基于输出反馈的非完整链式系统跟踪控制研究

针对非完整链式系统设计了基于输出反馈的全局跟踪控制律. 首先, 利用时变坐标变换和非自治系统的级联控制方法构造了状态观测器;然后对于时变坐标变换以后的误差系统继续利用非自治系统的级联控制方法设计了输出跟踪控制律. 区别于已有文献对于非完整链式系统跟踪控制问题的研究, 设计得到的输出跟踪控制律放松了参考轨迹所必需满足的不趋于零条件或持续激励条件. 结论表明在非完整链式系统跟踪控制问题 的研究中, 参考轨迹所必须满足的不趋于零的条件或者持续激励条件是不必要的. 最后的仿真结果验证了所给控制方法的有效性.     

Time‐varying linear controllers for exponential tracking of non‐holonomic systems in chained form

In this paper, the authors address the tracking problem for non‐holonomic systems in chained form with target signals that may exponentially decay to zero. By introducing a time‐varying co‐ordinate transformation and using the cascade‐design approach, smooth time‐varying controllers are constructed, which render the tracking‐error dynamics globally ??‐exponentially stable. The result shows that the popular condition of persistent excitation or not converging to zero for the reference signals is not necessary even for the globally ??‐exponential tracking of the chained‐form system. The effectiveness of the proposed controller is validated by simulation of two benchmark mechanical systems under non‐holonomic constraints. Copyright © 2006 John Wiley & Sons, Ltd.     

Global adaptive tracking for a class of nonlinear time-delay systems

This paper aims to extend the newly developed global adaptive regulation scheme to adaptive tracking for a general class of nonlinear systems with both parameter uncertainties and unknown time delay for all the system states. With a simple yet novel decomposition of some coupling functions derived from the introduction of a reference signal, a backstepping tracking control strategy is proposed which possesses the feature that for each design step, a dynamic gain is introduced to generate an additional term to counteract the system nonlinearities and parameter uncertainties. As a result, a memoryless adaptive state-feedback controller is obtained to achieve the global adaptive tracking.     

基于LMI的分布时滞系统输出动态反馈镇定

研究分布时滞系统的输出动态反馈镇定问题. 基于闭环系统的中立型变换及相应Lyapunov-Krasovskii泛函的构造与解析技巧, 建立了与时滞相关的控制器存在性判据. 在此基础上通过控制器参数化设计方法, 将控制器参数的求解归结为线性矩阵不等式解的形式. 仿真算例验证了方法的有效性     

Global asymptotic tracking for nonminimum‐phase nonlinear systems in output feedback form

The problem of global asymptotic tracking by output feedback is studied for a class of nonminimum‐phase nonlinear systems in output feedback form. It is proved that the problem is solvable by an n‐dimensional output feedback controller under the two conditions: (a) the nonminimum‐phase nonlinear system can be rendered minimum‐phase by a virtual output; and (b) the internal dynamics of the nonlinear system driven by a desired signal and its derivatives has a bounded solution trajectory. With the help of a new coordinate transformation, a constructive method is presented for the design of a dynamic output tracking controller. An example is given to validate the proposed output feedback tracking control scheme.     

On “uniformity” in definitions of global asymptotic stability for time-varying nonlinear systems

We discuss the lack of “uniformity” in definitions of uniform global asymptotic stability (UGAS) that have been used in various textbooks, monographs, and papers over the years. Sometimes UGAS is taken to be the combination of uniform local stability (ULS) and uniform global attractivity (UGA). Other times it also encompasses uniform global boundedness (UGB). This paper contains an explicit, smooth scalar example that shows that these definitions do not agree in general, even when the right-hand side is locally Lipschitz in the state uniformly in time (and thus bounded in time). We also discuss various notions of global asymptotic stability with relaxed uniformity (with respect to the initial time) requirements for the behavior of the solutions. In particular, we consider class- estimates and Lyapunov characterizations.     

Comments and improvement on “Robust control of state delayed systems with polytopic type uncertainties via parameter-dependent Lyapunov functionals”

The errors are pointed out in the above paper. And then, a new delay-dependent condition is presented for the robust stability of uncertain time-delay systems, which is an improvement on the corresponding results in the above paper.     

Persistency of excitation for continuous-time systems — Time-domain approach

This paper presents the time-domain approach to the analysis of the convergence of continuous-time adaptive control and estimation algorithms. The time-domain definition of persistently exciting signals is introduced and the convergence of estimation algorithms is established in the cases of open-loop and closed-loop systems. An application of the persistency of excitation theory to the design of a globally stable adaptive pole-placement controller is given.     

