Uncertain Nonlinearities Research Articles

Nussbaum-Based Adaptive Neural Networks Tracking Control for Nonlinear PDE-ODE Systems Subject to Deception Attacks.

In this article, the novel adaptive neural networks (NNs) tracking control scheme is presented for nonlinear partial differential equation (PDE)-ordinary differential equation (ODE) coupled systems subject to deception attacks. Because of the special infinite-dimensional characteristics of PDE subsystem and the strong coupling of PDE-ODE systems, it is more difficult to achieve the tracking control for coupled systems than single ODE system under the circumstance of deception attacks, which result in the states and outputs of both PDE and ODE subsystems unavailable by injecting false information into sensors and actuators. For efficient design of the controllers to realize the tracking performance, a new coordinate transformation is developed under the backstepping method, and the PDE subsystem is transformed into a new form. In addition, the effect of the unknown control gains and the uncertain nonlinearities caused by attacks are alleviated by introducing the Nussbaum technology and NNs. The proposed tracking control scheme can guarantee that all signals in the coupled systems are bounded and the good tracking performance can be achieved, despite both sensors and actuators of the studied systems suffering from attacks. Finally, a simulation example is given to verify the effectiveness of the proposed control method.

Fully distributed practical fixed-time fault-tolerant consensus of nonlinear multiagent systems

In this article, the practical fixed-time fault-tolerant consensus problem of a class of first-order nonlinear multiagent systems with actuator faults is investigated. Owing to the existence of uncertain actuator failures (multiplicative faults and additive faults) and non-linearities, it is challenging to study the fixed-time consensus problem of such multiagent systems in a fully distributed approach. To get over this challenge, a fully distributed adaptive protocol that utilizes adaptive techniques is proposed. Under this control protocol, multiagent systems can achieve consensus, and by adjusting controller parameters, the consensus error can converge to the acceptable bounded region in a fixed time. In addition, due to the introduction of adaptive parameters, the design of the control protocol is not dependent on any global network topology information, which means the control protocol is fully distributed. Therefore, the proposed scheme has better scalability and wider applicability. Finally, the simulation results are proposed to validate the fault-tolerant ability and fully distributed characteristics of the presented scheme.

Prescribed performance dynamic surface control based on dual extended state observer for 2-dof hydraulic cutting arm

In tunnel section forming operations, the boom-type roadheader tracking target trajectory with high precision is greatly significant in avoiding over and under excavation and improving excavation efficiency. However, there exist complex cutting loads, measurement noise, and model uncertainties, seriously degrading the tracking performance of traditional nominal model-based controllers. Hence, this study first fully analyzes the kinematics of all members of the cutting mechanism and establishes its complete multi-body dynamic model using the Lagrange method. Furthermore, a dual extended state observer is designed to estimate the mechanical system’s angular velocity and unmodeled disturbances and actuators’ uncertain nonlinearities. In particular, introducing a nonlinear filter replaces the traditional first-order filter in dynamic surface technology, overcoming the “explosion of complexity” while attenuating the conservatism of gains tuning. Then, a dual extended state observer-based prescribed performance dynamic surface controller is developed for roadheaders for the first time. Simultaneously, integrating an improved error transformation function into controller design effectively avoids the online computational burden caused by traditional logarithmic operations. Utilizing Lyapunov theory, the cutting system’s prescribed transient response and steady-state performance are guaranteed. Finally, the proposed controller’s effectiveness is verified by comparative experiments on the roadheader.

