一类非线性系统的自适应鲁棒输出反馈镇定

讨论了一类不确定非线性系统的鲁棒输出反馈镇定问题,其不确定性是部分已知 的.文中所得连续自适应鲁棒输出反馈控制器确保闭环系统终极一致有界.与已有文献结果 相比,关于未知参数估计的自适应律是连续的,而且闭环系统解的存在性在通常情况下能被 保证.进而,由于输出反馈控制器和自适应律的连续性,使得自适应鲁棒输出反馈控制器在 实际控制问题中易于实现,且使系统具有良好的品质.最后,通过数值算例进一步说明该文 的设计方案是有效的.     

Adaptive stabilizing state feedback controllers of uncertaindynamical systems with multiple time delays

The problem of robust stabilization for a class of uncertain dynamical systems with multiple delayed state perturbations is considered. In this paper, it is assumed that each perturbation is bounded by a linear function of delayed state with unknown gains, and an adaptation law is proposed to estimate these unknown gains. Moreover, by making use of the updated values of these unknown bounds we propose a memoryless state feedback controller for such a class of uncertain time-delay systems. Based on Lyapunov stability theory and Lyapunov-Krasovskii functional, it is shown that the closed-loop dynamical system resulting from the proposed adaptive robust control schemes is globally stable in the sense of uniform ultimate boundedness. Finally, a numerical example is given to demonstrate the validity of the results     

Decentralized adaptive neural control of nonlinear interconnected large-scale systems with unknown time delays and input saturation

In this paper, a novel decentralized adaptive neural control scheme is proposed for a class of interconnected large-scale uncertain nonlinear time-delay systems with input saturation. RBF neural networks (NNs) are used to tackle unknown nonlinear functions, then the decentralized adaptive NN tracking controller is constructed by combining Lyapunov–Krasovskii functions and the dynamic surface control (DSC) technique along with the minimal-learning-parameters (MLP) algorithm. The stability analysis subject to the effect of input saturation constrains are conducted with the help of an auxiliary design system based on the Lyapunov–Krasovskii method. The proposed controller guarantees uniform ultimate boundedness (UUB) of all the signals in the closed-loop large-scale system, while the tracking errors converge 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, and three problems of “computational explosion”, “dimension curse” and “controller singularity” are solved, respectively. Finally, a numerical simulation is presented to demonstrate the effectiveness and performance of the proposed scheme.     

Decentralised adaptive robust control of uncertain large-scale interconnected systems with multiple time-varying delays

The problem of decentralised adaptive robust stabilisation is considered for a class of uncertain large-scale time-delay interconnected dynamical systems. It is assumed that the upper bounds of the uncertainties, interconnection terms and external disturbances are unknown, and that the time-varying delays are any nonnegative continuous and bounded functions, and do not require that their derivatives have to be less than one. For such a class of uncertain large-scale time-delay interconnected systems, a new method is presented whereby a class of continuous memoryless decentralised local adaptive robust state feedback controllers is proposed. It is also shown that the solutions of uncertain large-scale time-delay interconnected systems can be guaranteed to be uniformly exponentially convergent towards a ball which can be as small as desired. In addition, since the proposed decentralised local adaptive robust state feedback controllers are completely independent of time delays, the results obtained in this article may also be applicable to a class of large-scale interconnected dynamical systems with uncertain time delays. Finally, a numerical example is given to demonstrate the validity of the results.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control 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.     

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.     

一类具有匹配时滞状态扰动的非线性系统自适应鲁棒镇定

讨论了一类具有时滞状态扰动的非线性系统的自适应鲁棒镇定问题,所考虑的时滞状态扰动的上界与时变函数相关并且含有未知参数.通过自适应律估计未知参数,并且利用估计值设计了鲁棒控制器.同时,基于Lyapunov_Krasovskii函数,证明了闭环系统具有一致最终有界意义下的鲁棒稳定性.最后,通过一个数值例子的仿真验证了结论的正确性.     

Adaptive fuzzy tracking control of nonlinear time-delay systems with unknown virtual control coefficients

In this paper, a novel adaptive fuzzy control scheme is proposed for a class of uncertain single-input and single-output (SISO) nonlinear time-delay systems with the lower triangular form. Fuzzy logic systems are used to approximate unknown nonlinear functions, then the adaptive fuzzy tracking controller is constructed by combining Lyapunov-Krasovskii functionals and the backstepping approach. The proposed controller guarantees uniform ultimate boundedness 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 is not more than the order of the systems under consideration. Finally, simulation studies are given to demonstrate the effectiveness of the proposed design scheme.     

数值界不确定性关联大系统分散鲁棒H∞控制

针对一类状态阵,控制输入阵及关联阵中存在数值界不确定性的关联大系统,研究其分散鲁棒H∞状态反馈和输出反馈控制器设计问题.基于有界实引理,推导出了其存在分散鲁棒H∞控制器的充分条件,即一组矩阵不等式有解.利用Schur补引理,通过固定不同变量,提出了一种构建分散控制器的同伦迭代线性矩阵不等式方法.所获得的控制器使闭环大系统鲁棒稳定,并且达到给定的H∞性能指标.最后用数值例子说明了所提的设计方法的有效性.     

Decentralized adaptive robust control for a class of large scale systems with uncertainties in the interconnections

The problem of decentralized control is considered for a class of time-varying large scale systems with uncertainties and external disturbances in the interconnections. In this paper, the upper bounds of the uncertainties and external disturbances are assumed to be unknown. The adaptation laws are proposed to estimate such unknown bounds, and by making use of the updated values of these unknown bounds, a class of decentralized linear and non-linear state feedback controllers are constructed. It is shown that by employing the proposed decentralized non-linear state feedback controllers, the solutions of the resulting adaptive closed-loop large scale system can be guaranteed to be uniformly bounded, and the states are uniformly asymptotically stable. By using the decentralized linear state feedback controllers, one can guarantee the uniform ultimate boundedness of the resulting adaptive closed-loop large scale system. Finally, a numerical example is given to demonstrate the validity of the results.     