On designing network‐based H ∞ controllers for stochastic systems

This paper is concerned with network‐based H _∞ stabilization for stochastic systems, where network‐induced delays, packet dropouts, and packet disorders are taken into account simultaneously. The packet disorders arising from both the sampler‐to‐controller channel and the controller‐to‐actuator channel are considered by introducing a logic controller and a logic zero‐order hold. The network‐induced delays and packet dropouts are modeled as a constant delay plus a non‐differentiable time‐varying delay in the input. By employing Lyapunov–Krasovskii functional approach, we establish results that parallel well‐known bounded real Lemmas. More specifically, these results provide conditions to bound the H _∞ level of the system, which means the worst case energy of the output of the system when subjected to a unitary norm deterministic disturbance signal. On the basis of these results, suitable network‐based H _∞ controllers are designed by using cone complementary linearization method. An air vehicle system is finally taken as an example to show the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Improved exponential stability for stochastic Markovian jump systems with nonlinearity and time‐varying delay

This paper is concerned with delay‐dependent exponential stability for stochastic Markovian jump systems with nonlinearity and time‐varying delay. An improved exponential stability criterion for stochastic Markovian jump systems with nonlinearity and time‐varying delay is proposed without ignoring any terms by considering the relationship among the time‐varying delay, its upper bound and their difference, and using both Itô's differential formula and Lyapunov stability theory. A numerical example is given to illustrate the effectiveness and the benefits of the proposed method. Copyright © 2009 John Wiley & Sons, Ltd.     

Global finite‐time stabilization via time‐varying output‐feedback for uncertain nonlinear systems with unknown growth rate

This paper considers the global finite‐time output‐feedback stabilization for a class of uncertain nonlinear systems. Comparing with the existing related literature, two essential obstacles exist: On the one hand, the systems in question allow serious parametric unknowns and serious time variations coupling to the unmeasurable states, which is reflected in that the systems have the unmeasurable states dependent growth with the rate being an unknown constant multiplying a known continuous function of time. On the other hand, the systems possess remarkably inherent nonlinearities, whose growth allows to be not only low‐order but especially high‐order with respect to the unmeasurable states. To effectively cope with these obstacles, we established a time‐varying output‐feedback strategy to achieve the finite‐time stabilization for the systems under investigation. First, a time‐varying state‐feedback controller is constructed by adding an integrator method, and by homogeneous domination approach, a time‐varying reduced‐order observer is designed to precisely rebuild the unmeasurable states. Then, by certainty equivalence principle, a desired time‐varying output‐feedback controller is constructed for the systems. It is shown that, as long as the involved time‐varying gain is chosen fast enough to overtake the serious parametric unknowns and the serious time variations, the output‐feedback controller renders that the closed‐loop system states converge to zero in finite time. Copyright © 2017 John Wiley & Sons, Ltd.     

Global stabilization and asymptotic tracking for a class of nonlinear systems by means of time‐varying feedback

A simple backstepping design scheme is proposed and sufficient conditions for non‐uniform in time global stabilization for parameterized systems by means of time‐varying feedback are established. Our methodology is applicable to a special class of systems that in general cannot be stabilized by static feedback and includes non‐holonomic systems in chained form. For this class of systems the main results on feedback stabilization enable us to derive sufficient conditions for the solvability of the tracking problem. Copyright © 2003 John Wiley & Sons, Ltd.     

Global tracking sliding mode control for a class of nonlinear systems via variable gain observer

A novel output‐feedback sliding mode control strategy is proposed for a class of single‐input single‐output (SISO) uncertain time‐varying nonlinear systems for which a norm state estimator can be implemented. Such a class encompasses minimum‐phase systems with nonlinearities affinely norm bounded by unmeasured states with growth rate depending nonlinearly on the measured system output and on the internal states related with the zero‐dynamics. The sliding surface is generated by using the state of a high gain observer (HGO) whereas a peaking free control amplitude is obtained via a norm observer. In contrast to the existing semi‐global sliding mode control solutions available in the literature for the class of plants considered here, the proposed scheme is free of peaking and achieves global tracking with respect to a small residual set. The key idea is to design a time‐varying HGO gain implementable from measurable signals. Copyright © 2010 John Wiley & Sons, Ltd.     

