Adaptive output feedback control of nonlinear systems with actuator failures

In this paper, a modified adaptive actuator failure compensation scheme is proposed for a class of uncertain multi-input and single-output (MISO) nonlinear systems in the output-feedback form. We first establish a new parametric model with unknown plant parameters and actuator failure parameters, which differs from some existing results. Then, an adaptive compensation controller is constructed by utilizing the backstepping technique. The boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to zero asymptotically. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed design scheme.     

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.     

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

An adaptive neural network (NN)-based output feedback controller is proposed to deliver a desired tracking performance for a class of discrete-time nonlinear systems, which are represented in non-strict feedback form. The NN backstepping approach is utilized to design the adaptive output feedback controller consisting of: (1) an NN observer to estimate the system states and (2) two NNs to generate the virtual and actual control inputs, respectively. The non-causal problem encountered during the control design is overcome by using a dynamic NN which is constructed through a feedforward NN with a novel weight tuning law. The separation principle is relaxed, persistency of excitation condition (PE) is not needed and certainty equivalence principle is not used. The uniformly ultimate boundedness (UUB) of the closed-loop tracking error, the state estimation errors and the NN weight estimates is demonstrated. Though the proposed work is applicable for second order nonlinear discrete-time systems expressed in non-strict feedback form, the proposed controller design can be easily extendable to an nth order nonlinear discrete-time system.     

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.     

Novel adaptive neural control design for nonlinear MIMO time-delay systems

In this paper, we address the problem of adaptive neural control for a class of multi-input multi-output (MIMO) nonlinear time-delay systems in block-triangular form. Based on a neural network (NN) online approximation model, a novel adaptive neural controller is obtained by constructing a novel quadratic-type Lyapunov-Krasovskii functional, which not only efficiently avoids the controller singularity, but also relaxes the restriction on unknown virtual control coefficients. The merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks, which reduces the number of the online adaptive learning laws considerably. The proposed controller guarantees that all closed-loop signals remain bounded, while the output tracking error dynamics converges to a neighborhood of the origin. A simulation example is given to illustrate the design procedure and performance of the proposed method.     

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 fuzzy backstepping output feedback control of nonlinear uncertain systems with unknown virtual control coefficients using MT-filters

In this paper, an adaptive fuzzy output feedback control approach is developed for a class of SISO nonlinear uncertain systems with unmeasured states and unknown virtual control coefficients. The fuzzy logic systems are used to model the uncertain nonlinear systems. The MT-filters and the state observer are designed to estimate the unmeasured states. Using backstepping design principle and combining the Nussbaum gain functions, an adaptive fuzzy output feedback control scheme is developed. It is proved that the proposed adaptive fuzzy control approach can guarantee all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error converges to a small neighborhood of origin. A simulation is included to illustrate the effectiveness of the proposed approach.     

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.     

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.     

Adaptive L_2 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.     

非线性不确定系统的直接自适应输出反馈模糊控制

针对一类单输入单输出非线性不确定系统，基于状态观测器并结合自适应模糊系统和滑模控制，提出一种稳定的直接自适应模糊输出反馈控制算法。该算法不需要系统状态可测的条件，并能保证闭环系统稳定。仿真结果表明了该方法的有效性。     

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.     

Two results for adaptive output feedback stabilization of nonlinear systems

The problem of (adaptive) stabilization by means of output feedback of a class of nonlinear systems is addressed and solved. The proposed method relies on the asymptotic reconstruction of a stabilizing state feedback control law, does not require stable zero dynamics nor the construction of a Lyapunov function for the closed loop system, and treats in a unified way unknown parameters and unmeasured states. The applicability of the proposed method is discussed via theoretical examples. Finally, it is shown that the proposed method yields a solution to the problem of output feedback regulation for a DC-to-DC power converter and the efficacy of the resulting controller is verified via experiments.     

Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach

The problem of global state regulation via output feedback is investigated for uncertain nonlinear systems. The class of uncertain systems under consideration is assumed to be dominated by a bounding system which is linear growth in the unmeasurable states but can be a polynomial function of the system output, with unknown growth rates. To achieve global state regulation in the presence of parametric uncertainty, we propose a non-identifier based output feedback control scheme by employing the idea of universal control integrated with the design of a linear high-gain observer, whose gains are composed of two components, both of them are not constant and need to be dynamically updated. In particular, we explicitly design a universal output feedback controller which globally regulates all the states of the uncertain system while maintaining global boundedness of the closed-loop system.     

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.     

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.     

Output feedback adaptive DSC for nonlinear systems with guaranteed L-infinity tracking performance

In this paper, the problem of output tracking for a class of uncertain nonlinear systems is considered. First, neural networks are employed to cope with uncertain nonlinear functions, based on which state estimation is constructed. Then, an output feedback control system is designed by using dynamic surface control (DSC). To guarantee the L-infinity tracking performance, an initialization technique is presented. The main feature of the scheme is that explosion of complex- ity problem in backstepping control is avoided, and there is no need to update the unknown parameters including control gains as well as neural networks weights, the adaptive law with one update parameter is necessary only at the first design step. It is proved that all signals of the closed-loop system are semiglobally uniformly ultimately bounded and the L-infinity performance of system tracking error can be guaranteed. Simulation results demonstrate the effectiveness of the proposed scheme.     

Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.     

Adaptive output control of a class of uncertain chaotic systems

In this paper, a new observer-based backstepping output control scheme is proposed for stabilizing and controlling a class of uncertain chaotic systems. The controller is designed through the use of a robust observer and backstepping technique. We firstly show that many chaotic systems as paradigms in the research of chaos can be transformed into a class of nonlinear systems in the feedback form. Secondly, the synchronization problem is converted to the tracking problem from control theory, thereby leading to the use of state observer design techniques. A new observer is utilized to estimate the unmeasured states. Unlike some existing methods for chaos control, no priori knowledge on the system parameters is required and only the output signal is available for control purpose. The Lyapunov functions are quadratic in the state estimates, the observer errors and the parameter estimation error based on the backstepping technique. It is shown that not only global stability is guaranteed by the proposed controller, but also both transient and asymptotic tracking performances are quantified as explicit functions of the design parameters so that designers can tune the design parameters in an explicit way to obtain the desired closed-loop behavior.     

一种简化的自适应神经网络输出反馈镇定

针对一类输出反馈非线性时滞系统,提出一种简化的自适应神经网络镇定算法.所设计的状态观测器和控制器不依赖于时滞.不同于现有的结果,系统的时滞项假定完全未知,仅采用一个神经网络补偿所有未知非线性函数,因此控制器设计更加简单,而且最终的闭环系统被证明是半全局渐近稳定的.仿真结果进一步验证了该控制方案的有效性.