Adaptive output feedback control for nonlinear time-delay systems using neural network

This paper extends the adaptive neural network （NN） control approaches to a class of unknown output feedback nonlinear time-delay systems. An adaptive output feedback NN tracking controller is designed by backstepping technique. NNs are used to approximate unknown functions dependent on time delay, Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the NN approximation errors. Based on Lyapunov- Krasovskii functional, the semi-global uniform ultimate boundedness of all the signals in the closed-loop system is proved, The feasibility is investigated by two illustrative simulation examples.     

Adaptive NN output‐feedback decentralized stabilization for a class of large‐scale stochastic nonlinear strict‐feedback systems

In this paper, the decentralized adaptive neural network (NN) output‐feedback stabilization problem is investigated for a class of large‐scale stochastic nonlinear strict‐feedback systems, which interact through their outputs. The nonlinear interconnections are assumed to be bounded by some unknown nonlinear functions of the system outputs. In each subsystem, only a NN is employed to compensate for all unknown upper bounding functions, which depend on its own output. Therefore, the controller design for each subsystem only need its own information and is more simplified than the existing results. It is shown that, based on the backstepping method and the technique of nonlinear observer design, the whole closed‐loop system can be proved to be stable in probability by constructing an overall state‐quartic and parameter‐quadratic Lyapunov function. The simulation results demonstrate the effectiveness of the proposed control scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

非线性关联系统自适应神经网络输出反馈分散控制

针对一类带有完全未知关联项的非线性大系统,提出一种自适应神经网络输出反馈分散控制方法.采用神经网络逼近未知的关联项,因此对关联项常做的假设如匹配条件,被上界函数所界定等不再要求.在神经元输入中采用参考信号取代关联信号,从而成功地避免了对关联信号的微分.保证了闭环系统所有信号半全局一致最终有界,证明了跟踪误差收敛于一个包含原点的小残集.     

Passive Control for Stochastic Interval Systems with Interval Time‐Varying Delay

This paper is concerned with the problem of delay‐dependent passive analysis and control for stochastic interval systems with interval time‐varying delay. The system matrices are assumed to be uncertain within given intervals, and the time delay is a time‐varying continuous function belonging to a given range. By the transformation of the interval uncertainty into the norm‐bounded uncertainty, partitioning the delay into two segments of equal length, and constructing an appropriate Lyapunov–Krasovskii functional in each segment of the delay interval, delay‐dependent stochastic passive control criteria are proposed without ignoring any useful terms by considering the information of the lower bound and upper bound for the time delay. The main contribution of this paper is that a tighter upper bound of the stochastic differential of Lyapunov–Krasovskii functional is obtained via a newly‐proposed bounding condition. Based on the criteria obtained, a delay‐dependent passive controller is presented. The results are formulated in terms of linear matrix inequalities. Numerical examples are given to demonstrate the effectiveness of the method.     

Free-matrix-based integral inequality for stability analysis of uncertain T-S fuzzy systems with time-varying delay

This paper focuses on further improved stability criteria for uncertain T-S fuzzy systems with timevarying delay by delay-partitioning approach and Free-Matrix-based integral inequality. A modified augmented Lyapunov-Krasovskii functional (LKF) is established by partitioning the delay in all integral terms. Then, on the basis of taking into account the independent upper bounds of the delay derivative in various delay intervals, some new results on tighter bounding inequalities, such as Peng-Park’s integral inequality and the Free-Matrix-based integral inequality are employed to effectively reduce the enlargement in bounding the derivative of LKF, therefore, less conservative results can be expected in terms of e _s and LMIs. Finally, three numerical examples are included to show that the proposed method is less conservative than existing ones.     

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.     

一种稳定的机器人神经网络控制器研究

研究一种稳定的机器人神经网络（ＮＮ）控制器，提出了由神经网络控制器和监督控制器构成的控制方案，给出了控制器的设计方法及ＮＮ学习自适应律，并基于Ｌｙａｐｕｎｏｖ方法证明了控制系统的稳定性和ＮＮ参数收敛性，仿真结果表明该控制方案具有良好的鲁棒性和参数收敛性，从而证明控制器的有效性。     

Improved results for linear discrete-time systems with an interval time-varying input delay

This paper addresses the problem of delay-dependent stability analysis and controller synthesis for a discrete-time system with an interval time-varying input delay. By dividing delay interval into multiple parts and constructing a novel piecewise Lyapunov–Krasovskii functional, an improved delay-partitioning-dependent stability criterion and a stabilisation criterion are obtained in terms of matrix inequalities. Compared with some existing results, since a tighter bounding inequality is employed to deal with the integral items, our results depend on less number of linear matrix inequality scalar decision variables while obtaining same or better allowable upper delay bound. Numerical examples show the effectiveness of the proposed method.     

