NN Approximation Research Articles

Neural network adaptive switched fault-tolerant control of uncertain nonlinear systems with full state constraints

This paper studies the neural network adaptive fault-tolerant control (NNAFTC) for a class of uncertain nonlinear systems with full state constraints. It is the first time to introduce switched adaptive fault compensation strategy for the controller design process. On the one hand, the proposed method overcomes the limitation needed to be given a prescribed local restriction region of the traditional state constraint schemes, such as log-type, tan-type and integral-type. On the other hand, the full-state constraint and switched fault-tolerant problem is effectively solved even if the existence of actuator failures. Concomitantly, the novel switched tuning functions, the NN approximation technique and the integral barrier Lyapunov functions (IBLF) are combined to construct the backstepping controllers and adaptation laws. It can be proved that all the closed-loop states are restricted in the proper compact sets for any given initial values. Finally, A simulation is shown to demonstrate the validity and advantages of the presented control approach.

Exponential ReLU Neural Network Approximation Rates for Point and Edge Singularities

In certain polytopal domains varOmega , in space dimension d=2,3, we prove exponential expressivity with stable ReLU Neural Networks (ReLU NNs) in H^1(varOmega ) for weighted analytic function classes. These classes comprise in particular solution sets of source and eigenvalue problems for elliptic PDEs with analytic data. Functions in these classes are locally analytic on open subdomains Dsubset varOmega , but may exhibit isolated point singularities in the interior of varOmega or corner and edge singularities at the boundary partial varOmega . The exponential approximation rates are shown to hold in space dimension d = 2 on Lipschitz polygons with straight sides, and in space dimension d=3 on Fichera-type polyhedral domains with plane faces. The constructive proofs indicate that NN depth and size increase poly-logarithmically with respect to the target NN approximation accuracy varepsilon >0 in H^1(varOmega ). The results cover solution sets of linear, second-order elliptic PDEs with analytic data and certain nonlinear elliptic eigenvalue problems with analytic nonlinearities and singular, weighted analytic potentials as arise in electron structure models. Here, the functions correspond to electron densities that exhibit isolated point singularities at the nuclei.

Asymptotic Tracking Control for Nonaffine Systems With Disturbances

This brief intends to address an adaptive asymptotic tracking control with prescribed performance function for a class of nonaffine systems with unknown disturbances. First, the nonaffine system is transformed into an affine system by using a set of alternative state variables. Subsequently, a prescribed performance function with predefined convergence rate, maximum overshoot and steady-state error is introduced. To achieve the asymptotic tracking control performance, the robust integral of the sign of the error (RISE) feedback term is utilized in the control design to reject the unknown external disturbances and NN approximation errors. Finally, an adaptive controller is presented so that the asymptotic tracking performance with guaranteed prescribed performance is achieved. Comparative experiments are provided to show the effectiveness of the proposed control scheme.

Integral reinforcement learning-based guaranteed cost control for unknown nonlinear systems subject to input constraints and uncertainties

This paper investigates guaranteed cost control (GCC) problem for nonlinear systems subject to input constraints and disturbances by utilizing the reinforcement-learning (RL) algorithm. Firstly, by establishing a modified Hamilton–Jacobi–Bellman (HJI) equation, which is difficult to be solved, a model-based policy iteration (PI) GCC algorithm is designed for input-constrained nonlinear systems with disturbances. Moreover, without requiring any knowledge of system dynamics, by designing an auxiliary system with a control law and an auxiliary disturbance policy, an online model-free GCC approach is developed by utilizing integral reinforcement learning (IRL) algorithm. To implement the proposed control algorithm, the actor and disturbance NNs are constructed to approximate the optimal control input and worst-case disturbance policy, while the critic NN is utilized to approximate optimal value function. Further, a synchronization weight update law is developed to minimize the NN approximation residual errors. The asymptotic stability of controlled systems is analyzed by applying the Lyapunov’s method. Finally, the effectiveness and feasibility of the proposed control method are verified by two nonlinear simulation examples.

