具有输入饱和的非线性关联大系统的分散控制

考虑了一类具有输入饱和的不确定非线性关联大系统的分散输出反馈鲁棒镇定问题,利用Riccati方程的方法和矩阵的Moore-Penrose逆给出了这类系统的一种分散输出反馈鲁棒镇定控制器的设计方法.同时,考虑了一类具有输入饱和的不确定非线性相似关联大系统,利用相似系统的结构特点,简化了分散输出反馈鲁棒镇定的条件.     

Decentralized adaptive tracking control of nonaffine nonlinear large-scale systems with time delays

This paper addresses the problem of decentralized tracking control of large-scale systems with uncertain nonaffine nonlinear isolated subsystems and nonlinear interconnections with time-varying delays. Based on Lyapunov-Krasovskii functional approach and implicit function theorem, a delay-independent decentralized tracking controller is proposed. Due to functional approximation capability of fuzzy logic systems (FLS), neither strict structure restrictions on the isolated subsystems nor a priori knowledge of the strong interconnections with time-varying delays is required in our control design. Furthermore, transient performance of the resulting closed-loop system is also addressed under an analytical framework. Finally, two numerical examples are provided to show the effectiveness of the proposed controller.     

Practical adaptive neural control of nonlinear systems with unknown time delays.

Practical adaptive neural control is presented for a class of nonlinear systems with unknown time delays in strict-feedback form. Using appropriate Lyapunov-Krasovskii functionals, the unknown time delays are compensated for. Controller singularity problems are solved by practical neural network control. A novel differentiable control function is provided such that the practical design can be carried out in the decoupled backstepping design. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed-loop system, and the tracking error is proven to converge to a small neighborhood of the origin.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Decentralized model reference adaptive control for interconnected systems with time-varying delays and unknown dead-zone inputs

In this study, the decentralized model reference adaptive control (DMRAC) problem is tackled for a class of time-varying delay interconnect systems that comprise unknown system matrices and unknown dead-zone inputs. Two robust adaptive control methods are proposed for state tracking based on the moderate matching time-varying delay nonlinear assumptions and the matching between the controlled system and reference model matrices, respectively. The control gain function is explicitly expressed, and it is applied to the adaptive law gains simultaneously. Moreover, a Lyapunov–Krasovskii functional with two integral functions is developed. Besides the properties of the type-B Nussbaum function, the circumstance where the system parameters are fully unknown is considered. As indicated by the results, all signals in the closed-loop system are bounded while fulfilling asymptotically tracked control objectives. The simulation example of this study verifies the effectiveness and feasibility of the proposed design method.     

Universal adaptive control of feedforward nonlinear systems with unknown input and state delays

This paper considers the problem of global asymptotic regulation via output feedback for a class of uncertain feedforward nonlinear systems with input and state delays, where the bounds of time delays are unknown. With the help of the high-gain scaling approach and the idea of universal adaptive control, we explicitly construct an adaptive output compensator with a novel positive dynamic gain which compensates simultaneously the unknown delays and the output growth rate with unknown constant. Based on such output compensator, we reduce the conservatism of the restrictive conditions imposed on nonlinearities to generalise the existing results. By the Lyapunov–Krasovskii theorem, a delay-independent controller design scheme is proposed to guarantee that all the closed-loop signals are globally bounded while rendering the states of original system and the estimate states to globally asymptotically converge to zero. Finally, two illustrative examples are given to show the usefulness of the proposed design method.     

Event-triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

This article is concerned with event-triggered adaptive tracking control design of strict-feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event-triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed-loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.     

具有动态不确定性互联大系统的分散自适应控制

对一类具有未建模动态结构相似形的严格反馈非线性互联大系统,提出一种基于神经网络的分散自适应动态面控制方案.该方案引入Lyapunov函数来约束未建模动态,利用神经网络逼近理论分析中所产生的未知非线性连续函数.通过Young’s不等式和三重求和项的分解,有效地处理了耦合作用项,并利用动态面控制技术,实现了系统的分散控制.与现有研究结果相比,所设计的分散控制律中不含有控制增益下界常数.通过构造的方法,利用动态面控制设计中引入的紧集有效地处理了未建模动态和分析中产生的不确定连续函数.理论分析证明了闭环控制系统中所有信号半全局一致终结有界,且跟踪误差收敛到原点的一个小邻域内.两个数值算例的仿真结果表明所提控制方案的有效性.     

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 neural network control of nonlinear systems with unknown time delays

In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.     

Decentralized adaptive stabilization of interconnected nonlinear systems with unknown non-symmetric dead-zone inputs

The decentralized adaptive stabilization method is proposed for uncertain interconnected nonlinear systems with unknown non-symmetric dead-zone inputs. The class of systems considered in this paper consists of strict-feedback nonlinear subsystems with unknown non-symmetric dead-zone inputs which interact through their outputs. The unknown nonlinear interaction terms are assumed to be bounded by nonlinear functions with unknown parameters. For the simple controller design, the local controller for each subsystem is systematically derived based on the dynamic surface design technique, without constructing the dead-zone inverse and requiring the bound information of dead-zone parameters (slopes and break-points). All unknown parameters of interconnected nonlinear systems are compensated by the adaptive technique. From Lyapunov stability theorem, it is proved that all signals in the interconnected closed-loop system with decentralized adaptive controllers are semi-globally bounded. Simulation results for tripled inverted pendulums demonstrate the effectiveness of the proposed approach.     