一类非线性时滞大系统的自适应鲁棒控制

研究一类包含参数不确定性和关联时滞的不确定时滞组合大系统的鲁棒控制问题。利用线性矩阵不等式技术和自适应参数估计方法，设计鲁棒自适应控制器，从而保证闭环系统渐近稳定。最后给出了仿真示例，说明了该方法的有效性。     

Adaptive fuzzy robust tracking controller design via small gain approach and its application

An adaptive fuzzy robust tracking control (AFRTC) algorithm is proposed for a class of nonlinear systems with the uncertain system function and uncertain gain function, which are all the unstructured (or nonrepeatable) state-dependent unknown nonlinear functions arising from modeling errors and external disturbances. The Takagi-Sugeno type fuzzy logic systems are used to approximate unknown uncertain functions and the AFRTC algorithm is designed by use of the input-to-state stability approach and small gain theorem. The algorithm is highlighted by three advantages: 1) the uniform ultimate boundedness of the closed-loop adaptive systems in the presence of nonrepeatable uncertainties can be guaranteed; 2) the possible controller singularity problem in some of the existing adaptive control schemes met with feedback linearization techniques can be removed; and 3) the adaptive mechanism with minimal learning parameterizations can be obtained. The performance and limitations of the proposed method are discussed. The uses of the AFRTC for the tracking control design of a pole-balancing robot system and a ship autopilot system to maintain the ship on a predetermined heading are demonstrated through two numerical examples. Simulation results show the effectiveness of the control scheme.     

Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems

This paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities. The unknown nonlinearities comprise two types of nonlinear functions: one naturally satisfies the "triangularity condition" and can be approximated by linearly parameterized neural networks, while the other is assumed to be partially known and consists of parametric uncertainties and known "bounding functions." With the utilization of iterative Lyapunov design and neural networks, the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied. The design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural-network approximation errors. It is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed-loop system signals.. The control performance can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Adaptive neural control for a class of nonlinearly parametric time-delay systems

In this paper, an adaptive neural controller for a class of time-delay nonlinear systems with unknown nonlinearities is proposed. Based on a wavelet neural network (WNN) online approximation model, a state feedback adaptive controller is obtained by constructing a novel integral-type Lyapunov-Krasovskii functional, which also efficiently overcomes the controller singularity problem. It is shown that the proposed method guarantees the semiglobal boundedness of all signals in the adaptive closed-loop systems. An example is provided to illustrate the application of the approach.     

Adaptive feedforward and feedback control of non-linear time-varying uncertain systems

An adaptive regulation scheme is proposed for a class of non-linear time-varying systems with parametric uncertainties. The proposed approach is based upon a combination of the adaptive backstepping design method and a feedforward control scheme to design a non-linear adaptive feedforward and feedback controller, such that robust output tracking can be achieved even in the presence of structured uncertainties, as well as time-varying, measurable disturbances. Although the systematic design procedure does not a priori satisfy the feedback linearizable system with triangular structures, however, the constructed condition must be satisfied to ensure that the control scheme has a stable inversion. Under the feasibility condition, the states of the resulting closed-loop system would be guaranteed boundedness and converge to a bounded set. Finally, the proposed methodology is illustrated by a chemical reactor example.     

A combined backstepping and small-gain approach to robust adaptive fuzzy control for strict-feedback nonlinear systems

In this paper, a robust adaptive tracking control problem is discussed for a general class of strict-feedback uncertain nonlinear systems. The systems may possess a wide class of uncertainties referred to as unstructured uncertainties, which are not linearly parameterized and do not have any prior knowledge of the bounding functions. The Takagi-Sugeno type fuzzy logic systems are used to approximate the uncertainties. A unified and systematic procedure is employed to derive two kinds of novel robust adaptive tracking controllers by use of the input-to-state stability (ISS) and by combining the backstepping technique and generalized small gain approach. One is the robust adaptive fuzzy tracking controller (RAFTC) for the system without input gain uncertainty. The other is the robust adaptive fuzzy sliding tracking controller (RAFSTC) for the system with input gain uncertainty. Both algorithms have two advantages, those are, semi-global uniform ultimate boundedness of adaptive control system in the presence of unstructured uncertainties and the adaptive mechanism with minimal learning parameterizations. Four application examples, including a pendulum system with motor, a one-link robot, a ship roll stabilization with actuator and a single-link manipulator with flexible joint, are used to demonstrate the effectiveness and performance of proposed schemes.     

Robust adaptive neuro-fuzzy control of uncertain nonholonomic systems

In this paper, we present an adaptive neuro-fuzzy controller design for a class of uncertain nonholonomic systems in the perturbed chained form with unknown virtual control coefficients and strong drift nonlinearities. The robust adaptive neuro-fuzzy control laws are developed using state scaling and backstepping. Semiglobal uniform ultimate bound-edness of all the signals in the closed-loop are guaranteed, and the system states are proven to converge to a small neigh-borhood of zero. The control performance of the closed-loop system is guaranteed by appropriately choosing the design parameters. By using fuzzy logic approximation, the proposed control is free of control singularity problem. An adaptive control-based switching strategy is proposed to overcome the uncontrollability problem associated with x 0 (t 0 ) = 0.