Nonlinear Uncertainties Research Articles

Resilient coordination of multi-agent systems in the presence of unknown heterogeneous actuation efficiency and coupled dynamics: distributed approaches

To guarantee the stability and performance of an overall heterogeneous multi-agent system, feedback control structures must be capable of addressing the presence of heterogeneous agent-based nonlinear uncertainties, unknown actuation performance, and coupling effects. Additionally, some tasks require agents to track the leader's state and reach different states in a distributed way. Therefore, this paper proposes a distributed adaptive controller that drives a set of agents to user-assigned positions in the presence of the mentioned heterogeneous system anomalies. To address actuator dynamics, a hedging-based reference model is used to decouple adaptive updating from the actuator dynamics. To deal with the coupled dynamics, an observer-based estimation algorithm is proposed. Finally, the low-frequency learning method is used to deal with the high-frequency control response and, therefore, to obtain a better transient performance. The overall closed-loop system's stability is investigated using the Lyapunov Stability Theory, and the Linear Matrix Inequalities (LMI) technique is employed to identify stability limits regarding the actuator bandwidths of each agent. Illustrative numerical examples are presented to demonstrate the designed controller's performance in a heterogeneous uncertain multi-agent system's dynamics with unknown actuation capabilities and coupled dynamics.

VpROM: a novel variational autoencoder-boosted reduced order model for the treatment of parametric dependencies in nonlinear systems

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction, such as Proper Orthogonal Decomposition. The limitation of the linear nature of such operators is typically tackled via a library of local reduction subspaces, which requires the assembly of numerous local ROMs to address parametric dependencies. Our work attempts to define a more generalisable mapping between parametric inputs and reduced bases for the purpose of generative modeling. We propose the use of Variational Autoencoders (VAEs) in place of the typically utilised clustering or interpolation operations, for inferring the fundamental vectors, termed as modes, which approximate the manifold of the model response for any and each parametric input state. The derived ROM still relies on projection bases, built on the basis of full-order model simulations, thus retaining the imprinted physical connotation. However, it additionally exploits a matrix of coefficients that relates each local sample response and dynamics to the global phenomena across the parametric input domain. The VAE scheme is utilised for approximating these coefficients for any input state. This coupling leads to a high-precision low-order representation, which is particularly suited for problems where model dependencies or excitation traits cause the dynamic behavior to span multiple response regimes. Moreover, the probabilistic treatment of the VAE representation allows for uncertainty quantification on the reduction bases, which may then be propagated to the ROM response. The performance of the proposed approach is validated on an open-source simulation benchmark featuring hysteresis and multi-parametric dependencies, and on a large-scale wind turbine tower characterised by nonlinear material behavior and model uncertainty.

Enhanced Gaussian-mixture-model-based nonlinear probabilistic uncertainty propagation using Gaussian splitting approach

Enhanced Gaussian-mixture-model-based nonlinear probabilistic uncertainty propagation using Gaussian splitting approach

Saturated adaptive control for high-order fully actuated systems with an extended state

ABSTRACT The present study focuses on controller design for high-order fully actuated systems that experience input saturation and are affected by bounded disturbances, such as nonlinear uncertainties and time-varying unknown parameters. A saturated adaptive controller is developed via the fully actuated system approach and the Lyapunov stability theory to achieve output control and reject disturbances. The disturbances are treated as an extended state and then estimated by introducing an extended state observer. An adaptive variable is used to handle the estimation error between the actual and estimated values of the disturbances. An auxiliary system is designed to mitigate the saturation effect. Lyapunov's direct method verifies that the estimation error, the tracking error, the adaptive state, and the auxiliary system state will eventually stabilise within a bounded ellipsoid. An illustration of spacecraft attitude control demonstrates the effectiveness of the proposed controller.

Bipartite containment control of nonlinear multi‐agent systems with unknown inputs and state constraints

SummaryThis article addresses the issue of bipartite containment tracking for nonlinear strict feedback multi‐agent systems (MASs) with disturbances and measurement uncertainties. To provides a better performance against strong disturbance, a coordination transformation is applied such that all the nonlinear functions, controller disturbances and measurement uncertainties are lumped into a single disturbance signal in the last state equation. Then, the lumped disturbance is compensated through a novel disturbance rebuilding method. Moreover, in order to get better control performance, state constraints are also considered through a nonlinear transformation function (NTF). Different from traditional methods dealing with the state constraint problems, the NTF method can avoid using any discontinuous Lyapunov function. Finally, an adaptive finite‐time distributed controller is established via the disturbance estimates, backstepping technique and fuzzy logic system (FLS). The performance of the controller is illustrated by a simulation example in which the bipartite containment formation of followers is realized in a practical finite time.

