Indirect adaptive control of nonlinear system via dynamic multilayer neural networks with multi‐time scales

This paper deals with adaptive nonlinear identification and trajectory tracking problem via dynamic multilayer neural network with different time scales. By means of a Lyapunov‐like analysis, we determine stability conditions for the on‐line identification. Then, a sliding mode controller is designed for trajectory tracking with consideration of the modeling error and disturbance. The main contributions of the paper lie in the following aspects. First, we extend our prior identification results of single‐layer dynamic neural networks with multi‐time scales to those of multilayer case. Second, the e‐modification in standard use in adaptive control is introduced in the on‐line update laws to guarantee bounded weights and bounded identification errors. Third, the potential singularity problem in controller design is solved by using new update laws for the NN weights so that the control signal is guaranteed bounded. The stability of proposed controller is proved by using Lyapunov function. Simulation results demonstrate the effectiveness of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.     

Indirect adaptive control of a class of marine vehicles

A nonlinear adaptive framework for bounded‐error tracking control of a class of non‐minimum phase marine vehicles is presented. The control algorithm relies on a special set of tracking errors to achieve satisfactory tracking performance while guaranteeing stable internal dynamics. First, the design of a model‐based nonlinear control law, guaranteeing asymptotic stability of the error dynamics, is presented. This control algorithm solves the tracking problem for the considered class of marine vehicles, assuming full knowledge of the system model. Then, the analysis of the zero‐dynamics is carried out, which illustrates the efficacy of the chosen set of tracking errors in stabilizing the internal dynamics. Finally, an indirect adaptive technique, relying on a partial state predictor, is used to address parametric uncertainties in the model. The resulting adaptive control algorithm guarantees Lyapunov stability of the errors and parameter estimates, as well as asymptotic convergence of the errors to zero. Numerical simulations illustrate the performance of the adaptive algorithm. Copyright © 2009 John Wiley & Sons, Ltd.     

Predictor‐based adaptive dynamic surface control for consensus of uncertain nonlinear systems in strict‐feedback form

This paper investigates the leader–follower consensus problem of uncertain nonlinear systems in strict‐feedback form. By parameterizations of unknown nonlinear dynamics of the agents, an adaptive dynamic surface control with the aid of predictors, tracking differentiators is proposed to realize output consensus of the multi‐agent systems. Unlike the existing adaptive consensus methods, the predictor errors are used to learn the unknown parameters, which can achieve fast learning without high‐frequency signals in control inputs. As a fast precise signal filter, the tracking differentiator is used in the control design instead of first‐order filters, which can further improve the control performance. Based on graph theory and Lyapunov stability theory, it is shown that the outputs of all followers ultimately synchronize to that of the leader with bounded tracking errors. Simulation results are provided to validate the effectiveness and advantage of the proposed consensus algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive fuzzy backstepping dynamic surface control for a class of MIMO nonlinear systems with input delays and state time‐varying delays

In this paper, an adaptive fuzzy backstepping dynamic surface control (DSC) approach is developed for a class of MIMO nonlinear systems with input delays and state time‐varying delays. The unknown continuous nonlinear functions are expressed as the linearly parameterized form by using the fuzzy logic systems, and then, by combining the backstepping technique, the appropriate Lyapunov–Krasovskii functionals, and the ‘minimal learning parameters’ algorithms with the DSC approach, the adaptive fuzzy tracking controller is designed. Our development is able to eliminate the problem of ‘explosion of complexity’ inherent in the existing backstepping‐based methods. It is proven that the proposed design method can guarantee that all the signals in the closed‐loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, simulation results are provided to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Cooperative adaptive neural partial tracking errors constrained control for nonlinear multi‐agent systems

This paper considers the problem of partial tracking errors constrained for high‐order nonlinear multi‐agent systems in strict‐feedback form. In the control design, radial‐based function neural networks are utilized to identify uncertain nonlinear functions, and a cooperative adaptive dynamic surface control is proposed to avoid the explosion of complexity in the backstepping technique. Based on the minimal learning parameter technique and the predefined performance approach, a novel cooperative adaptive neural network control method is developed. The proposed controller is able to guarantee that all the closed‐loop network signals are cooperative semi‐globally uniformly ultimately bounded, and partial tracking errors confine all times within the predefined bounds. Finally, simulation example and comparative example with previous methods are given to verify and clarify the effectiveness of the new design procedure. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive neural control for nonstrict‐feedback stochastic nonlinear time‐delay systems with input and output constraints

