Reduced-order observer-based output feedback control of nonlinear time-delay systems with prescribed performance

This paper studies the problem of output feedback control for a class of nonlinear time-delay systems with prescribed performance. The system is in the form of triangular structure with unmodelled dynamics. First, we introduce a reduced-order observer to provide the estimate of the unmeasured states. Then, by setting a new condition with the performance function, we design the state transformation with prescribed performance control. By employing backstepping method, we construct the output feedback controller. It is proved that the resulting closed-loop system is asymptotically stable and both transient and steady-state performance of the output are preserved with the changing supply function idea. Finally, a simulation example is conducted to show the effectiveness of the main results.     

Robust adaptive prescribed performance control for a class of nonlinear pure‐feedback systems

An adaptive prescribed performance control design procedure for a class of nonlinear pure‐feedback systems with both unknown vector parameters and unmodeled dynamics is presented. The unmodeled dynamics lie within some bounded functions, which are assumed to be partially known. A state transformation and an auxiliary system are proposed to avoid using the cumbersome formula to handle the nonaffine structure. Simultaneously, a parameter‐type Lyapunov function and L function are designed to ensure the prescribed performance of the pure‐feedback system. As illustrated by examples, the proposed adaptive prescribed performance control scheme is shown to guarantee global uniform ultimate boundedness. At the same time, this method not only guarantees the prescribed performance of the system but also makes the tracking error asymptotically close to a certain value or stable.     

Robust adaptive quantized DSC of uncertain pure‐feedback nonlinear systems with time‐varying output and state constraints

In this paper, the problem of neural adaptive dynamic surface quantized control is studied the first time for a class of pure‐feedback nonlinear systems in the presence of state and output constraint and unmodeled dynamics. The considered system is under the control of a hysteretic quantized input signal. Two types of one‐to‐one nonlinear mapping are adopted to transform the pure‐feedback system with different output and state constraints into an equivalent unconstrained pure‐feedback system. By designing a novel control law based on modified dynamic surface control technique, many assumptions of the quantized system in early literary works are removed. The unmodeled dynamics is estimated by a dynamic signal and approximated based on neural networks. The stability analysis indicates that all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the output and all the states remain in the prescribed time‐varying or constant constraints. Two numerical examples with a coarse quantizer show that the proposed approach is effective for the considered system.     

Output‐feedback control strategies of lower‐triangular nonlinear nonholonomic systems in any prescribed finite time

In this paper, output‐feedback control strategies are proposed for lower‐triangular nonlinear nonholonomic systems in any prescribed finite time. Specifically, by employing the input‐state–scaling technique, the controlled systems are firstly converted into lower‐triangular nonlinear systems, which makes it possible to study such systems using the high‐gain technique. Then, by introducing a scaling of the state by a function that grows unbounded toward the terminal time and proposing a high‐gain observer–prescribed finite time recovering the system states, the output‐feedback regulation control problem in any prescribed finite time is firstly achieved for nonlinear nonholonomic systems with unknown constant incremental rate. Moreover, by designing another time‐varying high gain, the output‐feedback stabilization control problem in any prescribed finite time is then achieved for nonlinear nonholonomic systems with a time‐varying incremental rate. Finally, a numerical example is introduced to show the effectiveness of proposed control strategies.     

Improved prescribed performance control for nonaffine pure‐feedback systems with input saturation

This work considers an input and output constraint control problem for pure‐feedback systems with nonaffine functions possibly being in‐differentiable. A locally semibounded and continuous condition for nonaffine functions is presented to guarantee the controllability, and the nonaffine system is transformed to an equivalent pseudoaffine one based on the mild condition. Combined with backstepping technique, a novel prescribed performance controller with new performance functions is constructed to circumvent high frequency chattering in control input. An auxiliary system with bounded compensation term is utilized in this paper, successfully avoiding the overrun of control input. The methodology achieves the desired transient and steady‐state performance and presents excellent robustness against the system uncertainty. Finally, two numerical simulations are performed to demonstrate the effectiveness of the proposed approach.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Adaptive finite‐time neural backstepping control for multi‐input and multi‐output state‐constrained nonlinear systems using tangent‐type nonlinear mapping

This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of “explosion of complexity.” By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme.     

离散时间部分状态反馈模型参考自适应控制

本文针对线性不确定性系统, 给出了部分状态反馈直接模型参考自适应控制设计方案以及详细的系统稳 定性、输出跟踪性能分析. 控制器设计基于降维观测器和参数化方法. 此方案采用反馈控制, 反馈信号不仅仅依赖 全状态信息或者输出信号, 而是任意不超过系统维数的可测信号. 因此, 部分状态反馈控制是包含状态反馈、输出 反馈控制的新的控制方案, 缓解了状态反馈对状态信息的限制, 降低了输出反馈控制结构的复杂性. 通过引入辅助 信号, 本文证明了输出匹配条件的存在性、所有闭环系统信号的有界性以及渐近输出跟踪性能. 仿真结果验证了该 方案的有效性.     