A novel control strategy of a variable-speed doubly-fed-induction-generator-based wind energy conversion system

Abstract This paper aims to address the issue of control of a variable-speed wind turbine based on doubly-fed induction generators. In this work, an effort is made to extract the maximum efficiency from a doubly-fed induction generator-based variable-speed wind turbine by controlling the rotor current. In the first step, a maximum power point tracking technique is used to extract the maximum power from the turbine. Then a stator-flux-oriented vector control strategy is employed to control the rotor-side current. Subsequently, a grid voltage vector-oriented control strategy is used to control the grid-side system of the grid-connected generator. Considering the nonlinearity and parameter uncertainty of the system, an active disturbance rejection controller with a sliding-mode-based extended-state observer is developed for the above-mentioned control strategies. Furthermore, the stability of the controller is tested and the performance of the controller is compared with the classical proportional–integral controller based on disturbance rejection, robustness and tracking capability in a highly non-linear wind speed variation scenario. Modelling, control and comparison are conducted in the MATLAB®/Simulink® environment. Finally, a real-time hardware set-up is presented using the dSPACE ds-1104 R&D processing board to validate the control scheme. From the result of the experiments, it is seen that the proposed controller takes 10–15 control cycles to settle to its steady-state values, depending on the control loop, whereas the conventional proportional–integral controller takes 60–75 control cycles. As a result, the settling time for the proposed control scheme is shorter than that of the proportional–integral controller.

Self-tuning PID feedback control method for magnetic suspension active vibration isolation system with parameters uncertainty

A self-tuning PID (Proportion-Integral-Derivative) control method based on the adaptive mechanism was proposed for the magnetic suspension active vibration isolation system with the characteristics of nonlinear, time-varying, and model parameter uncertainty. The controller identified the controlled object parameters online and solved the controller parameters in real time. To test the effectiveness of the proposed method, a six degree-of-freedom (DOF) magnetic suspension active vibration isolation system was designed and built. The six DOF dynamic model of the vibration isolation system with uncertain model parameters was derived for control. Experiments were carried out and compared with the control effects of the tradition PID control and cascade PID control algorithm. The experimental results show that the proposed self-tuning PID controller has more outstanding practicality and effectiveness in solving the model parameter uncertainty problem compared with the existing studies at home and abroad, and it also proves that the control method has a good isolation effect on the wide band disturbances.

Adaptive consensus tracking control for robotic manipulators with nonlinear time‐varying fault‐tolerant actuator and unknown control input directions

SummaryThe consensus tracking mechanism of a multi‐agent system consisting of third‐order nonlinear single joint manipulators was investigated in this study based on the pertinent industrial context. Unlike many previous studies on consensus control that presumed a known control direction, this investigation addressed the complex challenges posed by unknown control directions and time‐varying actuators. Specifically, we explored both time‐invariant and time‐varying actuator faults in scenarios wherein all parameters are unknown. The Nussbaum function was utilized to resolve time‐varying nonlinear fault‐tolerance and unknown control direction problems. In the design process of the control law, the backstepping method combining with Nussbaum function is adopted to address unmatched nonlinearity and unmatched uncertainty system, and the radial basis function neural network is used to approximate the unknown parameters The resulting control law allows all robotic manipulators to track the angle and angular velocity of the leader. Simulation results demonstrate the effectiveness of the proposed control scheme.

Low-Order Automatic Domain Splitting Approach for Nonlinear Uncertainty Mapping

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second-order Taylor expansions and polynomial bounding techniques is first introduced to estimate the Jacobian variation of a nonlinear transformation. This index is then embedded into a low-order automatic domain splitting algorithm that accurately describes the mapping of an initial uncertainty set through a generic nonlinear transformation by splitting the domain whenever nonlinearities grow above a predefined threshold. The algorithm is illustrated in the critical case of orbital uncertainty propagation, and it is coupled with a tailored merging process that limits the growth of the domains in time by recombining them when nonlinearities decrease. The low-order automatic domain splitting algorithm is then combined with Gaussian mixture models to accurately describe the propagation of a probability density function.

Distributed nonsingular terminal sliding mode control–based RBFNN for heterogeneous vehicular platoons with input saturation

In this paper, a distributed nonsingular terminal sliding mode control (NTSMC) is proposed for vehicular platoons subjected to nonlinear uncertainty, external disturbance, and input saturation. Due to the presence of input saturation, the platoon control becomes more complicated. However, only considering the impact of uncertainty on the system, input saturation will usually lead to a decline in the driving performance, even lead to string instability. First, the input saturation is compensated by a single parameter, which is simple and direct. The radial basis function neural network (RBFNN) based on disturbance observer is employed to compensate the nonlinear uncertainty and external disturbance, respectively. The basis function of neural network is only related to the velocity and acceleration of the leader. Therefore, the nonlinearity of the vehicle systems does not need to meet the matching conditions. Then, a distributed NTSMC is designed to realize the internal stability, which weakens the chattering of traditional sliding mode control (SMC) to some extent. In addition, the nonsingular problem in terminal sliding mode control (TSMC) is solved. The string stability is realized by employing a coupled sliding mode control (CSMC). Finally, simulation results demonstrate the effectiveness and feasibility of the proposed strategy.