Discrete-Time Event-Triggered Type-2 fuzzy wavelet neural network control for Multi-Motor servo system

This paper investigates a discrete-time event-triggered adaptive neural network control scheme for a multi-motor servo system (MMSS) to realize a desired position tracking performance. First, a discrete-time model of the MMSS, including a dead-zone and a nonlinear friction, is established based on the Euler’s discretization. Then, a discrete-time adaptive neural network controller is designed by integrating a type-2 fuzzy wavelet neural network (T2FWNN) and the backstepping technology. The neural network is not only used to estimate uncertain nonlinearities, but also can handle the non-causal problem caused by the conventional backstepping method. Meanwhile, a fixed threshold event-triggered mechanism along with the incorporation of a dead-zone operator is superimposed into the actual controller thus saving communicational resources. Besides, stability analysis proves that all the signals in the closed MMSS are bounded, and the position tracking error converges to a small neighborhood of the origin. Finally, abundant simulation experience results demonstrate the effectiveness and robustness of the proposed scheme.

Neural adaptive dynamic surface control for position tracking of electrohydraulic servo systems based on extended state observer

High-performance motion tracking of electro-hydraulic servo systems plays an important role in developing industrial technology. However, the system itself has parameter uncertainty, uncertain nonlinearity, and measurement noise, significantly decreasing the performance of conventional controllers designed based on nominal models. To improve the tracking performance of electro-hydraulic servo systems, an adaptive dynamic surface control method combining extended state observer and radial basis function neural network is proposed. Firstly, an extended state observer combining neural network output and parameter adaptation technology is designed without the need for speed and pressure feedback to observe the system’s unknown state variables and nonlinear matched disturbance. The design of neural networks is used to approximate mismatched disturbance with significant nonlinearity online. Then, the proposed extended state observer is introduced into the neural adaptive backstepping design, effectively compensating for simultaneous matched and mismatched disturbances, thereby suppressing most of the uncertain nonlinearity of the system. Meanwhile, online update of uncertain parameters further improves the tracking performance of the controller. In addition, the introduction of dynamic surface overcomes the “explosion of complexity” issue in backstepping design. The rigorous stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed controller is validated through comparative experiments on valve-controlled hydraulic cylinder.

Adaptive robust control of electromagnetic actuators with friction nonlinearity and uncertainty compensation

Friction nonlinearity and uncertainty are the main factors affecting the highly performance control of electromagnetic actuators. In this paper, a nonlinear adaptive robust control strategy is proposed of electromagnetic actuators with friction nonlinearity and uncertainty compensation. First, the dynamical model of the electromagnetic actuator is established considering nonlinearity and uncertainty. Then, an adaptive robust controller is designed based on the continuously differentiable friction model to ensure that the control input is continuously and bounded. In the design of the controller, the unfavorable effects of unknown parameters in the electromagnetic actuator are eliminated by constructing a parameter adaptive law. Meanwhile, in order to improve the tracking accuracy of the electromagnetic actuator, a nonlinear robust control law is designed to ensure the robustness of the controller. The stability analysis by Lyapunov function shows that the asymptotic tracking effect can be obtained when only parameter uncertainty exists in the closed-loop system of the electromagnetic actuator, and the consistent bounded stability can be ensured when the system also exists uncertain nonlinearity. Extensive comparative results verify the effectiveness of the proposed control method.

Position Control and Anti-Sway of Overhead Crane System with Uncertain Nonlinear Model

Position Control and Anti-Sway of Overhead Crane System with Uncertain Nonlinear Model

Output feedback distributed optimization algorithms of higher‐order uncertain nonlinear multi‐agent systems

AbstractOutput feedback distributed optimization problem is studied for higher‐order multi‐agent systems with uncertain nonlinearities, which are assumed to satisfy linear growth conditions. The agents dynamics are permitted to be heterogenous with different nonlinearities. The problem is solved by embedded control approach based output feedback distributed optimization algorithms. First, a first‐order optimal signal generator is designed, of which outputs reach the minimizer of the global cost function. Second, embedding the generator into the feedback loop and taking the outputs of the generator as the reference outputs of the agents, output feedback tracking controllers are designed for the higher‐order multi‐agent systems on the basis of nonseparation principle and feedback domination technique. Under the proposed control algorithms, all the agents outputs asymptotically approach a bounded neighbor region of the global minimizer. Simulations demonstrate the effectiveness of the proposed output feedback distributed optimization algorithms.

