Neural Network Approximation Errors Research Articles

Multiple Environment Integral Reinforcement Learning-Based Fault-Tolerant Control for Affine Nonlinear Systems.

This paper studies the fault-tolerant control (FTC) problem for unknown affine nonlinear systems with actuators faults. The considered types of faults are stuck (lock-in-place), loss-in-effectiveness (LIE), and bias, under which a part of the actuators is disabled. The objective is to find the remaining (not fully LIE) actuators, and manipulate them to obtain the best achievable performance in real time. First, considering that the best achievable performance is determined by the remaining actuators, a set of basic policies is predesigned with multiple levels of performances for different groups of activated actuators. Second, an identifier is designed based on history data to find the remaining actuators and, thus, the suitable predesigned basic policy. Third, to further accommodate the partial LIEs and biases, a compensator works together with the selected basic policy, to build the predesigned performance. In addressing the FTC problem, several techniques are developed: adjustable mechanisms are novelly integrated to deal with the state-dependent nonlinearities in neural network (NN) approximation, disturbances, and mismatch errors; history data are newly applied to estimate the faulty parameters; and a compensator is specially designed to deal with LIEs and biases in different input channels. Also in theory, the convergences of algorithms and the stability of closed-loop systems are proved, by formally giving the invariant sets of the initial state and the NN weights. Unlike the existing FTC methods dealing with LIE and bias based on model information to optimize the tracking error, this result can handle stuck faults without knowing system dynamics and satisfy different levels of performances described by Hamilton-Jacobi-Bellman equations. Finally, a simulation example of quadrotor unmanned aerial vehicle is given to verify the effectiveness of the proposed FTC scheme.

Robust platoon control of underactuated autonomous underwater vehicles subjected to nonlinearities, uncertainties and range and angle constraints

This paper studies the three-dimensional platoon control of multiple underactuated autonomous underwater vehicles (AUVs) subjected to environmental disturbances and model uncertainties. The main control objective is to design a tracking controller to force a platoon of AUVs to construct a convoy-like formation along feasible trajectories while each consecutive pair preserves a desired line-of-sight distance with limited communication range and every possible collision is avoided between consecutive vehicles. To achieve this objective, the prescribed performance function (PPF) methodology is employed to constrain the relative distance and angles between successive pairs during their motion. A robust neural network (NN), hyperbolic tangent function, and dynamic surface control technique are simultaneously utilized to propose the prescribed performance-based controller which is robust against completely unknown parameters, nonlinear hydrodynamic damping, actuators saturation nonlinearity, NN approximation errors and time-varying environmental disturbances. Lyapunov's direct method is used to prove that all signals of the closed-loop control system are bounded and the relative distance and angles converge to a neighbourhood of the origin. Finally, numerical computer simulations verify the proposed controller performance for offshore applications.

Adaptive neural finite-time formation control for multiple underactuated vessels with actuator faults

This paper proposes a novel neural finite-time formation control algorithm for multiple underactuated surface vessels with actuator faults. In the algorithm, the leader-follower formation problem is formulated as a two-stage tracking problem. First, to address the leader-follower configuration without the information of leader velocity, the virtual vessel is designed to track the reference trajectory of the leader. Second, an adaptive finite-time fault-tolerant control (AFFTC) algorithm is presented for the follower to track the virtual vessel. By fusion of the neural network (NN) and the fractional power, the model uncertainty is approximated and the finite-time convergence is obtained. Furthermore, a concise adaptive law is developed to compensate the upper bounded of NN weights and lump disturbance which include the approximation error of NN, control gain uncertainty, actuator faults and marine environmental disturbance. On the basis of Lyapunov theory, stability analysis proves that all the signals in the closed-loop system are practical finite-time stable. Finally, numerical simulations are performed to demonstrate the performance and superiority of the proposed algorithm.

Robust Tracking Control of the Euler-Lagrange System Based on Barrier Lyapunov Function and Self-Structuring Neural Networks.