Online adaptive optimal control for continuous-time nonlinear systems with completely unknown dynamics

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.     

Adaptive Backstepping Sliding Mode Control of Tractor-trailer System with Input Delay Based on RBF Neural Network

In this paper, an adaptive sliding mode neural network(NN) control method is investigated for input delay tractor-trailer system with two degrees of freedom. An uncertain camera-object kinematic tracking error model of a tractor car with n trailers with input delay is proposed. Radial basis function neural networks(RBFNNs) are applied to approximate the unknown functions in the error model. A sliding mode surface with variable structure control is designed by using backstepping method. Then, an adaptive NN sliding mode control method is thus obtained by combining Lyapunov-Krasovskii functionals. The controller realizes the global asymptotic trajectories tracking of the kinematics system. The stability of the closed-loop system is strictly proved by the Lyapunov theory. Matlab simulation results demonstrate the feasibility of the proposed method.

     

Adaptive neural network control of bilateral teleoperation with unsymmetrical stochastic delays and unmodeled dynamics

In this paper, adaptive NN control is proposed for bilateral teleoperation system with dynamic uncertainties, unknown external disturbances, and unsymmetrical stochastic delays in communication channel to achieve transparency and robust stability. Compared with previous passivity‐based teleoperation framework, the communication delays are unsymmetrical and stochastic. By partial feedback linearization using nominal dynamics, the nonlinear dynamics of the teleoperation system are transformed into two subsystems: local master/slave dynamics control and time‐delay motion tracking. By integrating Markov jump systems and adaptive parameters updating, adaptive NN control strategy is developed. The stability of the closed‐loop system and the boundedness of tracking errors are proved using Lyapunov–Krasovskii functional synthesis under specific linear matrix inequalities conditions. The proposed adaptive NN control is robust against motion disturbances, parametric uncertainties, and unsymmetrical stochastic delay, which effectiveness is validated by extensive simulation studies. Copyright © 2013 John Wiley & Sons, Ltd.     

New absolute stability results for Lurie systems with interval time‐varying delay based on improved Wirtinger‐type integral inequality

This work focuses on the absolute stability problem of Lurie control system with interval time‐varying delay and sector‐bounded nonlinearity. Firstly, we present a refined Wirtinger's integral inequality and establish an improved Wirtinger‐type double integral inequality. Secondly, a modified augmented Lyapunov‐Krasovskii functional (LKF) is constructed to analyze the stability of Lurie system, where the information on the lower and upper bounds of the delay and the delay itself are fully exploited. Based on the proposed integral inequalities and some bounding techniques, the upper bound of the derivative of the LKF can be estimated more tightly. Accordingly, the proposed absolute stability criteria, formulated in terms of linear matrix inequalities, are less conservative than those in previous literature. Finally, numerical examples demonstrate the effectiveness and advantage of the proposed method.     

Adaptive tracking control of uncertain MIMO nonlinear systems with time-varying delays and unmodeled dynamics

In this paper, adaptive neural tracking control is proposed based on radial basis function neural networks (RBFNNs) for a class of multi-input multi-output (MIMO) nonlinear systems with completely unknown control directions, unknown dynamic disturbances, unmodeled dynamics, and uncertainties with time-varying delay. Using the Nussbaum function properties, the unknown control directions are dealt with. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown upper bound functions of the time-varying delay uncertainties are compensated. The proposed control scheme does not need to calculate the integral of the delayed state functions. Using Young s inequality and RBFNNs, the assumption of unmodeled dynamics is relaxed. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.     

