reducing conservatism related to nonlinear uncertainty propagation while guaranteeing constraints satisfaction with a high probability. The performance is demonstrated on the example of a trajectory optimization problem for a simplified vehicle model with uncertain parameters.

An uncertainty principle on the Lorentz spaces

Via subtly combining the Plancherel theorem with various inequalities including Chebyshev’s inequality, generalized Hölder’s and Hausdorff–Young’s inequalities, we establish a new nonlinear uncertainty principle on the Lorentz spaces Lp,q(Rn) for whole ranges of the indexes p,q∈([1,∞)×(0,1])∪((1,∞)×(1,∞)).

Distributed Extended State Estimation for Complex Networks With Nonlinear Uncertainty.

This article studies the distributed state estimation issue for complex networks with nonlinear uncertainty. The extended state approach is used to deal with the nonlinear uncertainty. The distributed state predictor is designed based on the extended state system model, and the distributed state estimator is designed by using the measurement of the corresponding node. The prediction error and the estimation error are derived. The prediction error covariance (PEC) is obtained in terms of the recursive Riccati equation, and the upper bound of the PEC is minimized by designing an optimal estimator gain. With the vectorization approach, a sufficient condition concerning stability of the upper bound is developed. Finally, a numerical example is presented to illustrate the effectiveness of the designed extended state estimator.

Confidence-Aware Multiscale Learning for Online Modeling of Distributed Parameter Systems With Application to Curing Process

In industrial applications, the modeling of distributed parameter systems (DPSs) is of significance for process control and monitoring. Due to infinite dimension, spatiotemporal coupled dynamics, nonlinearity and model uncertainties, however, modeling and online applications of DPSs are very difficult. To address these issues, an online spatiotemporal modeling method is proposed based on confidence-aware multiscale learning. From the spacial-scale perspective, an evolutionary learning-based spatial basis function is designed by learning from two dimensionality reduction methods, including Karhunen-Lo <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\grave{e}$</tex-math></inline-formula> ve and diffusion maps. From the temporal-scale perspective, an efficient broad learning system is developed as reduced-order model to online address temporal dynamics of DPSs. As for the spatiotemporal-scale learning, Gaussian process regression is proposed as confidence-aware estimator to compensate for model generalization errors caused by spatiotemporal coupled dynamics. Through integration with the three-scale learning, the proposed method enables online confidence-aware prediction for DPSs. Experiments based on the curing process in snap curing oven demonstrate the effectiveness of proposed method.

Neuro-Based Consensus Seeking for Nonlinear Uncertainty Multi-Agent Systems Constrained by Dead-Zone Input

The topic about consensus target track seeking for high-order nonlinear multi-agent systems (MASs) with unmodeled dynamics, dynamic disturbances, and dead-zone input is considered in the paper. Using the strong nonlinear map characteristic of radial basis function neural networks (RBFNNs), the complex functions arising from recursive procedure are simplified. Also, inspired by input-to-state practical stability (ISpS), the authors construct a dynamical signal in order to counteract the impact of unmodeled dynamics and dynamic disturbances. The bounded inequality expression has been applied to tackle the unknown input of dead zone. Based on this, consensus control protocol suitable for nonlinear constraints has been constructed by using the recursive backstepping technique and adaptive neural network method. Theoretical analysis indicates not only the uniform boundary of all signals in the closed-loop under the neuro-based consensus controller, but uniform ultimate convergence of consensus tracking errors. The final simulations also confirmed the correctness of the theoretical analysis.