On stabilization of decentralized dynamic output feedback systems

A dynamic output feedback law is presented for large scale interconnected systems. If the coupling terms between the subsystems are neglected, the control scheme can be interpreted as decentralized reconstruction of the state variables from the output of the subsystems. A class of systems stabilizable by decentralized state feedback is investigated. A sufficient condition is determined for systems to be stabilizable with local state feedback and reconstruction with observers of full order. The resulting closed-loop systems are connectively stable. Moreover, any prescribed degree of stability can be achieved and the closed-loop systems are robust with respect to bounded nonlinearities in the couplings between the subsystems.     

不确定状态滞后系统时滞相关鲁棒H∞控制

研究了不确定状态滞后系统的鲁棒H∞控制问题,假定参数不确定性时变未知但有 界.基于LMI方法,提出了一种新的鲁棒无记忆状态反馈H∞,控制器的设计方法,得出的结 论与时滞大小有关,相对于时滞无关的结论具有较少的保守性.     

基于神经网络的一类非线性系统自适应输出跟踪

针对一类未知非线性系统,提出了一种输出反馈控制方法.首先,在假设系统状态已 知情况下设计状态反馈控制器,实现跟踪性能;然后,在系统状态不完全可测的情况下,通过 设计高增益观测器对系统的状态进行估计,实现输出反馈控制器设计,证明了所设计的输出 反馈控制器可以获得状态反馈控制器的性能.     

含有不确定性的非线性互联系统的鲁棒分散H∞控制

讨论了含有不确定性非线性互联系统的鲁棒分散Ｈ∞控制问题,建立了鲁棒Ｈ∞控制之间的联系,在这种联系基础上,基于Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ不等式给出了含有不确定性互联系统的鲁棒分散Ｈ∞控制问题存在的充分条件,分别构造出状态反 输出反发散控制器以确保闭环系统从外部干扰输入到控制输出的Ｌ２增益小于或等于一预先给定的正数。     

A multivariable MRAC scheme with application to a nonlinear aircraft model

This paper revisits the multivariable model reference adaptive control (MRAC) problem, by studying adaptive state feedback control for output tracking of multi-input multi-output (MIMO) systems. With such a control scheme, the plant-model matching conditions are much less restrictive than those for state tracking, while the controller has a simpler structure than that of an output feedback design. Such a control scheme is useful when the plant-model matching conditions for state tracking cannot be satisfied. A stable adaptive control scheme is developed based on LDS decomposition of the high-frequency gain matrix, which ensures closed-loop stability and asymptotic output tracking. A simulation study of a linearized lateral-directional dynamics model of a realistic nonlinear aircraft system model is conducted to demonstrate the scheme. This linear design based MRAC scheme is subsequently applied to a nonlinear aircraft system, and the results indicate that this linearization-based adaptive scheme can provide acceptable system performance for the nonlinear systems in a neighborhood of an operating point.     

Prescribed performance adaptive neural output control for a class of switched nonstrict‐feedback nonlinear time‐delay systems: State‐dependent switching law approach

This paper investigates the tracking problem for a class of uncertain switched nonlinear delayed systems with nonstrict‐feedback form. To address this problem, by introducing a new common Lyapunov function (CLF), an adaptive neural network dynamic surface control is proposed. The state‐dependent switching rule is designed to orchestrate which subsystem is active at each time instance. In order to compensate unknown delay terms, an appropriate Lyapunov‐Krasovskii functional is considered in the constructing of the CLF. In addition, a novel switched neural network–based observer is constructed to estimate system states through the output signal. To maintain the tracking error performance within a predefined bound, a prescribed performance bound approach is employed. It is proved that by the proposed output‐feedback control, all the signals of the closed‐loop system are bounded under the switching law. Moreover, the transient and steady‐state tracking performance is guaranteed by the prescribed performance bound. Finally, the effectiveness of the proposed method is illustrated by two numerical and practical examples.     

Observer‐based adaptive robust control of a class of nonlinear systems with dynamic uncertainties

In this paper, a discontinuous projection‐based adaptive robust control (ARC) scheme is constructed for a class of nonlinear systems in an extended semi‐strict feedback form by incorporating a nonlinear observer and a dynamic normalization signal. The form allows for parametric uncertainties, uncertain nonlinearities, and dynamic uncertainties. The unmeasured states associated with the dynamic uncertainties are assumed to enter the system equations in an affine fashion. A novel nonlinear observer is first constructed to estimate the unmeasured states for a less conservative design. Estimation errors of dynamic uncertainties, as well as other model uncertainties, are dealt with effectively via certain robust feedback control terms for a guaranteed robust performance. In contrast with existing conservative robust adaptive control schemes, the proposed ARC method makes full use of the available structural information on the unmeasured state dynamics and the prior knowledge on the bounds of parameter variations for high performance. The resulting ARC controller achieves a prescribed output tracking transient performance and final tracking accuracy in the sense that the upper bound on the absolute value of the output tracking error over entire time‐history is given and related to certain controller design parameters in a known form. Furthermore, in the absence of uncertain nonlinearities, asymptotic output tracking is also achieved. Copyright © 2001 John Wiley & Sons, Ltd.     