Adaptive Approximation Sliding-Mode Control of an Uncertain Continuum Robot with Input Nonlinearities and Disturbances

This paper develops an adaptive nonsingular fast terminal sliding-mode control (ANFTSMC) scheme for the continuum robot subjected to uncertain dynamics, external disturbances, and input nonlinearities (e.g., actuator deadzones/faults). Concretely, a function approximation technique (FAT) is utilized to estimate unknown robot dynamics and actuator deadzones/faults online. Furthermore, a disturbance observer (DO) is devised to make up for unknown external disturbances. Then, an ANFTSMC scheme combined with FAT and DO is developed, to expedite the restoration of the stability for the continuum robot. The proposed ANFTSMC not only can retain the benefits of traditional terminal sliding-mode control (TSMC), containing easy enforcement, quick response, and robustness to uncertainties but also dispose of the latent singularity for traditional faster TSMC designs. Afterward, the simulation results show that the proposed controller can effectively improve the trajectory tracking accuracy of the continuum robot, and the tracking root-mean-square errors are 0.0115 and 0.0128 rad. Finally, the effectiveness of ANFTSMC scheme is validated by experiments.

Adaptive finite‐time stabilizing control of fractional‐order nonlinear systems with unmodeled dynamics via sampled‐data output‐feedback

AbstractThis article realizes an adaptive finite‐time sampled‐data output‐feedback stabilization for a class of fractional‐order nonlinear systems with unmodeled dynamics and unavailable states. K‐filters are constructed to estimate unavailable states, a dynamic signal is introduced to handle unmodeled dynamics and neural networks were used to approximate uncertain nonlinearities existed in stabilizer construction. With the help of backstepping technique, an adaptive sampled‐data output‐feedback stabilizer is exported, and such stabilizer with allowable design parameters and sampling period can render the corresponding closed‐loop system reaches practically finite‐time stable, which can be demonstrated by means of selected Lyapunov function candidates. In the end, two simulations with a numerical and an engineering examples are presented to verify the effectiveness of the proposed scheme.

Dual cerebella model neural networks based robust adaptive output feedback control for electromechanical actuator with anti‐parameter perturbation and anti‐disturbance

SummaryTo realize a high‐accuracy tracking control of an electromechanical actuator in which only position signal is available, a new robust adaptive output feedback control strategy based on dual CMAC neural networks is proposed in this article. A high‐gain observer and a neural network are combined to estimate the unmeasured system states, in which a neural network is designed to estimate and compensate the system parameter estimation error and other uncertain nonlinearity to improve the performance of the traditional observer. A robust adaptive controller and another neural network are combined to decrease the impact of parameter perturbation and external disturbance and strengthen the system robustness. Lyapunov theorem is used to derive an on‐line weight adaption law for the two neural networks and an on‐line parameter adaptation law for the uncertain parameters to stabilize the system. Thus the parameter uncertainty and disturbance can be compensated with feedforward compensation technique. A nonlinear robust feedback term is designed to suppress the model compensation deviation. Considering the stronger approximation ability of CMAC basis function against RBF basis function, an improved CMAC neural network is introduced in the proposed controller. A large number of simulations and experiments show that the proposed controller has better tracking performance than many main‐stream output feedback controllers in present.

Adaptive Neural Finite-Time Control of Non-Strict Feedback Nonlinear Systems With Non-Symmetrical Dead-Zone.

The control design method for a class of non-strict feedback nonlinear systems is studied in this brief considering uncertain nonlinearities and unknown non-symmetrical input dead-zone. Combining with the finite-time command filtered backstepping (FCFB) technique, a novel finite-time adaptive control approach is proposed in which a neural network-based methodology is adopted to cope with the uncertain nonlinearities in the non-strict feedback form. The input dead-zone model is transformed into a simple linear system with unknown gain and bounded disturbance which is estimated by an adaptive factor. Using the finite-time Lyapunov theory, the system convergence is proved. And the effectiveness of the proposed control scheme is verified through comparative numerical simulations.

