Adaptive neural network dynamic surface control for perturbed nonlinear time-delay systems

This paper proposes an adaptive neural network control method for a class of perturbed strict-feedback nonlinear systems with unknown time delays. Radial basis function neural networks are used to approximate unknown intermediate control signals. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown time delay terms have been compensated. Dynamic surface control technique is used to overcome the problem of "explosion of complexity" in backstepping design procedure. In addition, the semiglobal uniform ultimate boundedness of all the signals in the closed-loop system is proved. A main advantage of the proposed controller is that both problems of "curse of dimensionality" and "explosion of complexity" are avoided simultaneously. Finally, simulation results are presented to demonstrate the effectiveness of the approach.     

Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

一类非线性切换系统的自适应神经动态面控制

针对一类严格反馈型不确定非线性切换系统,提出了一种鲁棒自适应神经动态面跟踪控制方案.该方案在基于共同Lyapunov函数的后推法设计中引入动态面控制(dynamic surface control,DSC)技术,利用径向基神经网络逼近构造的未知共同上界函数,并将滤波器输出导数取代传统中间变量作为神经网络输入,降低了网络输入维度;同时利用Young’s不等式技术有效减少了神经网络控制器的可调参数数目.此外,理论证明了该控制方案可以保证在任意切换下闭环系统所有信号半全局一致终结有界,且跟踪误差在有限时间收敛到零的小邻域内.实验结果表明了所提方法达到了很好的跟踪性能.     

Adaptive neural tracking control for a class of stochastic nonlinear systems

This paper investigates the problem of adaptive neural control design for a class of single‐input single‐output strict‐feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive ILC algorithms of nonlinear continuous systems with non-parametric uncertainties for non-repetitive trajectory tracking

In this article, two adaptive iterative learning control (ILC) algorithms are presented for nonlinear continuous systems with non-parametric uncertainties. Unlike general ILC techniques, the proposed adaptive ILC algorithms allow that both the initial error at each iteration and the reference trajectory are iteration-varying in the ILC process, and can achieve non-repetitive trajectory tracking beyond a small initial time interval. Compared to the neural network or fuzzy system-based adaptive ILC schemes and the classical ILC methods, in which the number of iterative variables is generally larger than or equal to the number of control inputs, the first adaptive ILC algorithm proposed in this paper uses just two iterative variables, while the second even uses a single iterative variable provided that some bound information on system dynamics is known. As a result, the memory space in real-time ILC implementations is greatly reduced.     

Adaptive output-feedback regulation for nonlinear delayed systems using neural network

A novel adaptive neural network （NN） output-feedback regulation algorithm for a class of nonlinear time-varying timedelay systems is proposed. Both the designed observer and controller are independent of time delay. Different from the existing results, where the upper bounding functions of time-delay terms are assumed to be known, we only use an NN to compensate for all unknown upper bounding functions without that assumption. The proposed design method is proved to be able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed system, and the system output is proved to converge to a small neighborhood of the origin. The simulation results verify the effectiveness of the control scheme.     

Adaptive neural network dynamic event-triggered control for strong interconnected stochastic nonlinear systems with output constraint

This paper proposes a dynamic event-triggered mechanism based command filtered adaptive neural network (NN) tracking control scheme for strong interconnected stochastic nonlinear systems with time-varying output constraints. By designing a state observer, the unmeasured states of the systems can be estimated. The NNs are utilized to handle the unknown intermediate functions. In the controller design process, the asymmetric time-varying barrier Lyapunov functions are used to guarantee that the systems outputs do not violate the constraint regions. By integrating the command filter with variable separation technique, the controller design process is more simple, and the problem of algebraic-loop can be solved which caused by interconnected functions. According to the Lyapunov stability theory, it can be ensured that all signals of the systems are bounded in probability. Finally, the availability of the developed control scheme can be showed by the simulation example.     

A novel optimal tracking control scheme for a class of discrete-time nonlinear systems using generalised policy iteration adaptive dynamic programming algorithm

In this paper, a novel iterative adaptive dynamic programming (ADP) algorithm, called generalised policy iteration ADP algorithm, is developed to solve optimal tracking control problems for discrete-time nonlinear systems. The idea is to use two iteration procedures, including an i-iteration and a j-iteration, to obtain the iterative tracking control laws and the iterative value functions. By system transformation, we first convert the optimal tracking control problem into an optimal regulation problem. Then the generalised policy iteration ADP algorithm, which is a general idea of interacting policy and value iteration algorithms, is introduced to deal with the optimal regulation problem. The convergence and optimality properties of the generalised policy iteration algorithm are analysed. Three neural networks are used to implement the developed algorithm. Finally, simulation examples are given to illustrate the performance of the present algorithm.     

