非线性系统与反向传输动力学级联的观察器设计

48 浏览量更新于2024-08-31 收藏 459KB PDF 举报

"这篇研究论文‘Observer design for a class of nonlinear system in cascade with counter-convecting transport dynamics’探讨了观察器设计问题，具体涉及一个非线性系统与反向对流传输动力学串联的场景。文章发表在《Kybernetika》杂志2016年第一期，由Xiushan Cai、Linling Liao、Junfeng Zhang和Wei Zhang共同撰写。" 在控制系统理论中，观察器设计是关键问题之一，尤其在处理复杂的动态系统时。这篇论文聚焦于一类特殊的系统结构，即常微分方程（ODE）与偏微分方程（PDE）串联的系统，其中ODE部分是一个全局Lipschitz非线性系统，而PDE部分则由一对反向对流传输动力学组成。这种结构在实际应用中常见，如热传导、流体动力学等领域。主要挑战在于状态观测只能依赖于PDE在终端边界的状态，而ODE与PDE之间的连接点无法直接测量。为解决这个问题，作者结合了反步设计方法（backstepping infinite-dimensional transformation）与高增益观察器技术。反步设计是一种强大的工具，它通过一系列的逆变换将原系统的控制或观察问题转化为易于处理的形式。而高增益观察器则能通过放大未测量状态的影响，以实现对整个系统的状态估计。论文中，作者构建了一种观察器，能够在没有直接测量ODE部分状态的情况下，有效地估计整个串联系统的状态。这一设计对于理解和改善这类系统的控制性能具有重要意义，尤其是在存在观测约束或不完全信息的情况下。此外，论文还可能涉及以下几个知识点： 1. **全局Lipschitz条件**：这是非线性系统分析中的一个重要性质，保证了系统的局部稳定性可以扩展到全局稳定性。 2. **偏微分方程（PDE）**：描述空间和时间变量之间关系的方程，广泛应用于物理、工程和生物学等领域。 3. **反向对流（Counter-convecting transport）**：在流体动力学中，指的是流体的流动方向与温度或浓度梯度方向相反的情况，这可能导致复杂的行为。 4. **反步设计**：这是一种控制理论中的设计方法，通过逆变换逐步设计控制器或观察器，使系统达到期望的性能。 5. **高增益观察器**：一种观察器设计策略，通过增加未测量状态的权重，使系统能够对这些状态进行准确估计。该论文在非线性系统控制理论和实际应用中具有深远影响，其观察器设计方法对于解决有观测限制的复杂系统问题提供了新的解决方案。

Observer design for a class of nonlinear system in cascade 77

observers have been proposed for several classes of nonlinear systems, including the high-

gain observer [17], sliding-mode observer [8], Luenberger-like observers [1]. Backstepping

method for the ﬁrst-order hyperbolic PDEs and application to systems with delays was in

[14]. The ﬁrst-order hyperbolic PDEs model a variety of physical systems. Speciﬁcally,

2×2 systems of ﬁrst order hyperbolic linear PDEs model processes such as open channels

[7], transmission lines [6], gas ﬂow pipelines [10] or road traﬃc models [9]. They also

have some resemblances with systems that model the gas-liquid ﬂow in oil production

pipes [15].

Stabilization of a system of n + 1 coupled ﬁrst-order hyperbolic linear PDEs with a

single boundary input was dealt with in [16]. The problem of boundary stabilization for

a quasilinear 2 × 2 system of ﬁrst-order hyperbolic PDEs was considered in [5]. Stabiliz-

ing control design for a broad class of nonlinear PDEs was in [18]. The convergence of

the feedback laws design in [18] was proved, and the stability properties of the closed-

loop system were established in [19]. Backstepping method was used to compensate a

class of nonlinear systems under wave actuator dynamics with moving boundary in [3].

An explicit feedback law that compensates the discrete-time nonlinear systems actuated

through transport dynamics was designed in [2]. Using the transport PDE to express the

delay, stability analysis is conducted with inﬁnite-dimensional backstepping transforma-

tions and by constructing a Lyapunov functional in [4]. Observer design and output

feedback stabilization for nonlinear multivariable systems with diﬀusion PDE-governed

sensor dynamics was studied in [20]. Compensating a string PDE in the actuation or

sensing path of an unstable linear ODE can be found in [11]. A boundary observer has

been developed for a cascade involving a linear ODE and a heat PDE equation in [12].

However, in the authors’ knowledge, observer design for a class of nonlinear systems in

cascade with counter-convecting transport dynamics doesn’t appear.

In this paper, the ideas of [11, 12] are extended to ODE-PDE cascades where the

ﬁnite-dimension subsystem is a class of nonlinear systems, while the PDE part is a pair

of counter-convecting transport dynamics. The aim is to accurately estimate the state of

the ODE subsystem and the state of the pair of counter-convecting transport dynamics.

One major diﬃculty is that the state observation only relies on the PDE state at the

terminal boundary, and the connection point between the ODE and the PDE blocs is

not accessible to be measured. The proposed observer, which combines the backstepping

inﬁnite-dimensional transformation with the high gain observer, provides state estimates

of both subsystems. It is shown that the observer error is asymptotically stable. The

proposed observer design method can be applied in the oil and gas industry.

The paper is organized as follows: In Section 2, system description is given. In Section

3 we present observer design and convergence analysis. An illustrative example is given

in Section 4. Some conclusions are drawn in Section 5.

For an n-vector, the norm | · | denotes the usual Euclidean norm. The argument of

the functions and of the functionals will be omitted or simpliﬁed whenever no confusion

can arise from the context. For example, one may denote a function f(X(t)) by simply

f(X).

剩余13页未读，继续阅读

weixin_38720050

粉丝: 3
资源: 876

非线性系统与反向传输动力学级联的观察器设计

Adaptive observer-based fast fault estimation of a leader-follower linear multi-agent system with actuator faults

Composite adaptive disturbance observer-based control for a class of nonlinear systems with multisource disturbance

Full-order observer-based actuator fault detection and reduced-order observer-based fault reconstruction for a class of uncertain nonlinear systems

Observer-based finite-time passive control for a class of uncertain time-delayed Lipschitz nonlinear systems

Sensor fault reconstruction for a class of 2-D nonlinear systems with application to fault compensation

Adaptive neural network output feedback control for a class of non-strict-feedback nonlinear systems with unknown control coefficients

Observer-based event-triggered adaptive fuzzy control for leader-following consensus of nonlinear strict-feedback systems

Fuzzy Observer-based Output Feedback Control Design of Discrete-time Nonlinear Systems: An Extended Dimension Approach

ExtremeLearningMachine资源共享-Nonlinear-discrete-time-neural-network-observer_2013_Neurocomputing.pdf

Neural observer-based adaptive compensation control for nonlinear time-varying delays systems with input constraints

最新资源