Discrete-time neural net controller for a class of nonlineardynamical systems

A family of two-layer discrete-time neural net (NN) controllers is presented for the control of a class of mnth-order MIMO dynamical system. No initial learning phase is needed so that the control action is immediate; in other words, the neural network (NN) controller exhibits a learning-while-functioning-feature instead of a learning-then-control feature. A two-layer NN is used which is linear in the tunable weights. The structure of the neural net controller is derived using a filtered error approach. It is indicated that delta-rule-based tuning, when employed for closed-loop control, can yield unbounded NN weights if: 1) the net cannot exactly reconstruct a certain required function, or 2) there are bounded unknown disturbances acting on the dynamical system. Certainty equivalence is not used, overcoming a major problem in discrete-time adaptive control. In this paper, new online tuning algorithms for discrete-time systems are derived which are similar to ϵ-modification for the case of continuous-time systems that include a modification to the learning rate parameter and a correction term to the standard delta rule     

Adaptive neural network output feedback control of stochastic nonlinear systems with dynamical uncertainties

In this paper, a robust adaptive neural network (NN) backstepping output feedback control approach is proposed for a class of uncertain stochastic nonlinear systems with unknown nonlinear functions, unmodeled dynamics, dynamical uncertainties and without requiring the measurements of the states. The NNs are used to approximate the unknown nonlinear functions, and a filter observer is designed for estimating the unmeasured states. To solve the problem of the dynamical uncertainties, the changing supply function is incorporated into the backstepping recursive design technique, and a new robust adaptive NN output feedback control approach is constructed. It is mathematically proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing design parameters appropriately. The simulation example and comparison results further justify the effectiveness of the proposed approach.     

Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive neural integral sliding‐mode control for tracking control of fully actuated uncertain surface vessels

This paper develops a novel adaptive neural integral sliding‐mode control to enhance the tracking performance of fully actuated uncertain surface vessels. The proposed method is built based on an integrating between the benefits of the approximation capability of neural network (NN) and the high robustness and precision of the integral sliding‐mode control (ISMC). In this paper, the design of NN, which is used to approximate the unknown dynamics, is simplified such that just only one simple adaptive rule is needed. The ISMC, which can eliminate the reaching phase and offer higher tracking performance compared to the conventional sliding‐mode control, is designed such that the system robust against the approximation error and stabilize the whole system. The design procedure of the proposed controller is constructed according to the backstepping control technique so that the stability of the closed‐loop system is guaranteed based on Lyapunov criteria. The proposed method is then tested on a simulated vessel system using computer simulation and compared with other state‐of‐the‐art methods. The comparison results demonstrate the superior performance of the proposed approach.     

Dynamic optimal learning rates of a certain class of fuzzy neuralnetworks and its applications with genetic algorithm

The stability analysis of the learning rate for a two-layer neural network (NN) is discussed first by minimizing the total squared error between the actual and desired outputs for a set of training vectors. The stable and optimal learning rate, in the sense of maximum error reduction, for each iteration in the training (back propagation) process can therefore be found for this two-layer NN. It has also been proven in this paper that the dynamic stable learning rate for this two-layer NN must be greater than zero. Thus it Is guaranteed that the maximum error reduction can be achieved by choosing the optimal learning rate for the next training iteration. A dynamic fuzzy neural network (FNN) that consists of the fuzzy linguistic process as the premise part and the two-layer NN as the consequence part is then illustrated as an immediate application of our approach. Each part of this dynamic FNN has its own learning rate for training purpose. A genetic algorithm is designed to allow a more efficient tuning process of the two learning rates of the FNN. The objective of the genetic algorithm is to reduce the searching time by searching for only one learning rate, which is the learning rate of the premise part, in the FNN. The dynamic optimal learning rates of the two-layer NN can be found directly using our innovative approach. Several examples are fully illustrated and excellent results are obtained for the model car backing up problem and the identification of nonlinear first order and second order systems.     

Adaptive neural output feedback control for stochastic nonlinear time-delay systems with unknown control directions

This paper first focuses on the problem of adaptive output feedback stabilization for a more general class of stochastic nonlinear time-delay systems with unknown control directions. By using a linear state transformation, the original system is transformed to a new system for which control design becomes feasible. Then a novel adaptive neural network (NN) output feedback control strategy, which only contains one adaptive parameter, is developed for such systems by combining the input-driven filter design, the backstepping technique, the NN’s parameterization, the Nussbaum gain function method and the Lyapunov–Krasovskii approach. The proposed control design guarantees that all signals in the closed-loop systems are 4-moment (or 2-moment) semi-globally uniformly bounded. Finally, two simulation examples are given to demonstrate the effectiveness and the applicability of the proposed control design.     