Adaptive Neural Fixed-Time Tracking Control for High-Order Nonlinear Systems.

The problem of adaptive neural fixed-time tracking control for high-order systems is addressed in this article. In order to handle the difficulties from the uncertain nonlinearities within the original systems, the radial basis function neural networks (RBF NNs) are introduced to approximate the unknown nonlinear functions, and the adding a power integrator is applied to overcome the obstacle from high-order terms. It is proven that all signals in the closed-loop system are bounded and the output signal can eventually converge to a small neighborhood of the reference signal. Simulation results further verify the approaches developed.

Event-Triggered Robust Adaptive Dynamic Programming for Multiplayer Stackelberg-Nash Games of Uncertain Nonlinear Systems.

In this article, an event-triggered robust adaptive dynamic programming (ETRADP) algorithm is developed to solve a class of multiplayer Stackelberg-Nash games (MSNGs) for uncertain nonlinear continuous-time systems. Considering the different roles of players in the MSNG, the hierarchical decision-making process is described as the designed value functions for the leader and all followers, which assist to transform the robust control problem of the uncertain nonlinear system into an optimal regulation problem of the nominal system. Then, an online policy iteration algorithm is formulated to solve the derived coupled Hamilton-Jacobi equation. Meanwhile, an event-triggered mechanism is designed to alleviate computational and communication burdens. Moreover, critic neural networks (NNs) are constructed to obtain the event-triggered approximate optimal control polices for all players, which constitute the Stackelberg-Nash equilibrium of the MSNG. By using Lyapunov's direct method, the stability of the closed-loop uncertain nonlinear system is guaranteed under the ETRADP-based control scheme in the sense of uniform ultimate boundedness. Finally, a numerical simulation is provided to demonstrate the effectiveness of the present ETRADP-based control scheme.

Neural Network-based Distributed Generalized Nash Equilibrium Seeking for Uncertain Nonlinear Multi-agent Systems

Neural Network-based Distributed Generalized Nash Equilibrium Seeking for Uncertain Nonlinear Multi-agent Systems

Barrier Lyapunov Function-Based Adaptive Output Feedback Prescribed Performance Controller for Hydraulic Systems With Uncertainties Compensation

In this paper, an adaptive output feedback prescribed performance controller is proposed for a hydraulic system with matched and mismatched uncertainties (including parametric uncertainties and uncertain nonlinearities), which always exist in physical hydraulic systems, and degrade the internal state stability and tracking response performance. By integrating the adaptive control and disturbance observer into the extended state observer, the matched and mismatched uncertainties can be feedforward compensated in the output feedback control. Then, based on the fusion of prescribed performance function and barrier Lyapunov function, the proposed practical method is designed via backstepping method for hydraulic systems, all states are maintained within a preset range by constraining the upper bound of the control errors and the output tracking error is kept within a predetermined boundary that decreases with time. Moreover, the stability of closed-loop system is analyzed by Lyapunov theory. Finally, comparative experimental results are obtained to verify the control performance of the proposed control strategy.

Distributed cooperative control of mechatronic system driving multiple electrohydraulic actuators with uncertain nonlinearity and communication delay

AbstractBeing different from many centralized mechatronic systems, the distributed transmission mechanism has the significant advantage such that realize cooperative task only based on small amount neighbour nodes with low computational complexity. In this study, a distributed cooperative control is proposed for multiple electrohydraulic system (MEHS) to guarantee the follower electrohydraulic node tracking the leader motion, based on the approach of directed spanning tree. Firstly, the MEHS model is constructed as three‐orders isomorphic nonlinear dynamics. Then, a disturbance observer is adopted to estimate uncertain nonlinearities caused by hydraulic parametric uncertainties and unknown external loads in the MEHS. To address unknown communication delays in the network topology of MEHS, a quasi‐synchronous controller is designed via Lyapunov–Krasovskii technique to guarantee that the synchronous errors asymptotically converge to a zero neighbourhood. Finally, the effectiveness of the proposed distributed synchronous control is verified by simulation results under uncertain nonlinearities and different communication delays.