Single‐network ADP for solving optimal event‐triggered tracking control problem of completely unknown nonlinear systems

In this paper, we propose an optimal event-triggered tracking control scheme for completely unknown nonlinear systems under the adaptive dynamic programming (ADP) framework. A data-driven model based on recurrent neural networks (RNNs) is first constructed to model the system uncertainties including the drift dynamics and the input gain matrix, and the modeling error caused by NN approximation is well eliminated through adding a compensation term in the data-driven model such that the model state can asymptotically track the system state. Apart from the traditional construction of optimal tracking controllers, in this paper, an augmented system is developed and a discounted performance function is considered to achieve the optimality. By employing the Bellman optimal principle, an event-triggered tracking Hamilton–Jacobi–Bellman (HJB) equation is then formulated. The approximate solution of the HJB equation can be obtained by virtue of a critic NN, which significantly simplifies the implementation architecture of ADP. Both the historical state data and the current state data are incorporated into the updating of the weight vector in the critic NN, in this circumstance, the persistence of excitation assumption is not needed anymore. It is strictly proven via Lyapunov stability theory that the tracking error state and the critic NN weight are uniformly ultimately bounded. Simulation results examine the validity of the design scheme.

Saturated observer‐based adaptive neural network leader‐following control of N tractors with n‐trailers with a guaranteed performance

AbstractThis article addresses the leader‐following neural network adaptive observer‐based control of N tractors connected to n trailers with the prescribed performance specifications. To propose the controller, a change of coordinates and a nonlinear error transformation are used to transform the constrained error dynamics to a new second‐order Euler‐Lagrange unconstrained error dynamics which inherits all structural properties of ith vehicle dynamic model. By combining a projection‐type neural network and an adaptive robust technique, a novel leader‐following saturated output‐feedback controller is proposed to force that ith vehicle tracks a virtual leader trajectory with the prescribed transient and steady‐state characteristics while reducing the actuator saturation risk and compensating all unknown dynamic model parameters, external disturbances, unmolded dynamics, and NN approximation errors. A saturated velocity observer is heuristically proposed to obviate the requirement for the velocity measurements of ith vehicle without any unwanted peaking. A Lyapunov‐based stability analysis is utilized to prove that all the tracking and state observation errors are semi‐globally uniformly ultimately bounded (SGUUB) and they converge to small bounds including the origin with a prescribed performance. At the end, computer simulations will be shown to validate the efficacy of the proposed controller in practice.

A Neural Network-Based Adaptive Backstepping Control Law With Covariance Resetting for Asymptotic Output Tracking of a CSTR Plant

A robust nonlinear adaptive controller merging a backstepping approach with neural networks is proposed for a nonlinear non-affine model. The work presented here is evaluated on a complex uncertain model of a continuous stirred tank reactor plant including an unknown varying parameter that enters the complexity model. By exploiting NN and adaptive backstepping approximation methods, an equivalent adaptive NN controller is constructed to achieve robust asymptotic output tracking control. The robustness to uncertainties as well as the lack of informative process data is the main enhancement of this work. This is attained through the implementation of the covariance resetting algorithm in the least square estimation of the NN weight tuning algorithm. The proposed novel control algorithm has been analyzed using Lyapunov analysis. In addition to excellent output trajectory tracking performance, the proposed approach has a profound benefit in terms of substantially lower control effort in comparison to the established work in the literature. In terms of applications in the petrochemical industry, lower control effort can translate to a more energy-efficient actuator, leading to lower costs over a long-run operation. The proposed method's feasibility for chemical process control was shown via numerical simulation.

Bottom-Following Control of Underactuated Unmanned Undersea Vehicles With Input Saturation

This article addresses the subject for bottom-following control of underactuated unmanned undersea vehicles (UUVs) with input saturation in the presence of unknown model uncertainties and unknown external disturbances. A robust adaptive dynamic surface bottom-following control scheme is developed based on the recursive sliding mode with nonlinear gains and neural networks, which can steer an underactuated UUV to precisely follow the bottom profile at a constant altitude as a basic feature. The bottom-following guidance law is derived based on the Serret-Frenet frame, the line of sight (LOS) and Lyapunov's direct technique. Then, the bottom-following controller is designed based on the recursive sliding mode and dynamic surface control (DSC), to stabilize the bottom-following errors. The radial basis function neural networks (RBF NNs) are employed to online approximate the uncertain dynamics of underactuated UUVs, while the adaptive laws are introduced to estimate the bounds of the RBF NN approximation errors and unknown environmental disturbances. Additionally, an auxiliary dynamic system (ADS) is presented to handle the effect of input saturation. The uniform boundedness of all the closed-loop signals is guaranteed via Lyapunov analysis. The simulation results are presented to verify and illustrate the effectiveness of the proposed control scheme.