Output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially-varying coefficients

This paper presents a backstepping solution for the output feedback control of general linear heterodirectional hyperbolic PDE-ODE systems with spatially varying coefficients. Thereby, the ODE is coupled to the PDE in-domain and at the uncontrolled boundary, whereas the ODE is coupled with the latter boundary. For the state feedback design, a two-step backstepping approach is developed, which yields the conventional kernel equations and additional decoupling equations of simple form. In order to implement the state feedback controller, the design of observers for the PDE-ODE systems in question is considered, whereby anti-collocated measurements are assumed. Exponential stability with a prescribed convergence rate is verified for the closed-system pointwise in space. The resulting compensator design is illustrated for a 4 × 4 heterodirectional hyperbolic system coupled with a third-order ODE modelling a dynamic boundary condition.     

Semi-global output regulation for linear systems with input saturation by composite nonlinear feedback control

To improve transient performance of output response, this paper applies composite nonlinear feedback (CNF) control technique to investigate semi-global output regulation problems for linear systems with input saturation. Based on a linear state feedback control law for a semi-global output regulation problem, a state feedback CNF control law is constructed by adding a nonlinear feedback part. The extra nonlinear feedback part can be applied to improve the transient performance of the closed-loop system. Moreover, an observer is designed to construct an output feedback CNF control law that also solves the semi-global output regulation problem. The sufficient solvability condition of the semi-global output regulation problem by CNF control is the same as that by linear control, but the CNF control technique can improve the transient performance. The effectiveness of the proposed method is illustrated by a disturbance rejection problem of a translational oscillator with rotational actuator system.     

Robust estimation‐free decentralized prescribed performance control of nonaffine nonlinear large‐scale systems

In this paper, a low‐complexity robust estimation‐free decentralized prescribed performance control scheme is proposed and analyzed for nonaffine nonlinear large‐scale systems in the presence of unknown nonlinearity and external disturbance. To tackle the high‐order dynamics of each tracking error subsystem, a time‐varying stable manifold involving the output tracking error and its high‐order derivatives is constructed, which is strictly evolved within the envelope of user‐specialized prescribed performance. Sequentially, a robust decentralized controller is devised for each manifold, under which the output tracking error and its high‐order derivatives are proven to converge asymptotically to a small residual domain with prescribed fast convergence rate. Additionally, no specialized approximation technique, adaptive scheme, and disturbance observer are needed, which alleviates the complexity and difficulty of robust decentralized controller design dramatically. Finally, 3 groups of illustrative examples are used to validate the effectiveness of the proposed low‐complexity robust decentralized control scheme for uncertain nonaffine nonlinear large‐scale systems.     

Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems

Two robust adaptive control schemes for single-input single-output (SISO) strict feedback nonlinear systems possessing unknown nonlinearities, capable of guaranteeing prescribed performance bounds are presented in this paper. The first assumes knowledge of only the signs of the virtual control coefficients, while in the second we relax this assumption by incorporating Nussbaum-type gains, decoupled backstepping and non-integral-type Lyapunov functions. By prescribed performance bounds we mean that the tracking error should converge to an arbitrarily predefined small residual set, with convergence rate no less than a prespecified value, exhibiting a maximum overshoot less than a sufficiently small prespecified constant. A novel output error transformation is introduced to transform the original “constrained” (in the sense of the output error restrictions) system into an equivalent “unconstrained”one. It is proven that the stabilization of the “unconstrained” system is sufficient to solve the problem. Both controllers are smooth and successfully overcome the loss of controllability issue. The fact that we are only concerned with the stabilization of the “unconstrained” system, severely reduces the complexity of selecting both the control parameters and the regressors in the neural approximators. Simulation studies clarify and verify the approach.     

Non-smooth state feedback prescribed performance control for interconnected nonlinear systems with unmodelled dynamics

This paper investigates the problem of non-smooth state feedback control for a group of high-order p-normal form interconnected nonlinear systems with prescribed performance. Each subsystem is in the form of triangular structure with the unmodelled dynamics. With the help of appropriate Lyapunov function, a state feedback controller is constructed via backstepping method. It is strictly proved that the closed-loop system is asymptotically stable and both transient and steady-state performances of the outputs are preserved. Finally, simulation results are presented to illustrate the effectiveness of proposed method.