一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

一类不确定非线性系统的鲁棒镇定器设计

本文研究了输入线性出现在状态方程中的一类不确定非线性系统的鲁棒镇定问题，通过状态坐标变换和具有反馈的输入变换将不确定非经恶性循环系统线性化，基于Lyapunov第二法，对不确定性满足匹配条件和不满足匹配条件时，给出参数不确定性非线性系统的鲁棒镇定规律，并给出计算实例。     

一类非线性系统的鲁棒H∞控制

研究一类可部分反馈线性化且具扰动三角结构的非线性参数不确定系统的鲁棒H∞控制问题,不确定参数属于已知紧集并以非线性形式进入系统.在输入到状态稳定的理论框架下,基于李雅谱诺夫函数和反演法构造出状态反馈控制器,使得闭环系统对所有允许的参数不确定性是内稳定的,且从扰动输入到输出有有界的L2-增益.控制器的设计不需解任何H am ilton-Jacob i方程,并给出仿真算例说明了该结论的可行性和有效性.     

一类非线性系统的鲁棒H ∞控制

研究一类可部分反馈线性化且具扰动三角结构的非线性参数不确定系统的鲁棒H∞控制问题,不确定参数属于已知紧集并以非线性形式进入系统.在输入到状态稳定的理论框架下,基于李雅谱诺夫函数和反演法构造出状态反馈控制器,使得闭环系统对所有允许的参数不确定性是内稳定的,且从扰动输入到输出有有界的L\-2-增益.控制器的设计不需解任何Hamilton-Jacobi方程,并给出仿真算例说明了该结论的可行性和有效性.     

一类参数不确定系统的鲁棒镇定

给出了一类参数不确定性系统的鲁棒镇定方法,首先对这类系统给出了一般描述,即这种系统的系统阵、输入阵都包含不确定参数,其非线性扰动项满足一定的约束条件.其次讨论了上述系统的基于代数黎卡提方程的正定解的鲁棒镇定方法.在应用方面,以包含静止同步补偿器(STATCOM)的电力系统为例,通过直接反馈线性化将上述系统转换为所讨论的线性系统.仿真结果验证了所提方法的控制效果.     

带有不确定性参数的多变量非线性系统的半全局实用镇定

研究一类含有零动态和不确定性参数的多输入多输出非线性系统的镇定问题,通过 构造一个组合Lyapunov函数,对非线性动态部分设计了一个控制器可半全局实用镇定整个 闭环系统的平衡点.仿真实例说明了所采用方法的有效性.     

具有自适应内模的一类非线性系统输出调节问题

研究一类包含未知非线性项的非线性系统的鲁棒输出调节问题.此类非线性系统由一包含未知参数的线性中性稳定的外系统驱动.首先运用调节器方程组解和标准内模将输出调节问题转化为镇定问题;然后给出控制律镇定闭环系统,同时利用镇定输入项和外系统信息设计出自适应内模方程.控制律使得闭环系统的信号全局最终有界,且误差被调节至预先设定的任意小的精度值.仿真结果验证了所提出设计方法的有效性.     

MIMO不确定仿射非线性系统输出反馈区域镇定

研究不确定仿射非线性系统的输出反馈镇定,在允许系统存在某类非匹配不确定性 的情况下,为系统构造出动态输出反馈鲁棒控制器,使相应闭环系统渐近稳定,并给出吸引域 的估计.     

一类非线性系统输出反馈的半全局实用镇定

研究了一类含有未知参数的非线性系统的半全局实用镇定问题,通过系统线性部分和零动态部分的Lyapunov函数构造了整个系统的Lyapunov函数,据此设计了使系统半全局实用稳定的状态反馈和动态输出反馈,且证明了只要未知参数不改变系统的相对阶,那么控制器是鲁棒的.仿真实例说明了所提出方法的有效性.     

励磁输入动态不确定的同步发电机鲁棒控制

非线性励磁控制如果没有考虑励磁输入存在的不确定性,可能影响其实际的控制效果。为了减小励磁输入动态不确定对发电机系统的影响,利用积分反推方法设计名义系统的虚控制,并加入非线性动态阻尼项对虚控制进行再设计,得到系统的鲁棒非线性控制率。控制率的设计未采用任何线性化方法,充分利用了系统的非线性特性。通过仿真试验,证实了该方法在输入动态不确定子系统满足最小相位、相对阶为零的条件下,可以保证发电机的功角、输出电压稳定。     

Global output-feedback stabilization for a class of stochastic non-minimum-phase nonlinear systems

In this paper, the problem of output-feedback stabilization is investigated for the first time for a class of stochastic nonlinear systems whose zero dynamics may be unstable. Under the assumption that the inverse dynamics of the system is stochastic input-to-state stabilizable, a stabilizing output-feedback controller is constructively designed by the integrator backstepping method together with a new reduced-order observer design and the technique of changing supply functions. It is shown that, under small-gain type conditions for small signals, the resulting closed-loop system is globally asymptotically stable in probability. The obtained results extend the existing methodology from deterministic systems to stochastic systems. An example is given to demonstrate the main features and effectiveness of the proposed output-feedback control scheme.     

