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 backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Stochastic high‐order internal model‐based adaptive TILC with random uncertainties in initial states and desired reference points

Many practical batch processes operate repetitively in industry and lack intermediate measurements for the interested process variables. Moreover, the initial states as well as the desired product objective often vary with different runs because of the existence of many uncertainties in practice. This work proposes a novel adaptive terminal iterative learning control method to deal with random uncertainties in desired terminal points and initial states. The run‐varying initial states are formulated by a stochastic high‐order internal model, which is further incorporated into the controller design. The desired terminal output is run dependent and is directly compensated like a feedback term in the controller. Only the system output at the endpoint of an operation is utilized to update the control signal. An estimation algorithm is designed to update the system Markov parameters as a whole. No explicit model information is involved in the controller design; thus, the proposed method is data driven and can be applied to nonlinear systems directly. Both the theoretical analysis and the simulation studies demonstrate the effectiveness of the proposed approach under random initial states and iteration‐varying referenced terminal points. Copyright © 2016 John Wiley & Sons, Ltd.     

Maximum power extraction on wind turbine systems using block‐backstepping with gradient dynamics control

In this work, a novel adaptive control scheme that allows driving a stand‐alone variable‐speed wind turbine system to its maximum power point is presented. The scheme is based on the regulation of the optimal rotor speed point of the wind turbine. In order to compute the rotor speed reference, a model‐based extremum‐seeking algorithm is derived. The wind speed signal is necessary to calculate this reference, and a novel artificial neural network is derived to approximate this signal. The neural network does not need off‐line learning stage, because a nonlinear dynamics for the weight vector is proposed. A block‐backstepping controller is derived to stabilize and to drive the system to the optimal power point; to avoid singularities, the gradient dynamics technique is applied to this controller. Numerical simulations are carried out to show the performance of the controller and the estimator. Copyright © 2016 John Wiley & Sons, Ltd.     

A new decoupling design of self‐tuning multivariable generalized predictive control

A novel robust decoupling method with multivariable generalized predictive control (MGPC) for a class of nonlinear systems is presented in an adaptive version. The cross‐coupling action and the non‐linear actors of the system are identified on‐line by a neural network. A feedforward compensation based on generalized predictive control, is proposed for decoupling control. A modified recursive least‐squares (RLS) algorithm can be used to estimate the linear parameters for time‐varying systems. Simulations are carried out and the results show the effectiveness of the proposed algorithm. Copyright © 1999 John Wiley & Sons, Ltd.     

Adaptive neural finite-time output-feedback tracking control for nonlinear stochastic nonstrict-feedback systems with input saturation

In this paper, an observer-based adaptive neural output-feedback control scheme is developed for a class of nonlinear stochastic nonstrict-feedback systems with input saturation in finite-time interval. The mean value theorem and the property of the smooth function are applied to cope with the difficulties caused by the existence of input saturation. According to the universal approximation capability of the radial basis function neural network, it will be utilized to compensate the unknown nonlinear functions. Based on the state observer, the finite-time Lyapunov stability theorem, we propose an adaptive neural output-feedback control scheme for nonlinear stochastic systems in nonstrict-feedback form. The developed controller guarantees that the system output signal can track the given reference signal trajectory, and all closed-loop signals are semi-globally finite-time stability in probability. The observer errors and the tracking error can converge to a small neighborhood of the origin. Finally, simulation results demonstrate the effectiveness of the developed control scheme.     

Prescribed performance adaptive fuzzy dynamic surface control of nonaffine time‐varying delayed systems with unknown control directions and dead‐zone input

In this paper, an adaptive prescribed performance control method is presented for a class of uncertain strict feedback nonaffine nonlinear systems with the coupling effect of time‐varying delays, dead‐zone input, and unknown control directions. Owing to the universal approximation property, fuzzy logic systems are used to approximate the uncertain terms in the system. Since there is no systematic approach to determine the required upper bounds of errors in control systems, the prior selection of control parameters to have a satisfactory performance is somehow impossible. Therefore, the prescribed performance technique as a solution is applied in this study to bring satisfactory performance indices to the system such as overshoot and steady state performance within a predetermined bound. Dynamic surface control strategy is also introduced to the proposed control scheme to address the “explosion of complexity” behavior existing in conventional backstepping methods. To ease the control design, the mean‐value theorem is utilized to transform the nonaffine system into the affine one. Moreover, with the help of this theorem, the unknown dead‐zone nonlinearity is separated into the linear and nonlinear disturbance‐like bounded term. The proposed method relaxes a prior knowledge of control direction by employing Nussbaum‐type functions, and the effect of time‐varying delays are compensated by constructing the proper Lyapunov‐Krasovskii functions. The proposed controller guarantees that all the closed‐loop signals are semiglobally uniformly ultimately bounded and the error evolves within the decaying prescribed bounds. In the end, in order to demonstrate the superiority of this method, simulation examples are given.     