Neuroadaptive integral robust control of visual quadrotor for tracking a moving object

Abstract This paper aims to achieve the visual quadrotor tracking for ground moving target in the presence of various uncertainties. In order to provide a stable quadrotor motion, the perspective image moments extracted from the defined virtual image plane are selected as the visual features to deduce a decoupled visual quadrotor model. Then a neuroadaptive integral robust controller is designed for the outer and inner loops of visual quadrotor within the image based visual servo (IBVS) framework, which enables error stabilization and improves the anti-disturbance capability. Then, the unknown lumped uncertainties consisting of parametric uncertainties and external disturbances are estimated via constructing a minimal learning parameter-neural network (MLP-NN) and compensated in the feedforward loop, subsequently the residual estimation errors are further suppressed by the structured robust integral of the sign of the error (RISE) feedback control law, hence a high-precise servo tracking performance can be expected. The innovations of the algorithm lie in, (1) with the NN approximation compensated in feedforward loop, the residual estimation errors in feedback loop are decreased, hence the conservatism that using high gains when facing large uncertainties is relaxed, (2) by means of the peculiarity of RISE control, asymptotic stability can be guaranteed with continuous and bounded control inputs, (3) using MLP technology, the number of NN learning parameters are decreased to only two for the closed-loop system, and the online computational load is greatly reduced. Finally, the validity and superiority of the proposed method are validated through affluent simulations and comparisons.

Neural observer-based adaptive prescribed performance control for uncertain nonlinear systems with input saturation

This paper is concerned with the problem of adaptive prescribed performance control for a class of uncertain strict-feedback nonlinear systems with input saturation. A novel indirect neural observer is presented with the ADALINE network incorporated into the conventional sliding mode term. The radial basis function neural network (RBFNN) approximation is utilized to handle the system uncertainties. By using the error transformation function, the tracking error is limited to the given boundary. Then, an auxiliary system is constructed to solve the problem of input saturation. Based on NN approximation and state observation results, a backstepping prescribed performance control scheme is proposed. The boundness of all closed-loop signals and the prescribed tracking performance are proved. Simulation results show the high performance of the designed technique.

HOSM observer based robust adaptive hypersonic flight control using composite learning

Abstract This paper investigates a composite learning controller for hypersonic longitudinal flight dynamics in presence of unknown dynamics. Different from previous designs, the controller is proposed without back-stepping through model transformation. This strategy simplifies the process of controller design and reduces the computation burden of parameter updating. For unknown dynamics, the radial basis function neural network (RBF NN) is used to approximate the lumped uncertainty. Base on the serial–parallel estimate model, the composite learning control scheme constructs a modeling error to evaluate the quality of learning. The highlight is that the composite learning includes the index of NN approximation performance which provides additional tuning of the system learning. Simulation results are presented and the effectiveness of the control strategy is verified.

Biomimetic Hybrid Feedback Feedforward Neural-Network Learning Control

This brief presents a biomimetic hybrid feedback feedforward neural-network learning control (NNLC) strategy inspired by the human motor learning control mechanism for a class of uncertain nonlinear systems. The control structure includes a proportional-derivative controller acting as a feedback servo machine and a radial-basis-function (RBF) NN acting as a feedforward predictive machine. Under the sufficient constraints on control parameters, the closed-loop system achieves semiglobal practical exponential stability, such that an accurate NN approximation is guaranteed in a local region along recurrent reference trajectories. Compared with the existing NNLC methods, the novelties of the proposed method include: 1) the implementation of an adaptive NN control to guarantee plant states being recurrent is not needed, since recurrent reference signals rather than plant states are utilized as NN inputs, which greatly simplifies the analysis and synthesis of the NNLC and 2) the domain of NN approximation can be determined a priori by the given reference signals, which leads to an easy construction of the RBF-NNs. Simulation results have verified the effectiveness of this approach.

Adaptive NN consensus tracking control of a class of nonlinear multi-agent systems

This paper proposes a novel robust adaptive consensus tracking control approach for a class of nonlinear multi-agent systems with modeling uncertainties and external disturbances. Radial Basis Function Neural Networks (RBFNNs) are used to approximate the unknown nonlinear function of agent׳s dynamic. Compared with existing NN consensus algorithms of nonlinear multi-agent systems, the proposed consensus control method only needs a small number of adjustable parameters, thus the online computation burden is greatly alleviated. In addition, by online updating the estimation of the NN approximation errors, the proposed consensus control approach can enhance the system robustness against modeling uncertainties. It is proven that all the signals of the multi-agent system are uniformly bounded and the consensus tracking errors converge to a small neighborhood of zero. A simulation is carried out to demonstrate the effectiveness of the proposed control method.