This paper investigates an adaptive neural tracking control for a class of nonstrict‐feedback stochastic nonlinear time‐delay systems with input saturation and output constraint. First, the Gaussian error function is used to represent a continuous differentiable asymmetric saturation model. Second, the appropriate Lyapunov‐Krasovskii functional and the property of hyperbolic tangent functions are used to compensate the time‐delay effects, the neural network is used to approximate the unknown nonlinearities, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. At last, based on Lyapunov stability theory, a robust adaptive neural control method is proposed, and the designed controller decreases the number of learning parameters and thus reduces the computational burden. It is shown that the designed neural controller can ensure that all the signals in the closed‐loop system are 4‐Moment (or 2 Moment) semi‐globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of the origin. Two examples are given to further verify the effectiveness of the proposed approach.     

Global adaptive learning control of robotic manipulators by output error feedback

This paper addresses the problem of designing a global, output error feedback based, adaptive learning control for robotic manipulators with revolute joints and uncertain dynamics. The reference signals to be tracked are assumed to be smooth and periodic with known period. By developing in Fourier series expansion the input reference signals of every joint, an adaptive, output error feedback, learning control is designed, which ‘learns’ the input reference signals by identifying their Fourier coefficients: global asymptotic and local exponential stability of the tracking error dynamics are obtained when the Fourier series expansion of each input reference signal is finite, while arbitrary small tracking errors are achieved otherwise. The resulting control is not model based and depends only on the period of the reference signals and on some constant bounds on the robot dynamics. Copyright © 2008 John Wiley & Sons, Ltd.     

Iterative learning control for nonlinear dynamic systems with randomly varying trial lengths

In this paper, we introduce an iterative learning control (ILC) scheme based on an iteratively moving average operator for nonlinear dynamic systems with randomly varying trial lengths. By using the iteratively moving average operator, the proposed ILC algorithm overcomes the limitation of traditional ILC that all trial lengths must be identical. It is shown that for nonlinear affine and non‐affine systems, the proposed learning algorithm works effectively to nullify the tracking error. In the end, two illustrative examples are presented to demonstrate the performance and the effectiveness of the proposed ILC scheme for nonlinear dynamic systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive control design for MIMO switched nonlinear systems with full state constraints

This paper presents an adaptive fuzzy control approach of multiple‐input–multiple‐output (MIMO) switched uncertain systems, which involve time‐varying full state constraints (TFSCs) and unknown disturbances. In the design procedure, the fuzzy logic systems are adopted to approximate the unknown functions in the systems. The adaptive fuzzy controller is set up by backstepping technique. According to the tangent barrier Lyapunov function (BLF‐Tan), a novel adaptive MIMO switched nonlinear control algorithm is designed. Under the rule of arbitrary switchings and the proposed control laws, it is demonstrated that all signals in the resulted system are semiglobally uniformly ultimately bounded (SGUUB) and the tracking error converges to a small neighborhood of zero with TFSCs. Furthermore, the simulation example validates the effectiveness of presented control strategy.     

基于 actor-critic 框架的在线积分强化学习算法研究

针对轮式移动机器人动力学系统难以实现无模型的最优跟踪控制问题,提出了一种基于actor-critic框架的在线积分强化学习控制算法。首先,构建RBF评价神经网络并基于近似贝尔曼误差设计该网络的权值更新律,以拟合二次型跟踪控制性能指标函数。其次,构建RBF行为神经网络并以最小化性能指标函数为目标设计权值更新律,补偿动力学系统中的未知项。最后,通过Lyapunov理论证明了所提出的积分强化学习控制算法可以使得价值函数,行为神经网络权值误差与评价神经网络权值误差一致最终有界。仿真和实验结果表明,该算法不仅可以实现对恒定速度以及时变速度的跟踪,还可以在嵌入式平台上进行实现。     