A global state feedback output regulating control for uncertain systems in strict feedback form

A family of single-input, single-output, nonlinear systems in strict feedback form with uncertain constant parameters which appear linearly and belong to a known compact set Π is considered. A global robust output regulation problem via state feedback is addressed and solved under the assumptions that the regulator equations are solvable in Π, the output equation does not depend on uncertain parameters, no modelled disturbances affect the system and the output reference signal is generated by a known exosystem whose state is bounded and available for feedback. Robust adaptive techniques are used to guarantee closed loop boundedness and to achieve, without requiring persistency of excitation, global asymptotic output regulation for a class of feedback linearizable systems which may have unbounded uncertain tracking dynamics or may not have a well-defined global relative degree.     

Robust H∞ control of uncertain linear impulsive stochastic systems

This paper develops robust stability theorems and robust H_∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H_∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

Input-to-State Stability of Time-Delay Systems: A Link With Exponential Stability

The main contribution of this technical note is to establish a link between the exponential stability of an unforced system and the input-to-state stability (ISS) via the Liapunov–Krasovskii methodology. It is proved that a system which is (globally, locally) exponentially stable in the unforced case is (globally, locally) input-to-state stable when it is forced by a measurable and locally essentially bounded input, provided that the functional describing the dynamics in the unforced case is (globally, on bounded sets) Lipschitz and the functional describing the dynamics in the forced case satisfies a Lipschitz-like hypothesis with respect to the input. Moreover, a new feedback control law is provided for delay-free linearizable and stabilizable time-delay systems, whose dynamics is described by locally Lipschitz functionals, by which the closed-loop system is ISS with respect to disturbances adding to the control law, a typical problem due to actuator errors.      

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Global robust output regulation control for cascaded nonlinear systems using the internal model principle

This article considers the global robust output regulation problem via output feedback for a class of cascaded nonlinear systems with input-to-state stable inverse dynamics. The system uncertainties depend not only on the measured output but also all the unmeasurable states. By introducing an internal model, the output regulation problem is converted into a stabilisation problem for an appropriately augmented system. The designed dynamic controller could achieve the global asymptotic tracking control for a class of time-varying reference signals for the system output while keeping all other closed-loop signals bounded. It is of interest to note that the developed control approach can be applied to the speed tracking control of the fan speed control system. The simulation results demonstrate its effectiveness.     

Asymptotic rejection of unmatched general periodic disturbances with nonlinear Lipschitz internal models

This article deals with asymptotic rejection of general periodic disturbances in a class of nonlinear systems by exploiting observer design with Lipschitz output nonlinearities for the internal model design. It is shown that a class of general periodic distances can be modelled as outputs of linear systems with nonlinear output functions. Based on this observation, a nonlinear observer design with output Lipschitz nonlinearities is investigated and integrated for the internal model design to estimate the phase and amplitude of the desired feedforward input for asymptotic disturbance rejection in a class of nonlinear systems with input-to-state stable zero dynamics. A number of problems on disturbance rejection can be formulated in the disturbance rejection form shown in this article to which the proposed nonlinear Lipschitz internal model can be applied. Two examples are included to demonstrate the proposed design strategies.     

Input-to-state stability of switched systems and switching adaptive control

In this paper we prove that a switched nonlinear system has several useful input-to-state stable (ISS)-type properties under average dwell-time switching signals if each constituent dynamical system is ISS. This extends available results for switched linear systems. We apply our result to stabilization of uncertain nonlinear systems via switching supervisory control, and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide ISS properties with respect to the estimation errors. Detailed illustrative examples are included.     

Global Robust Output Regulation for a Class of Switched Nonlinear Systems with Nonlinear Exosystems

The problem of global robust output regulation for a class of switched nonlinear systems with nonlinear exosystems is investigated in this paper where not all subsystems are stabilizable. First, as an extension of the concept of non‐switched internal model, this paper defines a switched internal model, which together with the plant is called the switched augmented system. Also, we show that the problem of output regulation for the switched nonlinear system can be converted into a global robust regulation problem of the switched augmented system. Second, based on the average dwell time method, the global robust regulation problem under a class of switching signals with average dwell time is solved, which leads to the solution of the problem of global robust output regulation. Finally, an example is provided to demonstrate the effectiveness of the proposed design approach.