This article studies the robust tracking control problems of Euler–Lagrange (EL) systems with uncertainties. To enhance the robustness of the control systems, an asymmetric tan-type barrier Lyapunov function (ATBLF) is used to dynamic constraint position tracking errors. To deal with the problems of the system uncertainties, the self-structuring neural network (SSNN) is developed to estimate the unknown dynamics model and avoid the calculation burden. The robust compensator is designed to estimate and compensate neural network (NN) approximation errors and unknown disturbances. In addition, a relative threshold event-triggered strategy is introduced, which greatly saves communication resources. Under the proposed robust control scheme, tracking behavior can be implemented with disturbance and unknown dynamics of the EL systems. All signals in the closed-loop system are proved to be bounded by stability analysis, and the tracking error can converge to the neighborhood near the origin. The numerical simulation results show the effectiveness and the validity of the proposed robust control scheme.

Adaptive synchronization of marine surface ships using disturbance rejection without leader velocity

This work realizes the adaptive neural disturbance rejection for the leader–follower cooperative synchronization of surface ships with model perturbations and ocean disturbances without leader velocity measurements. The virtual ship alleviates the requirements on leader ship’s velocities such that the information requirements are only position and heading on the leader ship. The adaptive neural networks approximate model perturbations. The robustifying term attenuates neural network approximation errors. The adaptive neural network-based disturbance observer achieves the disturbance rejection which is integrated with the dynamic surface control technique. The supply ship synchronization control system is ensured to be practical stable. The synchronization control realizes the ship’s cooperative synchronization navigation. Simulations with comparisons validate the synchronization scheme.

Distributed synchronisation control of unknown nonlinear systems with an active leader

This paper investigates the optimal synchronisation problem for unknown nonlinear heterogeneous multi-agent systems (MASs) with an active leader and disturbances. Due to the external input signal of the active leader, the resulted uncooperative behaviours and unpredictability increase difficulty to derive the analytical solution of the coupled Bellman equation. To this end, we develop a distributed model reference adaptive critic learning algorithm with a hierarchical and distributed synchronisation control framework, which transforms the synchronisation problem of unknown nonlinear MASs into that of defined reference ones. Moreover, the algorithm extends our previous work to the distributed MASs, so that it is guaranteed that all the agents reach an agreement with the minimised transient errors and robustness against the disturbances and the neural network (NN) approximation errors. It is proved that the local neighbour tracking errors and the NN weight estimation errors are uniformly ultimately bounded via Lyapunov stability theory. A simulation example for multi-manipulator systems demonstrates the effectiveness of the algorithm.

Model-Free Adaptive Optimal Control for Unknown Nonlinear Multiplayer Nonzero-Sum Game.

In this article, an online adaptive optimal control algorithm based on adaptive dynamic programming is developed to solve the multiplayer nonzero-sum game (MP-NZSG) for discrete-time unknown nonlinear systems. First, a model-free coupled globalized dual-heuristic dynamic programming (GDHP) structure is designed to solve the MP-NZSG problem, in which there is no model network or identifier. Second, in order to relax the requirement of systems dynamics, an online adaptive learning algorithm is developed to solve the Hamilton-Jacobi equation using the system states of two adjacent time steps. Third, a series of critic networks and action networks are used to approximate value functions and optimal policies for all players. All the neural network (NN) weights are updated online based on real-time system states. Fourth, the uniformly ultimate boundedness analysis of the NN approximation errors is proved based on the Lyapunov approach. Finally, simulation results are given to demonstrate the effectiveness of the developed scheme.

Neural network-based adaptive trajectory tracking control of underactuated AUVs with unknown asymmetrical actuator saturation and unknown dynamics

In this paper neural-network (NN) based adaptive trajectory tracking control scheme has been designed for underactuated Autonomous Underwater Vehicles (AUVs) which are subjected to unknown asymmetrical actuator saturation and unknown dynamics. First, some control preliminaries and assumptions along with AUV kinematic & kinetic models and trajectory tracking problems are elaborated. Secondly, the tracking error model and tracking guidance law are derived based on the theory of relative motion and the principle of approach angle respectively. Then the kinematic controller is designed by using the backstepping technique and Lyapunov theory. Similarly, AUV kinetic controller is designed by using the NN compensation and adaptive estimation techniques which is termed as NN-based adaptive controller (NNAC). Pertinently, a novel bounded saturation function has been developed to describe the unknown asymmetrical actuator saturation. The NN is adopted to approximate the complex AUV hydrodynamics and differential of desired tracking velocities. The bound of the generalized disturbance, which is composed of NN approximation error and ocean disturbances, are approximated based on the adaptive estimation technique. To analyze the stability of the developed NNAC, Lyapunov theory and backstepping technique are utilized by considering the control actions on different saturation sections. Finally, effectiveness and superiority of the proposed NNAC are validated through two sets of comparative simulation studies.