Adaptive robust control of a class of nonlinear systems in semi‐strict feedback form with non‐uniformly detectable unmeasured internal states

This paper proposes a novel control method for a special class of nonlinear systems in semi‐strict feedback form. The main characteristic of this class of systems is that the unmeasured internal states are non‐uniformly detectable, which means that no observer for these states can be designed to make the observation error exponentially converge to zero. In view of this, a projection‐based adaptive robust control law is developed in this paper for this kind of system. This method uses a projection‐type adaptation algorithm for the estimation of both the unknown parameters and the internal states. Robust feedback term is synthesized to make the system robust to uncertain nonlinearities and disturbances. Although the estimation error for both the unknown parameters and the internal states may not converge to zero, the tracking error of the closed‐loop system is proved to converge to zero asymptotically if the system has only parametric uncertainties. Furthermore, it is theoretically proved that all the signals are bounded, and the control algorithm is robust to bounded disturbances and uncertain nonlinearities with guaranteed output tracking transient performance and steady‐state accuracy in general. The class of system considered here has wide engineering applications, and a practical example—control of mechanical systems with dynamic friction—is used as a case study. Simulation results are obtained to demonstrate the applicability of the proposed control methodology. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive finite‐time formation tracking control for multiple nonholonomic UAV system with uncertainties and quantized input

An adaptive finite‐time formation tracking control approach is proposed for multiple unmanned aerial vehicle (UAV) system with quantized input signals in this paper. The UAVs are described by nonholonomic kinematic model and autopilot model with uncertainties. An enhanced hysteretic quantizer is introduced to avoid chattering, and some restrictions are released by using a new quantization decomposition method. Based on backstepping technique and finite‐time Lyapunov stability theory, the adaptive finite‐time controller is designed for the trajectory tracking of the multi‐UAV formation. The nonholonomic constraints are solved by a transverse function. A transformation is introduced to the control input signals to eliminate the quantization effect. Stability analysis proves that the tracking errors can converge to a small neighborhood of the origin within finite time and all the closed‐loop signals are semiglobally finite‐time bounded. The effectiveness of the proposed control approach is validated by simulation and experiment.     

Adaptive neural network control for stochastic constrained block structure nonlinear systems with dynamical uncertainties

Stochastic adaptive dynamic surface control is presented for a class of uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems with unmodeled dynamics and full state constraints in this paper. The controller is constructed by combining the dynamic surface control with radial basis function neural networks for the MIMO stochastic nonlinear systems. The nonlinear mapping is applied to guarantee the state constraints being not violated. The unmodeled dynamics is disposed through introducing an available dynamic signal. It is proved that all signals in the closed‐loop system are bounded in probability and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four‐moment and the state constraints are confirmed in probability. Simulation results are offered to further illustrate the effectiveness of the control scheme.     

An input–output linearization algorithm‐based control for optimization of DFIG

This paper proposes an input–output linearization‐based active power control strategy to maximize the energy production of a doubly fed induction generator (DFIG)‐based wind energy conversion system (WECS). The DFIG‐based wind turbine is a nonlinear system, and the nonlinear behavior will result in tracking errors. The proposed control strategy utilizing state feedback successfully deals with the nonlinear behavior existing in the WECS. Such a control will linearize the system input and output first. Then, the control loop and parameters can be designed by the linear system control algorithm. The simulations carried in MATLAB/Simulink demonstrate that the proposed control strategy is effective and promising. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.     

Real‐time identification of nonlinear multiple‐input–multiple‐output systems with unknown input time delay using Wiener model with Neuro‐Laguerre structure

In this article, a real‐time block‐oriented identification method for nonlinear multiple‐input–multiple‐output systems with input time delay is proposed. The proposed method uses the Wiener structure, which consists of a linear dynamic block (LDB) followed by a nonlinear static block (NSB). The LDB is described by the Laguerre filter lattice, whereas the NSB is characterized using the neural networks. Due to the online adaptation of the parameters, the proposed method can cope with the changes in the system parameters. Moreover, the convergence and bounded modeling error are shown using the Lyapunov direct method. Four practical case studies show the effectiveness of the proposed algorithm in the open‐loop and closed‐loop identification scenarios. The proposed method is compared with the recently published methods in the literature in terms of the modeling accuracy, parameter initialization, and required information from the system.     