基于模型参考的神经网络自适应控制器

在过去30年,线性系统理论为经典控制的发展作出了巨大贡献。文章提供了一种能用于非线性动态系统控制的控制策略,其中的自适应设计可以解决时变系统的控制问题。文章提出的基于参考模型的神经网络结构可以用于线性、非线性系统的自适应控制,并且在线性仿真系统环境对该神经网络控制器进行了测试。     

Passivity‐based control for stabilization,regulation and tracking purposes of a class of nonlinear systems

In this paper, a new passivity‐based control (PBC) scheme based on state feedback is proposed in order to solve tracking, regulation and stabilization problems for a class of multi‐input multi‐output (MIMO) nonlinear systems expressed in the normal form, with time‐invariant parameters and locally bounded reference weakly minimum phase. For the proposed control scheme two new different state feedbacks, one non‐adaptive for the case when the system parameters are assumed to be known and the other adaptive for the case of unknown parameters, are developed. For the adaptive case it is assumed that the unknown parameters appear linearly in the equations. Analysis of the transient behaviour of the proposed control schemes is presented through the simulation of two examples. Copyright © 2006 John Wiley & Sons, Ltd.     

Iterative learning control for non‐repetitive trajectory tracking of robot manipulators with joint position constraints and actuator faults

In this work, we present a novel iterative learning control (ILC) scheme for a class of joint position constrained robot manipulator systems with both multiplicative and additive actuator faults. Unlike most ILC literature that requires identical reference trajectory from trail to trail, in this work the reference trajectory can be non‐repetitive over the iteration domain without assuming the identical initial condition. A tan‐type Barrier Lyapunov Function is proposed to deal with the constraint requirements which can be both time and iteration varying, with ILC update laws adopted to learn the iteration‐invariant system uncertainties, and robust methods used to compensate the iteration and time varying actuator faults and disturbances. We show that under the proposed ILC scheme, uniform convergence of the full state tracking error beyond a small time interval in each iteration can be guaranteed over the iteration domain, while the constraint requirements on the joint position vector will not be violated during operation. An illustrative example on a two degree‐of‐freedom robotic manipulator is presented to demonstrate the effectiveness of the proposed control scheme. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

Decentralized adaptive control of nonlinear large‐scale pure‐feedback interconnected systems with time‐varying delays

In this paper, an adaptive decentralized neural control problem is addressed for a class of pure‐feedback interconnected system with unknown time‐varying delays in outputs interconnections. By taking advantage of implicit function theorem and the mean‐value theorem, the difficulty from the pure‐feedback form is overcome. Under a wild assumption that the nonlinear interconnections are assumed to be bounded by unknown nonlinear functions with outputs, the difficulties from unknown interconnections are dealt with, by introducing continuous packaged functions and hyperbolic tangent functions, and the time‐varying delays in interconnections are compensated by Lyapunov–Krasovskii functional. Radial basis function neural network is used to approximate the unknown nonlinearities. Dynamic surface control is successfully extended to eliminate ‘the explosion of complexity’ problem in backstepping procedure. To reduce the computational burden, minimal learning parameters technique is successfully incorporated into this novel control design. A delay‐independent decentralized control scheme is proposed. With the adaptive neural decentralized control, only one estimated parameter need to be updated online for each subsystem. Therefore, the controller is more simplified than the existing results. Also, semiglobal uniform ultimate boundedness of all of the signals in the closed‐loop system is guaranteed. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

A small‐gain approach for adaptive output‐feedback NN control of switched pure‐feedback nonlinear systems

This paper investigates the problem of adaptive output‐feedback neural network (NN) control for a class of switched pure‐feedback uncertain nonlinear systems. A switched observer is first constructed to estimate the unmeasurable states. Next, with the help of an NN to approximate the unknown nonlinear terms, a switched small‐gain technique‐based adaptive output‐feedback NN control scheme is developed by exploiting the backstepping recursive design scheme, input‐to‐state stability analysis, the common Lyapunov function method, and the average dwell time (ADT) method. In the recursive design, the difficulty of constructing an overall Lyapunov function for the switched closed‐loop system is dealt with by decomposing the switched closed‐loop system into two interconnected switched systems and constructing two Lyapunov functions for two interconnected switched systems, respectively. The proposed controllers for individual subsystems guarantee that all signals in the closed‐loop system are semiglobally, uniformly, and ultimately bounded under a class of switching signals with ADT, and finally, two examples illustrate the effectiveness of theoretical results, which include a switched RLC circuit system.     

Adaptive variable universe of discourse fuzzy control for a class of nonlinear systems with unknown dead zones

In this paper, based on an adaptive nonbackstepping design algorithm, we proposed a novel variable universe of discourse fuzzy control (VUDFC) approach for a class of single‐input–single‐output strict‐feedback nonlinear systems with unknown dead‐zone inputs. Firstly, we convert the form of system into a normal form on the basis of some new state variables and coordinate transformation; at the same time, state‐feedback control is changed to output‐feedback control. Secondly, we design observers to estimate the new unmeasurable states. Then, different from considering the traditional backstepping‐based fuzzy control scheme, we introduce a direct VUDFC scheme, which is mainly based on changing of contraction‐expansion factors to modify the universe of discourse online, and fuzzy rules can automatically reproduce to develop the control performance; thus, the size of initial rule base is greatly reduced. This new algorithm can alleviate tracking error, improve the accuracy of the system, and strengthen robustness. Lastly, according to Lyapunov theorem analysis, we prove that all the signals in the closed‐loop system can be guaranteed to be stable, and the output can track the reference signal very well. Simulation results illustrated the effectiveness of the proposed VUDFC approach.     