Direct adaptive control for a class of discrete‐time unknown nonaffine nonlinear systems using neural networks

SummaryIn this paper, a direct adaptive state‐feedback control approach is developed for a class of nonlinear systems in discrete‐time (DT) domain. We study MIMO unknown nonaffine nonlinear DT systems and employ a two‐layer NN to design the controller. By using the presented method, the NN approximation is able to cancel the nonlinearity of the unknown DT plant. Meanwhile, pretraining is not required, and the weights of NNs used in adaptive control are directly updated online. Moreover, unlike standard NN adaptive controllers yielding uniform ultimate boundedness results, the tracking error is guaranteed to be uniformly asymptotically stable by utilizing Lyapunov's direct method. Two illustrative examples are provided to demonstrate the effectiveness and the applicability of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.

Learning from Adaptive Neural Control of Electrically-Driven Mechanical Systems

This study presents deterministic learning from adaptive neural control of unknown electrically-driven mechanical systems. An adaptive neural network system and a high-gain observer are employed to derive the controller. The stable adaptive tuning laws of network weights are derived in the sense of the Lyapunov stability theory. It is rigorously shown that the convergence of partial network weights to their optimal values and locally accurate NN approximation of the unknown closed-loop system dynamics can be achieved in a stable control process because partial Persistent Excitation (PE) condition of some internal signals in the closed-loop system is satisfied. The learned knowledge stored as a set of constant neural weights can be used to improve the control performance and can also be reused in the same or similar control task. Numerical simulation is presented to show the effectiveness of the proposed control scheme.

Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems

AbstractA globally stable decentralized adaptive backstepping neural network tracking control scheme is designed for a class of large‐scale systems with mismatched interconnections. Under the assumption that the subsystems share the reference signals from the other subsystems, neural networks are used to approximate the unknown interconnections dependent on all reference signals such that the NN approximation domain can be determined a priori based on the bounds of reference signals. The proposed control approach can guarantee that all closed‐loop signals are globally uniformly ultimately bounded and that the tracking errors converge to a small residual set around the origin. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Asymptotic Adaptive Neural Network Tracking Control of Nonholonomic Mobile Robot Formations

In this paper, asymptotically stable control laws are developed for leader---follower based formation control using backstepping in order to accommodate the dynamics of the robots and the formation. First, a kinematic controller is developed around control strategies for single mobile robots and the idea of virtual leaders. The virtual leader is replaced with a physical mobile robot leader, and an auxiliary velocity control law is developed in order to prove the global asymptotic stability of the followers which in turn allows the local asymptotic stability of the entire formation. A novel approach is taken in the development of the dynamical controller such that the torque control inputs for the follower robots include the dynamics of the follower robot as well as the dynamics of its leader, and two cases are considered--the case when the robot dynamics are known and the case when they are unknown. In the first case, a robust adaptive control term is utilized to account for unmodeled dynamics. For the latter, a robust adaptive term is augmented with a NN control law to achieve asymptotic tracking performance in contrast with most NN controllers where a bounded tracking error result is shown. Additionally, the NN approximation error is assumed to be a function of tracking errors instead of a constant upper bound, which is commonly found in the literature. The stability of the follower robots as well as the entire formation is demonstrated in each case using Lyapunov methods and numerical results are provided.

Adaptive Neural Control of MIMO Nonlinear Systems in Block-triangular Pure-feedback Form

In this paper, an adaptive neural control scheme is proposed for a class of MIMO nonlinear systems in block-triangular pure-feedback form. The MIMO system is composed of interconnected subsystems. Each subsystem is in the pure-feedback form with all the nonlinearities unknown. Firstly, we design for each subsystem an adaptive neural controller by using backstepping methodology. With the help of NN approximation, there is no need to solve the implicit functions for the explicit virtual controls to cancel the unknown functions in backstepping design. Secondly, by exploiting the structure properties of the MIMO system, we conclude the stability of the whole closed-loop MIMO system by stability analysis of all the signals in the closed-loop in a nested iterative manner. Semi-global uniform ultimate boundedness of all the signals in the closed-loop of MIMO nonlinear systems is guaranteed. The outputs of the systems are proven to converge to small neighborhoods of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.

Modified Fokker-Planck approach to steady-state distributions in plasmas.

A diffusion-equation approach to the collisional radiative recombination and ionization processes in plasmas is improved in order to be applicable to low density plasmas. Dense excited levels are assumed to be quasicontinuous and thus treated by Fokker-Planck equations in the nearest neighbor (nn) approximation, and a few levels lying below the bottleneck are retained explicitly as a discrete set. These coupled equations are solved iteratively, which in turn allows incorporation of the corrections to the nn approximation. The method has been tested for the simple hydrogen plasma in a steady state. The numerical results agree with the exact solutions. Extensions of this approach to nonequilibrium plasmas and complex plasmas of heavy ions are discussed.