Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

纯反馈非线性离散系统的自适应神经网络控制

针对一类未知的纯反馈非线性离散系统,提出了基于反步法设计的自适应神经网络控制方法.为避免反步法设计中可能出现的因果矛盾问题,首先将系统进行等价变换,然后利用隐函数定理证实了理想虚拟控制输入和实际控制输入的存在性.利用高阶神经网络估计这些控制量,并基于反步法设计自适应神经网络控制系统,证明了闭环系统半全局一致最终有界.仿真结果验证了所提出方法的有效性.     

Adaptive neural network control for a class of uncertain nonlinear systems in pure-feedback form

A procedure is developed for the design of adaptive neural network controller for a class of SISO uncertain nonlinear systems in pure-feedback form. The design procedure is a combination of adaptive backstepping and neural network based design techniques. It is shown that, under appropriate assumptions, the solution of the closed-loop system is uniformly ultimately bounded.     

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.     

基于最小二乘算法及神经网络的非线性离散系统的自适应控制

针对有关文献所设计的控制律，在一较弱的条件下，去掉了符号运算部分，证明该控制律可避免“零除”问题，提高了运算速度。对于这种基于神经网络和LS算法的自适应控制问题，证明了系统状态落入一紧集中，闭环系统的所有信号都是有界的，且系统输出和参考输出之间的跟踪误差收敛于以零为原点的某一有界球中。     

Adaptive neural control of nonlinear MIMO systems with unknown time delays

In this paper, a novel adaptive NN control scheme is proposed for a class of uncertain multi-input and multi-output (MIMO) nonlinear time-delay systems. RBF NNs are used to tackle unknown nonlinear functions, then the adaptive NN tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The proposed controller guarantees uniform ultimate boundedness (UUB) of all the signals in the closed-loop system, while the tracking error converges to a small neighborhood of the origin. An advantage of the proposed control scheme lies in that the number of adaptive parameters for each subsystem is reduced to one, triple problems of “explosion of complexity”, “curse of dimension” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

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.     

Dissipative-based adaptive neural control for nonlinear systems

A dissipative-based adaptive neural control scheme was developed for a class of nonlinear uncertain systems with unknown nonlinearities that might not be linearly parameterized. The major advantage of the present work was to relax the requirement of matching condition, i.e., the unknown nonlinearities appear on the same equation as the control input in a state-space representation, which was required in most of the available neural network controllers. By synthesizing a state-feedback neural controller to make the closed-loop system dissipative with respect to a quadratic supply rate, the developed control scheme guarantees that the L2-gain of controlled system was less than or equal to a prescribed level. And then, it is shown that the output tracking error is uniformly ultimate bounded. The design scheme is illustrated using a numerical simulation.     

Adaptive neural network predictive control for nonlinear pure feedback systems with input delay

This paper presents an adaptive neural control design for nonlinear pure-feedback systems with an input time-delay. Novel state variables and the corresponding transform are introduced, such that the state-feedback control of a pure-feedback system can be viewed as the output-feedback control of a canonical system. An adaptive predictor incorporated with a high-order neural network (HONN) observer is proposed to obtain the future system states predictions, which are used in the control design to circumvent the input delay and nonlinearities. The proposed predictor, observer and controller are all online implemented without iterative predictive calculations, and the closed-loop system stability is guaranteed. The conventional backstepping design and analysis for pure-feedback systems are avoided, which renders the developed scheme simpler in its synthesis and application. Practical guidelines on the control implementation and the parameter design are provided. Simulation on a continuous stirred tank reactor (CSTR) and practical experiments on a three-tank liquid level process control system are included to verify the reliability and effectiveness.     

Adaptive motion control using neural network approximations

In this paper, we present a new adaptive technique for tracking control of mechanical systems in the presence of friction and periodic disturbances. Radial Basis Functions (RBFs) are used to compensate for the effects of nonlinearly occurring parameters in the friction and periodic disturbance model. Theoretical analysis, such as stability and transient performance, is provided. Furthermore, the performance of the adaptive RBF controller and its non-adaptive counterpart are compared.     