Optimal tracking control for unknown nonlinear systems with uncertain input saturation: A dynamic event-triggered ADP algorithm

This paper is devoted to proposing a novel dynamic event-triggered adaptive dynamic programming (ADP) algorithm to tackle the tracking control problem of unknown nonlinear systems with uncertain input saturation. Initially, an augmented system is established to address the investigated optimal tracking control issue with a discounted cost function. An online identifier based on neural networks (NNs) is designed to recover the unknown system dynamics. Furthermore, the controller design consists of two parts, including the optimal control policy for the nominal system and the NN-based feedforward compensator. In particular, the latter leverages adaptive NN techniques to cope with uncertain input constraints which can be deemed as uncertain saturation nonlinearities. A critic NN is constructed to obtain the approximate optimal control policy for the nominal system. Moreover, rather than traditional time-triggered and static event-triggered control schemes, an adaptive dynamic event-triggering condition is designed to determine the system sampling as well as the controller execution to further reduce transmission and computation burden. The introduction of an internal dynamic variable in possession of a positive constant lower bound can realize the dynamic adjustment of triggering threshold and effectively exclude Zeno behavior. Notice that the weights of identifier NN and critic NN are updated simultaneously, only at the event-triggering instants. Subsequently, the Lyapunov-based theoretical analysis is conducted to confirm the uniform ultimate boundedness of the tracking error and all the NN weight estimation errors. Eventually, the feasibility and effectiveness of the developed algorithm are validated by means of two simulation examples.

High-Precision Tip Tracking of a Flexible Link Manipulator Using Two-Time Scale Adaptive Robust Control

A flexible link manipulator (FLM) has advantages of greater payload-to-manipulator-weight ratio, safer operation, and lower energy consumption compared with the rigid manipulator, which has promising demands in various industrial and aerospace applications. However, the internal dynamics of the system is easy to be unstable due to its nonminimum phase characteristics, and there exists severe parametric uncertainties and uncertain nonlinearities in its dynamics, which has brought many difficulties in the precise tip tracking control and effective vibration suppression. In this article, the entire mathematical model of the FLM is established with assumed mode method and actuator dynamics. Then, the system is decomposed into a slow subsystem and a fast subsystem through introducing an adjustable time-scale factor according to a new output redefined dynamics with uncertainties from truncated vibration modes and unknown disturbances of system. A two-time scale adaptive robust control (TTSARC) scheme, which consists of an adaptive robust control for the slow subsystem and a state feedback control for the fast subsystem, is proposed to effectively handle parametric uncertainties and uncertain nonlinearities as well as improve behavior of internal dynamics. Moreover, the clear connection of achievable performances and control parameters based on the stability analysis of the entire system is addressed. The experimental results indicate that precise tip tracking with small link deflection for the FLM working on different conditions can be achieved with the proposed TTSARC.

Sliding-mode control of electro-hydraulic positioning tracking system combining K-observer and nonlinear disturbance observer

High-precision position control of hydraulic systems is of great significance in industrial applications. However, unknown external force disturbance, measurement noise, and other uncertain nonlinearities widely exist in electro-hydraulic servo systems, which severely degrade the system performance. To handle this problem, a sliding-mode controller based on K-observer with nonlinear disturbance observer is proposed for electro-hydraulic position systems in this article. The nonlinear disturbance observer is to estimate and eliminate the time-varying external force disturbance. The sliding-mode controller based on K-observer is to reach low gain observation of states and improve the system performance by reducing the chattering of the sliding-mode algorithm. The proposed controller is proved to be stable by the Lyapunov stability criterion. Comparative experiments support that the controller has high precision and strong robustness.