Adaptive neural network command filtered backstepping control of pure‐feedback systems in presence of full state constraints

An adaptive neural network (NN) command filtered backstepping control is proposed for the pure‐feedback system subjected to time‐varying output/stated constraints. By introducing a one‐to‐one nonlinear mapping, the obstacle caused by full stated constraints is conquered. The adaptive control law is constructed by command filtered backstepping technology and radial basis function NNs, where only one learning parameter needs to be updated online. The stability analysis via nonlinear small‐gain theorem shows that all the signals in closed‐loop system are semiglobal uniformly ultimately bounded. The simulation examples demonstrate the effectiveness of the proposed control scheme.     

Active fault tolerant control of piecewise affine systems with reference tracking and input constraints

An active fault tolerant control (AFTC) method is proposed for discrete‐time piecewise affine (PWA) systems. Only actuator faults are considered. The AFTC framework contains a supervisory scheme, which selects a suitable controller in a set of controllers such that the stability and an acceptable performance of the faulty system are held. The design of the supervisory scheme is not considered here. The set of controllers is composed of a normal controller for the fault‐free case, an active fault detection and isolation controller for isolation and identification of the faults, and a set of passive fault tolerant controllers (PFTCs) modules designed to be robust against a set of actuator faults. In this research, the piecewise nonlinear model is approximated by a PWA system. The PFTCs are state feedback laws. Each one is robust against a fixed set of actuator faults and is able to track the reference signal while the control inputs are bounded. The PFTC problem is transformed into a feasibility problem of a set of LMIs. The method is applied on a large‐scale live‐stock ventilation model. Copyright © 2013 John Wiley & Sons, Ltd.     

Self‐recurrent wavelet neural network–based identification and adaptive predictive control of nonlinear dynamical systems

In this paper, the problem of simultaneous identification and predictive control of nonlinear dynamical systems using self‐recurrent wavelet neural network (SRWNN) is addressed. The structure of the SRWNN is a modification of the wavelet neural network (WNN). Unlike WNN, the neurons present in the hidden layer of SRWNN contain the weighted self‐feedback loops. Dynamic back‐propagation algorithm is employed to derive the necessary parameter update equations. To further improve the convergence speed of the parameters, a time‐varying (adaptive) learning rate is used. Four simulation examples are considered for testing the effectiveness of the proposed method. Furthermore, some disturbance rejection tests are also performed on the proposed method. The results obtained through the simulation study confirm the effectiveness of the proposed method.     

Intelligent control using multiple models and neural networks

Most adaptive control algorithms for nonlinear discrete time systems become invalid when the controlled systems have non‐minimum phase properties and large uncertainties. In this paper, an intelligent control method using multiple models and neural networks (NN) is developed to deal with those problems. The proposed control method includes a set of fixed controllers, a re‐initialized neural network (NN) adaptive controller and a free‐running NN adaptive controller. The bounded‐input‐bounded‐output (BIBO) stability and performance convergence of the system are guaranteed by the free‐running adaptive controller, while the multiple fixed controllers and the re‐initialized adaptive controller are used to improve the transient response. Simulation results are presented to demonstrate the effectiveness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive neural dynamic surface control of MIMO nonlinear time delay systems with time‐varying actuator failures

In this paper, an adaptive dynamic surface control approach is developed for a class of multi‐input multi‐output nonlinear systems with unknown nonlinearities, bounded time‐varying state delays, and in the presence of time‐varying actuator failures. The type of the considered actuator failure is that some unknown inputs may be stuck at some time‐varying values where the values, times, and patterns of the failures are unknown. The considered actuator failure can cover most failures that may occur in actuators of the systems. With the help of neural networks to approximate the unknown nonlinear functions and combining the dynamic surface control approach with the backstepping design method, a novel control approach is constructed. The proposed design method does not require a priori knowledge of the bounds of the unknown time delays and actuator failures. The boundedness of all the closed‐loop signals is guaranteed, and the tracking errors are proved to converge to a small neighborhood of the origin. The proposed approach is employed for a double inverted pendulums benchmark as well as a chemical reactor system. The simulation results show the effectiveness of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.     

On the terminal region of model predictive control for non‐linear systems with input/state constraints

This paper addresses the terminal region of model‐based predictive control (MPC) for non‐linear systems with control input and state constraints. Based on a stability condition of non‐linear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilizing control law to enlarge the terminal region and thus the domain of attraction of the non‐linear MPC is proposed. An LMI based optimization approach is developed to choose the terminal weighting item and fictitious terminal stabilizing control law so as to enlarge the terminal region of the non‐linear MPC method. The proposed method is illustrated by a numerical example and compares favourably with existing results. Copyright © 2003 John Wiley & Sons, Ltd.