Robust backstepping control of nonlinear systems using neuralnetworks

A controller is proposed for the robust backstepping control of a class of general nonlinear systems using neural networks (NNs). A tuning scheme is proposed which can guarantee the boundedness of tracking error and weight updates. Compared with adaptive backstepping control schemes, we do not require the unknown parameters to be linear parametrizable. No regression matrices are needed, so no preliminary dynamical analysis is needed. One salient feature of our NN approach is that there is no need for the off-line learning phase. Three nonlinear systems, including a one-link robot, an induction motor, and a rigid-link flexible-joint robot, were used to demonstrate the effectiveness of the proposed scheme     

基于DSC后推法的非线性系统的鲁棒自适应NN控制

针对一类具有不确定系统函数和方向未知的不确定增益函数的非线性系统, 提出了一种鲁棒自适应神经网络控制算法. 本算法采用RBF神经网络(Radial based function neural network, RBF NN)逼近模型不确定性, 外界干扰和建模误差采用非线性阻尼项进行补偿, 将动态面控制(Dynamic surface control, DSC)与后推方法结合, 消除了反推法的计算膨胀问题, 降低了控制器的复杂性; 尤其是采用Nussbaum函数处理系统中方向未知的不确定虚拟控制增益函数, 不仅可以避免可能存在的控制器奇异值问题, 而且还能使得整个系统的在线学习参数显著减少, 与DSC方法优点结合, 使得控制算法的计算量大为减少, 便于计算机实现. 稳定性分析证明了所得闭环系统是半全局一致最终有界(Semi-global uniformly ultimately bounded, SGUUB)的, 并且跟踪误差可以收敛到原点的一个较小邻域. 最后, 计算机仿真结果表明了本文所提出控制器的有效性.     

Multilayer neural-net robot controller with guaranteed trackingperformance

A multilayer neural-net (NN) controller for a general serial-link rigid robot arm is developed. The structure of the NN controller is derived using a filtered error/passivity approach. No off-line learning phase is needed for the proposed NN controller and the weights are easily initialized. The nonlinear nature of the NN, plus NN functional reconstruction inaccuracies and robot disturbances, mean that the standard delta rule using backpropagation tuning does not suffice for closed-loop dynamic control. Novel online weight tuning algorithms, including correction terms to the delta rule plus an added robust signal, guarantee bounded tracking errors as well as bounded NN weights. Specific bounds are determined, and the tracking error bound can be made arbitrarily small by increasing a certain feedback gain. The correction terms involve a second-order forward-propagated wave in the backpropagation network. New NN properties including the notions of a passive NN, a dissipative NN, and a robust NN are introduced.     

Neural Network Adaptive Robust Control Of Siso Nonlinear Systems In A Normal Form

In this paper, performance oriented control laws are synthesized for a class of single‐input‐single‐output (SISO) n‐th order nonlinear systems in a normal form by integrating the neural networks (NNs) techniques and the adaptive robust control (ARC) design philosophy. All unknown but repeat‐able nonlinear functions in the system are approximated by the outputs of NNs to achieve a better model compensation for an improved performance. While all NN weights are tuned on‐line, discontinuous projections with fictitious bounds are used in the tuning law to achieve a controlled learning. Robust control terms are then constructed to attenuate model uncertainties for a guaranteed output tracking transient performance and a guaranteed final tracking accuracy. Furthermore, if the unknown nonlinear functions are in the functional ranges of the NNs and the ideal NN weights fall within the fictitious bounds, asymptotic output tracking is achieved to retain the perfect learning capability of NNs. The precision motion control of a linear motor drive system is used as a case study to illustrate the proposed NNARC strategy.     

Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.     

Adaptive NN prescribed performance control for nonlinear systems with output dead zone

This paper investigates adaptive neural network (NN) prescribed performance output tracking control problem for a class of strict-feedback nonlinear systems with output dead zone. By introducing a Nussbaum function, the problem of unknown virtual control coefficient is resolved, which is caused by the nonlinearity in the output dead zone. By designing the state observer and utilizing backstepping recursive design technique, a new adaptive NN control method is proposed. It is shown that all the signals of the resulting closed-loop system are bounded and the tracking error remains an adjustable neighborhood of the origin with the predefined performance under the effect of output dead zone. Finally, a simulation example is given at the simulation part, which further demonstrate the effectiveness of proposed control method.

     

Robust adaptive control for uncertain nonlinear systems with unknown control directions and actuator nonlinearity

A robust adaptive control scheme is proposed for a class of uncertain nonlinear systems in strict feedback form with both unknown control directions and non-symmetric dead-zone nonlinearity based on backstepping design.The conditions that the dead-zone slopes and the boundaries are equal and symmetric are removed by simplifying nonlinear dead-zone input model,the assumption that the priori knowledge of the control directions to be known is eliminated by utilizing Nussbaum-type gain technique and neural networks(NN) approximation capability.The possible controller singularity problem and the effect of dead-zone input nonlinearity are avoided perfectly by combining integral Lyapunov design with sliding mode control strategy.All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the system is proven to be converged to a small neighborhood of the origin.Simulation results demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive neural network control of uncertain nonholonomic systems with strong nonlinear drifts

In this paper, robust adaptive neural network (NN) control is presented to solve the control problem of nonholonomic systems in chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive NN control laws are developed using state scaling and backstepping. Uniform ultimate boundedness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neighborhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. The proposed adaptive NN control is free of control singularity problem. An adaptive control based switching strategy is used to overcome the uncontrollability problem associated with x0 (t0) = 0. The simulation results demonstrate the effectiveness of the proposed controllers.     