Direct Adaptive Fuzzy Control with Prescribed Tracking Accuracy for Orbit Adjustment of Satellites

In this paper, we investigate the orbit-adjustment problem of satellite systems in the presence of nonlinear uncertainties in kinematics and dynamics. We propose a novel direct adaptive fuzzy control scheme with prescribed tracking accuracy to address uncertain nonlinear dynamics by employing advanced fuzzy logic systems and integrating a class of sophisticated smooth functions, thereby ensuring convergence of the tracking error within a precisely defined interval. The ingeniously designed control scheme guarantees negative semi-definiteness of the Lyapunov function, ensuring boundedness for all variables. Moreover, our groundbreaking control approach requires only one adaptive law, completely eliminating any direct correlation with the number of nonlinear functions. Simulation results unequivocally validate the remarkable effectiveness and superiority of our innovative control approach.

Disturbance Observer-Based Model Predictive Control for an Unmanned Underwater Vehicle

This work addresses the motion control problem for a 4-degree-of-freedom unmanned underwater vehicle (UUV) in the presence of nonlinear dynamics, parametric uncertainties, system constraints, and time-varying external disturbances. A disturbance observer-based control scheme is proposed, which is structured around the model predictive control (MPC) method integrated with an extended active observer (EAOB). Compared to the conventional disturbance observer, the developed EAOB has the ability to handle both external disturbances and system/measurement noises simultaneously. The EAOB leverages a combination of sensor measurements and a system dynamic model to estimate disturbances in real-time, which allows continuous estimation and compensation of time-varying disturbances back to the controller. The proposed disturbance observer-based MPC is implemented by feeding the estimated disturbances back into the MPC’s prediction model, which forms an effective adaptive controller with a parameter-varying model. The proposed control strategy is validated through simulations in a Gazebo and robot operating system environment. The results show that the proposed method can effectively reject unpredictable disturbances and improve the UUV’s control performance.

Distributed Robust Fault Estimation for Multiagent Systems Based on Transition Variable Estimator.

This article investigates the distributed robust fault estimation for a class of multiagent systems with actuator faults and nonlinear uncertainties. To estimate the actuator faults and system states simultaneously, a novel transition variable estimator is constructed. Compared with existing similar results, the fault estimator existing condition is not necessary for designing the transition variable estimator. Furthermore, the bounds of the faults and their derivatives can be unknown in designing the estimator for each agent in the system. The parameters of the estimator are calculated by using Schur decomposition and linear matrix inequality algorithm. Finally, the performance of the proposed method is demonstrated through experiments of wheeled mobile robots.

Reinforcement Learning-Based Adaptive Optimal Control for Nonlinear Systems With Asymmetric Hysteresis.

This article investigates the adaptive optimal tracking problem for a class of nonlinear affine systems with asymmetric Prandtl-Ishlinskii (PI) hysteresis nonlinearities based on actor-critic (A-C) learning mechanisms. Considering the huge obstacles arising from the uncertainty of hysteresis nonlinearity in actuators, we develop a scheme for the conflict between the construction of Hamilton functions and hysteresis nonlinearity. The actuator hysteresis forces the input into a hysteresis delay, thus preventing the Hamilton function from getting the current moment's input instantly and thus making optimization impossible. In the first step, an inverse model is constructed to compensate for the hysteresis model with a shift factor. In the second step, we compensate for the control input by designing a feedback controller and incorporating the estimation and approximation errors into the Hamilton error. Optimal control, the other part of the actual control input, is obtained by taking partial derivatives of the Hamiltonian function after the nonlinearities have been circumvented. At the end, a simulation is given to validate the developed solution.

Dynamic event-triggered consensus control for nonlinear multi-agent systems under DoS attacks.

In this paper, we investigated leader-following consensus control for nonlinear multi-agent systems (MASs) experiencing denial-of-service (DoS) attacks. We proposed a distributed control strategy incorporating an adaptive scheme and a state feedback control gain to eliminate the effects of system nonlinear dynamics and uncertainties. In addition, we introduced a dynamic event-triggered control (DETC) to minimize the utilization of communication resources. Finally, we provided simulation results to show the validity of the proposed approach.

Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests

The reflooding phase, a crucial recovery process after a loss of coolant accident (LOCA) in reactors, involves cooling overheated fuel rods with subcooled water. Its complex nature, notably in its flow regime and heat transfer, makes prediction challenging, resulting in high uncertainty and computation cost. In this study, we utilized the data assimilation (DA) technique to enhance the prediction of reflooding phenomena and subsequently deployed machine learning models to predict the accuracy of the safety and performance analysis code (SPACE) simulation. To generate the dataset for the machine learning model, we employed the sampling method for highly nonlinear system uncertainty analysis (STARU), providing a high-quality dataset for a complex problem such as a reflooding simulation. In this dataset, the physical models were assimilated under their selected uncertainty bands and utilized the effective sampling approach of STARU, generating the high-quality output and efficient enhancement of SPACE predictions. Consequently, the implemented machine learning model can be used to enhance model development and uncertainty quantification (UQ) analysis using the system code.

Adaptive neural network H∞$H_\infty$ control for offshore platform with input delay and nonlinearity

AbstractIn this work, an adaptive learning robust controller is proposed to suppress the vibration of offshore platforms, which are subject to waves, winds, varying control delays and parametric perturbations. To realize nonlinear uncertainty approximation under the bounded performance, the controller incorporates both an online adaptive part and an offline fixed part. The adaptive part constructed by neural networks adjusts online, while the fixed part is obtained by regulating the performance. Importantly, adaptive updating strategy does not require accurate values or upper bounds for real‐time control delay or uncertainty. Several comparable experiments demonstrate the feasibility and effectiveness in vibration‐suppression of the designed adaptive controller in shallow/deep water. This scheme significantly reduces system response variations due to structural and hydrodynamic uncertainty, as well as additional random environmental forces caused by winds.

Fractional order sliding mode control for linear maglev synchronous motor based on an adaptive fixed-time extended state observer

In order to improve the tracking accuracy of the linear maglev synchronous motor maglev system with non-linear, strongly coupled, and other uncertainty problems, a fixed-time fractional order terminal sliding mode control (FFTSMC) strategy based on adaptive fixed-time extended state observer (AFxESO) is proposed. Firstly, a fast AFxESO is constructed and an adaptive law is designed to dynamically adjust the gain to reduce the estimation error and measurement noise, which enables the observer to accurately estimate the perturbation of the unknown boundary in a fixed-time. Secondly, a new FFTSM controller is designed by applying the theory of fractional order calculus, which can speed up the system convergence and suppress the chattering problem in SMC. Then, using the Lyapunov stability theory, it is demonstrated that the proposed AFxESO-FFTSM control scheme can guarantee the global fixed-time convergence of the system to equilibrium and the convergence time is dependent on the selection of the controller parameters, which effectively overcomes the drawbacks of finite-time control. Finally, the feasibility and superiority of the proposed strategy are verified on the linear maglev synchronous motor system experiment platform.

Adaptive constrained tracking control for dynamical actuator driven linear 2 × 2 hyperbolic PDE systems with nonlinear uncertainties

The paper develops an adaptive constrained tracking control technique for a class of 2 × 2 hyperbolic partial differential equation (PDE) systems with boundary actuator dynamics, which are described by a set of ordinary differential equations (ODEs) in the presence of unknown parametric nonlinearities. Since the control input only appears in the uncertain ODE subsystem rather than directly on the boundary of PDE subsystem, the control task becomes quite difficult and the existing direct boundary control approaches are ineffective. Moreover, in this paper, a more challenging problem is considered such that the controlled output and the states of ODE actuators are constrained. To this end, by utilizing finite and infinite dimensional backstepping techniques, barrier Lyapunov functions (BLFs) and adaptive methods, a novel adaptive tracking control approach is proposed. It is the first time that such a constrained tracking control problem is addressed for the PDE-ODE coupled systems considered in this paper. On the basis of the presented method, the rigorous theoretical proof is provided to show that the PDE controlled output and all the states of the ODE actuator stay within the predefined compact sets. Finally, the results are illustrated via a comparative numerical simulation.

An Intelligent Control and a Model Predictive Control for a Single Landing Gear Equipped with a Magnetorheological Damper

Aircraft landing gear equipped with a magnetorheological (MR) damper is a semi-active system that contains nonlinear behavior, disturbances, uncertainties, and delay times that can have a huge impact on the landing’s performance. To solve this problem, this paper adopts two types of controllers, which are an intelligent controller and a model predictive controller, for a landing gear equipped with an MR damper to improve the landing gear performance considering response time in different landing cases. A model predictive controller is built based on the mathematical model of the landing gear system. An intelligent controller based on a neural network is designed and trained using a greedy bandit algorithm to improve the shock absorber efficiency at different aircraft masses and sink speeds. In this MR damper, the response time is assumed to be constant at 20 ms, which is similar to the response time of the commercial MR damper. To verify the efficiency of the proposed controllers, numerical simulations compared with a passive damper and a skyhook controller in different landing cases are executed. The major finding indicates that the suggested controller performs better in various landing scenarios than other controllers in terms of shock absorber effectiveness and adaptability.