An adaptive feedback linearized model predictive controller design for a nonlinear multi-input multi-output system

In this work, an adaptive feedback linearized model predictive control (AFLMPC) scheme is proposed to compensate system uncertainty for a class of nonlinear multi-input multi-output system. Initially, a feedback linearization technique is used to transform the nonlinear dynamics into an exact linear model, thereafter, a model predictive control scheme is designed to obtain the desired tracking performance. A suitable constraint mapping algorithm has been developed to map input constraints to the new virtual input of the proposed control scheme. The proposed control scheme utilizes multiple estimation model and the concept of second-level adaptation technique Pandey et al. (2014) to handle the parametric uncertainty in real-time. Hence, the adaptive term in the control scheme is used to counteract the effect of model uncertainties and parameter adaptation errors. The effectiveness of the proposed AFLMPC control algorithm has been verified successfully in simulation as well as the experimental setup of the TRMS model. The unavailable states of the nonlinear system have been estimated using an extended Kalman filter based state observer. The performance of the proposed control algorithm has been compared with other existing nonlinear control techniques in simulation and experimental validation.     

Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

In this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Convergence theory for multi‐input discrete‐time iterative learning control with Coulomb friction,continuous outputs,and input bounds

In this paper we consider the problem of discrete‐time iterative learning control (ILC) for position trajectory tracking of multiple‐input, multiple‐output systems with Coulomb friction, bounds on the inputs, and equal static and sliding coefficients of friction. We present an ILC controller and a proof of convergence to zero tracking error, provided the associated learning gain matrices are scalar‐scaled with a sufficiently small positive scalar. We also show that non‐diagonal learning gain matrices satisfying the same prescribed conditions do not lead to the same convergence property. To the best of our knowledge, for problems with Coulomb friction, this paper represents a first convergence theory for the discrete‐time ILC problem with multiple‐bounded‐inputs and multiple‐outputs; previous work presented theory only for the single‐input, single‐output problem. Copyright © 2004 John Wiley & Sons, Ltd.     

Learning‐based iterative modular adaptive control for nonlinear systems

In this paper, we study the problem of adaptive trajectory tracking control for a class of nonlinear systems with structured parametric uncertainties. We propose to use an iterative modular approach: we first design a robust nonlinear state feedback that renders the closed‐loop input‐to‐state stable (ISS). Here, the input is considered to be the estimation error of the uncertain parameters, and the state is considered to be the closed‐loop output tracking error. Next, we propose an iterative adaptive algorithm, where we augment this robust ISS controller with an iterative data‐driven learning algorithm to estimate online the parametric uncertainties of the model. We implement this method with two different learning approaches. The first one is a data‐driven multiparametric extremum seeking method, which guarantees local convergence results, and the second is a Bayesian optimization‐based method called Gaussian Process Upper Confidence Bound, which guarantees global results in a compact search set. The combination of the ISS feedback and the data‐driven learning algorithms gives a learning‐based modular indirect adaptive controller. We show the efficiency of this approach on a two‐link robot manipulator numerical example.     

Algorithms of adaptive tracking of unknown multisinusoidal signals in linear systems with arbitrary input delay

The problem of adaptive tracking control is addressed for the class of linear time‐invariant plants with known parameters and arbitrary known input delay. The reference signal is a priori unknown and is represented by a sum of biased harmonics with unknown amplitudes, frequencies, and phases. Asymptotic tracking is provided by predictive adjustable control with parameters generated by one of three designed adaptation algorithms. The first algorithm is based on a gradient scheme and ensures zero steady‐state tracking error with all signals bounded. The other two algorithms additionally involve the scheme with fast parametric convergence improving the closed‐loop system performance. In all the algorithms, the problem of delay compensation is resolved by special augmentation of tracking error. The adjustable control law proposed do not require identification of the reference signal parameters.