Cooperative formation control for multiple surface vessels based on barrier Lyapunov function and self-structuring neural networks

This paper studies the cooperative formation control problem of multiple surface vessels based on the barrier Lyapunov function and self-structuring neural networks with uncertainties and unknown disturbances. To constrain and prevent a consistency error that is too large, a tan-type barrier Lyapunov function is employed to dynamically restrain the formation of tracking errors. To handle the model uncertainties, self-structured neural networks are used to approximate the unknown parameters of the dynamics model and to avoid large computational burden. An adaptive law is developed to estimate and compensate for unknown disturbances and neural network approximation errors. Under the proposed distributed cooperative formation control law, formation behavior among vessels can be achieved through any directed communication topological network and an inaccurate model of each vessel. All signals in the closed-loop system are proven to be semi-globally uniformly ultimately bounded on the initial bounded conditions, and the formation tracking error converges to a small neighborhood of origin. The simulations evaluate the performance of the proposed controller, and verify the effectiveness of the proposed method.

Robust adaptive motion tracking of piezoelectric actuated stages using online neural-network-based sliding mode control

Robust and precise motion tracking for micro-electro-mechanical systems in the presence of inherent nonlinearity and external disturbance is of great importance in many applications. Due to high sensitivity to environmental variations, the entire model or some parameters of the system tend to change unexpectedly. Existing offline nonlinearity models are computationally intensive and may be not suitable under system perturbations. In this work, for a class of piezoelectric actuated (PEA) system, a new online neural-network-based sliding mode control (OLNN-SMC) scheme is developed to obtain robust adaptive precision motions. The nonlinearity of the PEA system is identified online and compensated using singularity-free neural networks (NNs). To alleviate the residual NN approximation errors and meanwhile maintain robust stability under external disturbance, a feedback sliding-mode is synthesized into the control law. Considering unknown and varying disturbances, an adaptive mechanism is designed to achieve robust adaptive motion tracking. The controller is implemented and evaluated through experiments on a PEA platform. Results show that the proposed OLNN-SMC is superior to existing proportional-integral-derivative control with disturbance observer (PID+DOB) and adaptive sliding mode control (ASMC) in terms of sinusoidal tracking and disturbance rejection. In particular, the root-mean-square (RMS) errors for sinusoidal tracking at 0.1–10 Hz using the proposed OLNN-SMC are reduced by 83.5% compared with the cases using PID+DOB or ASMC.

Compensator-based approximate optimal control for affine nonlinear systems with input constraints and unmatched disturbances

This paper develops a novel approximate optimal control method for a class of constrained continuous-time nonlinear systems in the presence of disturbances via adaptive dynamic programming (ADP) technique. First, an auxiliary dynamic compensator is introduced to deal with the input constraints. Through augmenting the original system with the designed auxiliary compensator, the design of constrained optimal controller is circumvented by stabilizing the equivalent augmented system. Then, the cost function is appropriately redefined by introducing an additional function connected with disturbances for the augmented nominal system in order to compensate the effect of unmatched disturbances. Next, the solution of associated Hamilton-Jacobi-Bellman (HJB) equation is solved online with weight adaptation law using neural networks (NNs). Furthermore, an additional robustifying term is utilized to compensate the effect of the approximation error of NNs, and thus the asymptotic stability of the closed-loop system is guaranteed. Finally, all signals of the closed-loop system are proved to be asymptotic convergence by using Lyapunov method. Simulation examples demonstrate the effectiveness of the proposed scheme.