Adaptive neural control of stochastic nonlinear systems with multiple time-varying delays and input saturation

This paper investigates the problem of adaptive neural control for a class of strict-feedback stochastic nonlinear systems with multiple time-varying delays, which is subject to input saturation. Via the backstepping technique and the minimal learning parameters algorithm, the problem is solved. Based on the Razumikhin lemma and neural networks’ approximation capability, a new adaptive neural control scheme is developed. The proposed control scheme can ensure that the error variables are semi-globally uniformly ultimately bounded in the sense of four-moment, while all the signals in the closed-loop system are bounded in probability. Two simulation examples are provided to demonstrate the effectiveness of the proposed control approach.     

非线性互联系统的分散混合自适应智能控制

针对一类高阶互联MIMO非线性系统，利用TS模糊系统和神经网络的通用逼近能力，在神经网络控制器中引入模糊基函数，提出一种分散混合自适应智能控制器设计的新方案．基于等价控制思想，设计分散自适应控制器，无需计算TS模型．通过对不确定项进行自适应估计，取消了其存在已知上界的假设．通过理论分析，证明了闭环智能控制系统所有信号有界，跟踪误差收敛到零．     

Decentralized adaptive control for large-scale time-delay systems with dead-zone input

In this paper, a decentralized adaptive control scheme is proposed to address output tracking of a class of interconnected time-delay subsystems with the input of each loop preceded by an unknown dead-zone. Each local controller is designed using the backstepping technique and consists of a new robust control law and new updating laws. Unknown time-varying delays are compensated by using appropriate Lyapunov-Krasovskii functionals. Furthermore, by introducing a new smooth dead-zone inverse, the proposed backstepping design is able to eliminate the effects resulting from dead-zone nonlinearities in the input. It is shown that the proposed controller can guarantee not only stability, but also good transient performance.     

Decentralized tracking control for linear uncertain interconnected systems with time delays

This paper investigates the robust output tracking problem for a class of large‐scale linear uncertain systems with interactions and time delays. Time delays exist in both states and controls. Using the Riccati equation, a procedure for determining decentralized linear control laws is presented such that the closed‐loop system asymptotically tracks the reference output and rejects any constant but unknown disturbances. The main feature of this approach is that the uncertain systems may contain time delays in both states and controls as well as in interactions between subsystems. A numerical example is included to show the results. Copyright © 2008 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decentralized adaptive neural fixed-time tracking control of constrained interconnected nonlinear systems with partially unmeasurable states

This article devises a new adaptive fixed-time tracking control strategy for interconnected nonlinear systems containing partially unmeasurable states and time-varying output constraints. Radial basis function neural networks, as function approximators, are utilized to model the unknown functions, and the partially unmeasurable states of the systems are estimated by a reduced-order observer. By constructing a transferred function, system outputs are directly constrained in a time-varying constraint bound. Meanwhile, the first-order sliding mode differentiators are utilized to reduce the computational burden caused by the repeated differentiations of virtual controllers. Under the Lyapunov function and the fixed-time theory, the decentralized adaptive fixed-time controllers are constructed. It is proved that the closed-loop systems are fixed-time stable and the output signals are restricted in the bounded compact set. Finally, two simulation examples demonstrate the validity of the proposed control scheme.     

Globally decentralized adaptive backstepping neural network tracking control for unknown nonlinear interconnected systems

A globally stable decentralized adaptive backstepping neural network tracking control scheme is designed for a class of large‐scale systems with mismatched interconnections. Under the assumption that the subsystems share the reference signals from the other subsystems, neural networks are used to approximate the unknown interconnections dependent on all reference signals such that the NN approximation domain can be determined a priori based on the bounds of reference signals. The proposed control approach can guarantee that all closed‐loop signals are globally uniformly ultimately bounded and that the tracking errors converge to a small residual set around the origin. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Decentralized filtering adaptive constrained tracking control for interconnected nonlinear systems

This paper presents a novel decentralized filtering adaptive constrained tracking control framework for uncertain interconnected nonlinear systems. Each subsystem has its own decentralized controller based on the established decentralized state predictor. For each subsystem, a piecewise constant adaptive law will generate total uncertainty estimates by solving the error dynamics between the host system and decentralized state predictor with the neglection of unknowns, whereas a decentralized filtering control law is designed to compensate both local and mismatched uncertainties from other subsystems, as well as achieve the local objective tracking of the host system. The achievement of global objective depends on the achievement of local objective for each subsystem. In the control scheme, the nonlinear uncertainties are compensated for within the bandwidth of low‐pass filters, while the trade‐off between tracking and constraints violation avoidance is formulated as a numerical constrained optimization problem which is solved periodically. Priority is given to constraints violation avoidance at the cost of deteriorated tracking performance. The uniform performance bounds are derived for the system states and control inputs as compared to the corresponding signals of a bounded closed‐loop reference system, which assumes partial cancelation of uncertainties within the bandwidth of the control signal. Compared with model predictive control (MPC) and unconstrained controller, the proposed control architecture is capable of solving the tracking control problems for interconnected nonlinear systems subject to constraints and uncertainties.     

Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions

In this paper, the authors investigate a decentralized adaptive output-feedback controller design for large-scale nonlinear systems with input saturations and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems. This point is a main contribution of this paper compared with previous output-feedback control approaches which assume that the time-delayed bounding functions only depend on measurable output variables. The bounding functions are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique based on neural networks. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

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.