A simple robust controller for a class of nonlinear systems

A new robust state‐feedback controller is designed to solve the tracking problem of a class of nonlinear uncertain systems. The contributions of our paper are threefold: Firstly, a new robust state‐feedback controller with a simple structure is derived. Owing to its simplicity, less computation is needed. What is more, for polynomial‐type uncertainties, a much simpler controller can be derived directly without the need of computing partial derivatives. Secondly, a technique that leaves positive functions used in the nonlinear damping terms to be chosen freely is introduced which may enable us to find out a good one among all candidate positive functions to reduce the control effort and to design a ‘softer’ controller. Thirdly, the assumption made in non‐adaptive robust control schemes where the bounding functions are required to be exactly known is relaxed, and the assumption on the reference signal is relaxed too. When our robust controller is applied, the simulations show that better performance can be achieved with less control effort. Copyright © 2000 John Wiley & Sons, Ltd.     

Design of an amplitude-bounded output feedback adaptive neural control with guaranteed componentwise performance

This paper proposes a methodology for the design of a mixed output feedback linear and adaptive neural controller that guarantees componentwise boundedness of the tracking error within an a priori specified compact polyhedron for an uncertain nonlinear system. The approach is based on the design of a robust invariant ellipsoidal set where the adaptive neural network (NN) control is modeled as an amplitude-bounded signal. A linear error observer is employed to recover the unmeasured states, and a linear gain controller is used to enforce the containment of the ellipsoidal set within the performance polyhedron. The analysis and design of the observer and linear controller is set up as an LMI problem. The linear observer/controller scheme is then augmented with a general adaptive NN element having the purpose of approximating and compensating for the unknown nonlinearities thus providing performance improvement. The only requirement for the adaptive control signals is that their amplitudes must be confined within pre-specified limits. For this purpose, a novel mechanism called adaptive control redistribution is introduced to manage the adaptive NN control confinement during the online operation. A numerical example is used to illustrate the design methodology.     

Adaptive Neural Dynamic Surface Control For Nonlinear Pure‐Feedback Systems With Multiple Time‐Varying Delays: A Lyapunov‐Razumikhin Method

This paper focuses on the problem of adaptive neural control for a class of uncertain nonlinear pure‐feedback systems with multiple unknown time‐varying delays. The considered problem is challenging due to the non‐affine pure‐feedback form and the unknown system functions with multiple unknown time‐varying delays. Based on a novel combination of mean value theorem, Razumikhin functional method, dynamic surface control (DSC) technique and neural network (NN) parameterization, a new adaptive neural controller which contains only one parameter is developed for such systems. Moreover, The DSC technique can overcome the problem of ‘explosion of complexity’ in the traditional backstepping design procedure. All closed‐loop signals are shown to be semi‐globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. Two simulation examples are given to verify the effectiveness of the proposed design.     

Integrated design of a linear/neuro-adaptive controller in the presence of norm-bounded uncertainties

Adaptive neural controllers are often criticised for the lack of clear and easy design methodologies that relate adaptive neural network (NN) design parameters to performance requirements. This study proposes a methodology for the design of an integrated linear-adaptive model reference controller that guarantees component-wise boundedness of the tracking error within an a priori specified compact domain. The approach is based on the design of a robust invariant ellipsoidal set where both the NN reconstruction error and the neuro-adaptive control are considered as bounded persistent uncertainties. We show that all the performance and control requirements for the closed-loop system can be expressed as linear matrix inequality constraints. This brings the advantage that feasibility and optimal design parameters can be effectively computed while solving a linear optimisation problem. An advantage of the method is that it allows a systematic and quantitative evaluation of the interplay between the design parameters and their impact on the requirements. This produces an integrated linear/neuro-adaptive performance-oriented design methodology. A numerical example is used to illustrate the approach.     

FPGA implementation of a pulse density neural network with learning ability using simultaneous perturbation

Hardware realization is very important when considering wider applications of neural networks (NNs). In particular, hardware NNs with a learning ability are intriguing. In these networks, the learning scheme is of much interest, with the backpropagation method being widely used. A gradient type of learning rule is not easy to realize in an electronic system, since calculation of the gradients for all weights in the network is very difficult. More suitable is the simultaneous perturbation method, since the learning rule requires only forward operations of the network to modify weights unlike the backpropagation method. In addition, pulse density NN systems have some promising properties, as they are robust to noisy situations and can handle analog quantities based on the digital circuits. We describe a field-programmable gate array realization of a pulse density NN using the simultaneous perturbation method as the learning scheme. We confirm the viability of the design and the operation of the actual NN system through some examples.