Neural‐network‐embedded distributed average tracking of agents with matching unknown nonlinearities

AbstractThis paper studies a distributed average tracking problem for a class of networked agents subject to heterogeneous unknown nonlinearities. The object is to design distributed protocols so as to drive these dynamic agents cooperatively tracking the average of multiple unknown signals. First, an initialize‐free robust algorithm is designed for each agent incorporating a local filter, a neural network (NN) compensator, and state‐dependent coupling gains with its neighbors. Here the filter is crucial for seeking the average of multiple references signals and is necessary due to the existence of uncertainties in the agents' dynamics. Then, by using adaption schemes, the algorithm is extended to a dynamic version releasing the requirement of certain global information such as the eigenvalues of the network Laplacian and the NN approximation errors. Both algorithms are rigorously proved to guarantee asymptotical average tracking with the help of well‐designed Lyapunov candidates. Finally, two illustrative examples are provided to validate the theoretical results.

Distributed adaptive neural network consensus for a class of uncertain nonaffine nonlinear multi-agent systems

This paper considers the distributed adaptive neural consensus tracking control problem for a class of uncertain nonaffine nonlinear multi-agent systems. By making use of the Taylor expansion technique, the nonaffine nonlinear control input of each subsystem is successfully separated under a weaker decoupling condition, and then, the distributed adaptive control is developed via neural networks (NNs) technique. By introducing the compensation adaptive laws with positive time-varying integrable functions to effectively handle the disturbances and the NN approximation errors in backstepping design process, a new distributed adaptive neural controller is constructed by means of the local output tracking error information of neighborhood agents. It can be proved that all the subsystem outputs asymptotically track to a desired reference trajectory. The efficiency of the established control strategy is demonstrated by the simulation experiment.

Neural network based adaptive rise control of tank gun systems

With the development of the all-electric fourth-generation tank, higher requirements have been put forward for the accuracy and response speed of tank gun control and the traditional tank gun system modeling methods and control strategies failed to meet the requirements. For this reason, a neural network based adaptive robust integral of the error sign (ARISE) control for tank gun system is proposed considering two-axis dynamic coupling and nonlinear friction characteristics. Firstly, a two-axis coupling nonlinear dynamic model of the tank gun system is established and a continuous static friction model is used to characterize the nonlinear friction characteristics of the system. Then, an adaptive law is designed based on the desired position instruction to realize the online update of unknown system parameters. In addition, the neural network is used to compensate other unmodeled dynamic errors and the influence of neural network approximation error is suppressed by the nonlinear integral robust control term. The stability analysis results show that the proposed neural network based adaptive robust integral of the sign of the error control strategy can obtain excellent asymptotic tracking performance, and the simulation results verify its effectiveness.

Adaptive tracking control of robot manipulators with input saturation and time‐varying output constraints

AbstractThis paper investigates adaptive tracking control in task space for robot manipulators with uncertain system dynamics, input saturation, and time‐varying output constraints simultaneously. An auxiliary system is constructed to compensate the effect of the input saturation, and an asymmetric barrier Lyapunov function (BLF) is applied to tackle time‐varying output constraints, while radial basis function (RBF) neural networks (NN) are used to approximate the unknown closed‐loop dynamics. By introducing a disturbance observer (DO), unknown external disturbances from humans and environment are estimated, and NN approximation errors are compensated. A novel adaptive NN tracking controller is designed to guarantee all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded (UUB), while the tracking errors and observer errors converge to a small neighborhood of zero, and the time‐varying output constraints are not violated. Moreover, the adaptive tracking control of redundant robot manipulators is studied, and the subtask and task space tracking of redundant robot manipulators are realized simultaneously, while the stability of the system is proved by Lyapunov stability theory. Finally, some simulation results are presented to verify the effectiveness and superiority of the proposed control scheme.