增长率为输出的未知多项式非线性系统的全局输出反馈跟踪

本文研究了一类增长线性地依赖于不可测状态非线性系统的输出反馈自适应实用跟踪问题.很不同的是,本文所研究系统的增长率是输出的未知多项式(系数未知、幂次已知),且关于被跟踪参考信号的假设相当弱(仅本身和其导数为已知的),为解决该问题,通过灵活采用通用控制和死区的思想和方法,引入了带有新型动态增益的观测器来重构不可测的系统状态,进而构造了自适应输出反馈跟踪控制器.可以证明,当控制器中的设计参数适当选取时,闭环系统所有状态有界,并且跟踪误差趋于事先给定的充分小的区域.数值仿真说明了所提方法的有效性.     

Global output‐feedback stabilization for a class of stochastic nonlinear systems via sampled‐data control

In this paper, the global sampled‐data output‐feedback stabilization problem is considered for a class of stochastic nonlinear systems. First, based on output‐feedback domination technique and emulation approach, a systematic design procedure for sampled‐data output‐feedback controller is proposed for a class of stochastic lower‐triangular nonlinear systems. It is proved that the proposed sampled‐data output‐feedback controller will stabilize the given stochastic nonlinear system in the sense of mean square exponential stability. Because of the domination nature of the proposed control approach, it is shown that the proposed control approach can also be used to handle the global sampled‐data output‐feedback stabilization problems for a more general class of stochastic non‐triangular nonlinear systems. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.     

PDα‐type iterative learning control for fractional‐order linear continuous‐time switched systems

For a class of fractional‐order linear continuous‐time switched systems specified by an arbitrary switching rule, this paper proposes a PD^α‐type fractional‐order iterative learning control algorithm. For systems disturbed by bounded measurement noise, the robustness of PD^α‐type algorithm is first discussed in the iteration domain and the tracking performance is analyzed. Next, a sufficient condition for monotone convergence of the algorithm is studied when external noise is absent. The results of analysis and simulation illustrate the feasibility and effectiveness of the proposed control algorithm.     

Exponentially convergent control laws for nonholonomic systems in power form

This paper introduces a method for constructing exponentially convergent control laws for n-dimensional nonholonomic systems in power form. The methodology is based on the construction of a series of nested invariant manifolds for the closed-loop system under a linear control law. A recursive algorithm is presented which uses these manifolds to construct a three-dimensional system in power form. It is shown that the feedback controller for the original system is the one for this three-dimensional system with a proper choice of the gains.     

Global Practical Tracking for Nonlinear Systems With More Unknowns via Adaptive Output‐Feedback

This paper investigates the global practical tracking via adaptive output‐feedback for a class of uncertain nonlinear systems. Essentially different from the closely related literature, the system under investigation possesses unknown time‐varying control coefficients and a polynomial‐of‐output growth rate, and meanwhile, the system nonlinearities and the reference signal allow serious unknowns. For this, an adaptive observer is designed to reconstruct the system unmeasured states, where a new dynamic gain is introduced to compensate the serious unknowns in the system nonlinearities and the reference signal. Based on this and by backstepping technique, an adaptive output‐feedback controller is successfully designed, such that all the states of the closed‐loop system are bounded, and the tracking error will be prescribed sufficiently small after a finite time. A numerical simulation is provided to demonstrate the effectiveness of the proposed method.     

一类基于模糊逻辑系统的非线性系统自适应跟踪控制

利用非线性不确定系统的动态数学模型和模糊逻辑系统，对不确定性的输出信息，设计出被控系统的自适应鲁棒跟踪控制器和模糊逻辑系统参数估计的自适应律．在较弱的假设条件下，证明了这种控制器能使被控系统的状态及参数估计误差一致终极有界．仿真实例表明，所提出的方法是有效的．     

基于T-S模糊模型非线性网络控制系统改进H∞跟踪控制

研究一类非线性网络控制系统改进H∞跟踪控制问题, 该类网络控制系统中非线性被控对象和被跟踪对象分别采用Takagi-Sugeno(T-S)模糊模型和线性稳定参考模型描述. 首先通过综合考虑网络中的数据传输时滞和数据丢包影响, 采用输入时滞法和并行分布补偿技术, 建立基于零阶保持器刷新时刻的系统状态跟踪误差模型. 然后利用改进的自由权矩阵方法, 并结合Lyapunov直接法给出系统满足H∞跟踪性能的充分条件以及模糊控制器的设计方法. 最后仿真实例表明本文方法的有效性和相比已有方法的优越性.