Adaptive output feedback tracking control of stochastic nonlinear systems with dynamic uncertainties

In this paper, adaptive output feedback tracking control is developed for a class of stochastic nonlinear systems with dynamic uncertainties and unmeasured states. Neural networks are used to approximate the unknown nonlinear functions. K‐filters are designed to estimate the unmeasured states. An available dynamic signal is introduced to dominate the unmodeled dynamics. By combining dynamic surface control technique with backstepping, the condition in which the approximation error is assumed to be bounded is avoided. Using It ô formula and Chebyshev's inequality, it is shown that all 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 illustrate the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive neural output feedback tracking control for a class of nonlinear systems

In this paper, an adaptive neural output feedback control scheme based on backstepping technique and dynamic surface control (DSC) approach is developed to solve the tracking control problem for a class of nonlinear systems with unmeasurable states. Firstly, a nonlinear state observer is designed to estimate the unmeasurable states. Secondly, in the controller design process, radial basis function neural networks (RBFNNs) are utilised to approximate the unknown nonlinear functions, and then a novel adaptive neural output feedback tracking control scheme is developed via backstepping technique and DSC approach. It is shown that the proposed controller ensures that all signals of the closed-loop system remain bounded and the tracking error converges to a small neighbourhood around the origin. Finally, two numerical examples and one realistic example are given to illustrate the effectiveness of the proposed design approach.     

Observer-critic structure-based adaptive dynamic programming for decentralised tracking control of unknown large-scale nonlinear systems

In this paper, a decentralised tracking control (DTC) scheme is developed for unknown large-scale nonlinear systems by using observer-critic structure-based adaptive dynamic programming. The control consists of local desired control, local tracking error control and a compensator. By introducing the local neural network observer, the subsystem dynamics can be identified. The identified subsystems can be used for the local desired control and the control input matrix, which is used in local tracking error control. Meanwhile, Hamiltonian-Jacobi-Bellman equation can be solved by constructing a critic neural network. Thus, the local tracking error control can be derived directly. To compensate the overall error caused by substitution, observation and approximation of the local tracking error control, an adaptive robustifying term is employed. Simulation examples are provided to demonstrate the effectiveness of the proposed DTC scheme.     

Adaptive neural control for strict-feedback stochastic nonlinear systems with time-delay

The problem of robust stabilization is investigated for strict-feedback stochastic nonlinear time-delay systems via adaptive neural network approach. Neural networks are used to model the unknown packaged functions, then the adaptive neural control law is constructed by a novel Lyapunov-Krasovskii functional and backstepping. It is shown that all the variables in the closed-loop system are semi-globally stochastic bounded, and the state variables converge into a small neighborhood in the sense of probability.     

Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints

An adaptive neural tracking control is investigated for a class of nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints and saturation input. First, the continuous differentiable saturation model is employed to ensure the input constraint, and a barrier Lyapunov function is designed to achieve the full-state constraint. Second, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time-delay terms, and neural networks are employed to approximate the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive controller is proposed to guarantee 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 neighbourhood of the origin. Two examples are shown to further demonstrate the effectiveness of the proposed control scheme.     

Adaptive dynamic surface control for MIMO nonlinear time-varying systems with prescribed tracking performance

In this paper, an adaptive dynamic surface control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear time-varying systems. By fusing a bound estimation approach, a smooth function and a time-varying matrix factorisation, the obstacle caused by unknown time-varying parameters is circumvented. The proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step. Moreover, all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot. Such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

This paper contributes to dynamic surface asymptotic tracking for a class of uncertain nonlinear systems in strict‐feedback form. By utilizing the nonlinear filters with a positive time‐varying integral function, an adaptive state feedback controller is explicitly designed via a dynamic surface approach, where the compensating term with the estimate of an unknown bound is introduced to eliminate the effect raised by the boundary layer error at each step. Compared with the existing results in the literature, the proposed control scheme not only avoids the issue of “explosion of complexity” inherent in the backstepping procedure but also holds the asymptotic output tracking. Finally, simulation results are presented to verify the effectiveness of the proposed methodology.     

Adaptive neural network tracking control for uncertain nonlinear systems with input delay and saturation

In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

Adaptive L2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set.Moreover,the generalized matching conditions are also relaxed in the proposed L2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.     

非线性扩展结构大系统自适应神经网络跟踪控制

针对一类非线性关联大系统在结构扩展时的跟踪控制问题, 提出一种采用自适应神经网络的控制方法. 该方法要求在不改变原结构系统控制律的前提下设计新加入子系统的控制律和自适应律, 使扩展后所有子系统都具有很好的跟踪性能. 这里主要利用神经网络的逼近功能以及Backstepping 技术来设计自适应律和控制律, 通过Lyapunov 理论证明在该控制器的作用下闭环系统的所有信号均是有界的, 并可使系统准确跟踪. 仿真结果验证了所提出方法的有效性.

     

一类非线性系统基于Backstepping的自适应鲁棒神经网络控制

针对一类未知非线性系统提出了一种基于Backstepping的自适应神经网络控制方法, 放松了满足匹配条件, 要求神经网络逼近误差的边界已知等一些限制性的假设. 扩展了自适应backstepping和自适应神经控制的适用范围, 整个闭环系统表明是最终一致有界的, 跟踪误差收敛于原点的一个大小可调的邻域.