Observer-based adaptive control for nonlinear input-delay systems with unknown control directions

This paper investigates the problem of adaptive control for strict-feedback nonlinear systems with input delay and unknown control directions. The Nussbaum function is utilised to deal with the unknown control directions and a novel compensation system is introduced to handle the time-varying input delay. By using neural network(NN) approximation and backstepping approaches, an adaptive NN controller is designed which can guarantee the semi-global boundedness of all the signals in the closed-loop system. Two simulation examples are also given to illustrate the effectiveness of the proposed method.     

未知输出反馈非线性时滞系统自适应神经网络跟踪控制

An adaptive output feedback neural network tracking controller is designed for a class of unknown output feedback nonlinear time-delay systems by using backstepping technique. Neural networks are used to approximate unknown time-delay functions. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the neural network reconstruction error. Based on Lyapunov-Krasoviskii functional, the semi-global uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop system is proved. The arbitrary output tracking accuracy is achieved by tuning the design parameters and the neural node number. The feasibility is investigated by an illustrative simulation example.     

Adaptive Neural Tracking Control for Unknown Output Feedback Nonlinear Time-delay Systems

An adaptive output feedback neural network tracking controller is designed for a class of unknown output feedback nonlinear time-delay systems by using backstepping technique.Neural networks are used to approximate unknown time-delay functions.Delay-dependent filters are intro- duced for state estimation.The domination method is used to deal with the smooth time-delay basis functions.The adaptive bounding technique is employed to estimate the upper bound of the neural network reconstruction error.Based on Lyapunov-Krasoviskii functional,the semi-global uniform ultimate boundedness(SGUUB)of all the signals in the closed-loop system is proved.The arbitrary output tracking accuracy is achieved by tuning the design parameters and the neural node number. The feasibility is investigated by an illustrative simulation example.     

A suite of robust controllers for the manipulation of microscale objects.

A suite of novel robust controllers is introduced for the pickup operation of microscale objects in a microelectromechanical system (MEMS). In MEMS, adhesive, surface tension, friction, and van der Waals forces are dominant. Moreover, these forces are typically unknown. The proposed robust controller overcomes the unknown contact dynamics and ensures its performance in the presence of actuator constraints by assuming that the upper bounds on these forces are known. On the other hand, for the robust adaptive critic-based neural network (NN) controller, the unknown dynamic forces are estimated online. It consists of an action NN for compensating the unknown system dynamics and a critic NN for approximating a certain strategic utility function and tuning the action NN weights. By using the Lyapunov approach, the uniform ultimate boundedness of the closed-loop manipulation error is shown for all the controllers for the pickup task. To imitate a practical system, a few system states are considered to be unavailable due to the presence of measurement noise. An output feedback version of the adaptive NN controller is proposed by exploiting the separation principle through a high-gain observer design. The problem of measurement noise is also overcome by constructing a reference system. Simulation results are presented and compared to substantiate the theoretical conclusions.     

Decentralized output-feedback neural control for systems with unknown interconnections.

An adaptive backstepping neural-network control approach is extended to a class of large-scale nonlinear output-feedback systems with completely unknown and mismatched interconnections. The novel contribution is to remove the common assumptions on interconnections such as matching condition, bounded by upper bounding functions. Differentiation of the interconnected signals in backstepping design is avoided by replacing the interconnected signals in neural inputs with the reference signals. Furthermore, two kinds of unknown modeling errors are handled by the adaptive technique. All the closed-loop signals are guaranteed to be semiglobally uniformly ultimately bounded, and the tracking errors are proved to converge to a small residual set around the origin. The simulation results illustrate the effectiveness of the control approach proposed in this correspondence.     

云存储多异构文件联合延迟尾概率凸优化分析

随着擦除码技术的流行,分布式存储中高数据可靠性和高空间效率存储性能逐渐实现,但是降低尾部延迟仍然是一个有待解决的问题。为此,提出一种量化和优化擦除编码存储系统尾延迟的算法框架。对于任意服务时间分布和异构文件,推导给出尾部延迟上界。提出了一个优化模型,使得所有文件在服务器上放置的加权延迟尾概率和访问请求文件的服务器选择共同最小化,并证明了其非凸问题特性,以便采用一种高效的交替优化算法求解。此外,通过描述延迟分布尾部的渐近行为,以闭合形式对任意擦除编码存储的服务延迟的尾部指数进行数学量化,证明了基于概率调度的算法是（渐近）最优的。实验结果表明,在实际工作负载下擦除编码存储系统的尾部延迟显著降低。