Finite-time adaptive tracking control of marine vehicles with complex unknowns and input saturation

In this paper, a finite-time adaptive tracking control (FATC) scheme based on nonsingular terminal sliding mode (NTSM) is proposed for trajectory tracking of a marine vehicle with complex unknowns and input saturation. First, a finite-time tracking differentiator (FTD) is designed to acquire the smooth position signal and its derivative. Besides, an adaptive assistant system is introduced to overcome the adverse effects caused by the nonlinear saturation factors. And then, the non-singular terminal sliding surface is constructed to achieve finite-time stability considering the position error and velocity error of the marine vehicle. Subsequently, to attenuate unknown uncertainties, the radial basis function neural network (RBFNN) is adopted to approximate the model uncertainties. Moreover, the adaptive law is introduced to estimate the boundary value of neural network approximation error and external disturbances. It can be proved that the proposed FATC scheme can make the trajectory tracking errors converge to a tiny neighborhood near zero in a finite time. Simulation studies and comprehensive comparisons based on a 76.2m supply vessel are exhaustively provided to confirm the effectiveness and superiority of the proposed FATC scheme.

Adaptive Backstepping Fuzzy Neural Controller Based on Fuzzy Sliding Mode of Active Power Filter

An adaptive backstepping fuzzy neural network (FNN) controller using a fuzzy sliding mode controller is designed to suppress the harmonics and improve the performance of a shunt active power filter (APF). A backstepping method transforms the APF system into a series of subsystems and uses the virtual control to simplify the controller design. A FNN controller is utilized to approach the nonlinear APF system. An adaptive fuzzy system is employed to adjust the sliding gain to compensate the approximation error of neural network and diminish the chattering. The weights of the fuzzy neural network and fuzzy system parameters are adjusted in real-time to guarantee the asymptotic stability of the designed control system. Simulation and experiemental studies indicate the validitiy of the proposed control method, demonstrating the good compensation performance and strong robustness.

Adaptive Robust of RBF Neural Network Control Based on Model Local Approximation Method for Upper Limb Rehabilitation Robotic Arm

For the problem of patient spasm disturbance and random disturbance of external environment in rehabilitation process of upper limb rehabilitation arm, Considering the approximation ability of neural network for arbitrary functions, an adaptive robust of radial basis function (RBF) neural network control algorithm based on model local approximation is proposed. This control algorithm introduces robust term to reduce the approximation error of neural network and the robustness of the rehabilitation manipulator control system is improved. The system can also obtain good track tracking performance under the condition of patient spasm disturbance and random disturbance of external environment. The asymptotic stability of the control system is proved by the stability theory of Lyapunov. Simulation results show that the proposed control algorithm has good control performance.

Robust Adaptive Control of Maximum Power Point Tracking for Wind Power System

A novel data-driven robust approximate optimal Maximum Power Point Tracking (MPPT) control method is proposed for the wind power generation system by using the adaptive dynamic programming (ADP) algorithm. First, a data-driven model is established by a recurrent neural network (NN) to reconstruct the wind power system dynamics using available input-output data. Then, in the design of the controller, based on the obtained data-driven model, the ADP algorithm is utilized to design the approximate optimal tracking controller, which consists of the steady-state controller and the optimal feedback controller. Ulteriorly, developing a robustifying term to compensate for the NN approximation errors introduced by implementing the ADP method. Based on the Lyapunov approach, it proves the stability of the designed model and controller to show that the proposed controller guarantees the system power asymptotically tracking the maximum power. Finally, the simulation results demonstrate that the control method stabilizes the tip speed ratio near the optimal value when the wind speed is lower than the rated wind speed. Moreover, the tracking response speed of the proposed method is fast, which enhances the stability and robustness of the system.

A direct NN‐approximation control for uncertain nonaffine systems with unknown control direction

SummaryIn this paper, we present an adaptive neural network (NN) controller for uncertain nonaffine systems with unknown control direction. Most of the previous NN‐based controllers included a damping term in the adaptive law of NN weights to ensure the closed‐loop stability. The estimated error of the NN weights as well as the tracking error were therefore increased, relying not only on the size of the NN approximation error but also on the ideal NN weights. Compared with those, the proposed controller evades using the damping term through combining a novel adaptive algorithm and a switching mechanism to update the weights. The NN thus can directly approach a target controller with satisfactory accuracy even if the control direction is unknown. Stability analysis shows that the tracking error and the estimated error of NN weights both converge to small neighbors of 0 which solely depend on the NN approximation error. At last, simulations on a Duffing‐Holmes chaotic model show the effectiveness of the proposed controller in comparison to another NN‐based method.