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 NN control for a class of strict-feedback discrete-time nonlinear systems

In this paper, both full state and output feedback adaptive neural network (NN) controllers are presented for a class of strict-feedback discrete-time nonlinear systems. Firstly, Lyapunov-based full-state adaptive NN control is presented via backstepping, which avoids the possible controller singularity problem in adaptive nonlinear control and solves the noncausal problem in the discrete-time backstepping design procedure. After the strict-feedback form is transformed into a cascade form, another relatively simple Lyapunov-based direct output feedback control is developed. The closed-loop systems for both control schemes are proven to be semi-globally uniformly ultimately bounded.     

Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems

An adaptive output feedback control methodology is developed for a class of uncertain multi-input multi-output nonlinear systems using linearly parameterized neural networks. The methodology can be applied to non-minimum phase systems if the non-minimum phase zeros are modeled to a sufficient accuracy. The control architecture is comprised of a linear controller and a neural network. The neural network operates over a tapped delay line of memory units, comprised of the system's input/output signals. The adaptive laws for the neural-network weights employ a linear observer of the nominal system's error dynamics. Ultimate boundedness of the error signals is shown through Lyapunov's direct method. Simulations of an inverted pendulum on a cart illustrate the theoretical results.     

块控非线性系统自适应神经网络控制

针对一类含有非匹配不确定性的块控型多输入多输出非线性系统,提出一种基于反演技术和RBF神经网络的控制系统设计方案.通过引入一种改进型的Lyapunov函数,避免了控制矩阵未知情况下可能出现的奇异问题.在控制系统设计过程中,充分应用鲁棒自适应控制技术,解决了多输入多输出结构不确定性所带来的设计难题,得到了系统所有状态量将全局指数收敛至原点附近一个邻域的结论.最后的仿真结果表明了设计方案的正确性.     

Neural-network adaptive controller for nonlinear systems and its application in pneumatic servo systems

In this paper, a novel control law is presented, which uses neural-network techniques to approximate the affine class nonlinear system having unknown or uncertain dynamics and noise disturbances. It adopts an adaptive control law to adjust the network parameters online and adds another control component according to H-infinity control theory to attenuate the disturbance. This control law is applied to the position tracking control of pneumatic servo systems. Simulation and experimental results show that the tracking precision and convergence speed is obviously superior to the results by using the basic BP-network controller and self-tuning adaptive controller.     

Adaptive neural control for MIMO nonlinear systems with state time-varying delay

In this paper,adaptive neural control is proposed for a class of multi-input multi-output(MIMO)nonlinear unknown state time-varying delay systems in block-triangular control structure.Radial basis function(RBF)neural networks (NNs)are utilized to estimate the unknown continuous functions.The unknown time-varying delays are compensated for using integral-type Lyapunov-Krasovskii functionals in the design.The main advantage of our result not only efficiently avoids the controller singularity,but also relaxes the restriction on unknown virtual control coefficients.Boundedness of all the signals in the closed-loop of MIMO nonlinear systems is achieved,while The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories.The feasibility is investigated by two simulation examples.     

一类非线性系统的自适应神经网络控制

针对一类具有非仿射函数和下三角结构的、受干扰未知的非线性系统,提出一种新的自适应神经网络控制方法．它是严格反馈不确定系统和纯反馈系统的更一般化表达．在Backstepping设计思想基础上,证明了闭环信号的半全局最终一致有界性,并很好地处理了控制方向和控制奇异问题．通过仿真验证了该方法的有效性．     

A neural network solution for fixed-final time optimal control of nonlinear systems

In this paper, fixed-final time optimal control laws using neural networks and HJB equations for general affine in the input nonlinear systems are proposed. The method utilizes Kronecker matrix methods along with neural network approximation over a compact set to solve a time-varying HJB equation. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated on an example.     

A neural network model predictive controller

A neural network controller is applied to the optimal model predictive control of constrained nonlinear systems. The control law is represented by a neural network function approximator, which is trained to minimize a control-relevant cost function. The proposed procedure can be applied to construct controllers with arbitrary structures, such as optimal reduced-order controllers and decentralized controllers.