基于信息熵的非线性动态系统的宏观分析*

本文针对一类Ｉｔｏ型随机非线性动态系统，分别基于微观ＦＰＫ方程和宏观信息熵方法推断系统特性，进而分析系统的熵结构，结果表明，宏观方法不仅能获得与微观方法相似的结果，而且能以统一简洁的方式各类系统，通过对一类非线性动态系统的应用进一步说明宏观信息熵分析方法。     

导弹俯仰振荡非线性动态稳定性分析

研究了导弹非线性动态稳定性的分析方法。采用联立导弹的运动方程和流体动力学方程,建立了导弹绕平衡攻角作纵向俯仰振荡运动的数学模型,并用非线性动力学理论定性分析了模型的动态稳定性,得出影响导弹俯仰振荡运动稳定性的关键因素。以某返回舱为例,求解耦合方程,验证了方法的可靠性。针对某型号跳跃滑翔式导弹滑翔段中动态特性严峻的六个状态进行数值仿真,结果表明导弹在滑翔段是动态稳定的,方法用于导弹非线性稳定性的分析是可行的。     

一类非线性LC电路的分析与模拟

给出一类非线性LC电路的状态分析和数值模拟：将电容的电荷表示为相位角的简谐函数,电路的响应频率表示为相位角关于时间的变化率;以电路的响应频率为未知函数,对状态方程进行近似求解;算出时间随相位角变化的近似关系式;给出电路的相图、电容的电荷以及电感的磁通链随时间变化关系式及数值模拟,结果与数值积分法吻合良好。     

非线性系统研究动态与展望

本文对近几年非线性控制系统的进展情况作了综合报导。文章共分三个部分:第一部分强调:什么是反馈意义下的非线性系统;第二部分介绍了近几年非线性控制系统研究中较集中的八个方面的问题;第三部对非线性控制理论今后主要研究动向作了预测。     

非线性随机时滞系统的稳定性与应用

首先考虑了不确定性的一族非线笥随机时滞系统,建立了这种系统的均方指数稳定与几乎必须指数稳定的充分准则,其准则是时滞无关的,然后应用这些充分条件到一类不确定的随机时滞神经网络,得到了这咱神经网络指数稳定的产用判据。本文的结果是最近文献中某些结果的推广,最后一个数值例子说明的所给准则的有效性。     

一类高次随机非线性系统的自适应动态面控制

针对一类含非线性参数高次随机非线性系统的输出跟踪控制问题,基于自适应增加幂次积分方法,利用参数分离技术和动态面技术,给出了一种自适应光滑状态反馈控制器设计方法。利用Sigmoid函数设计参数自适应律,保证了其导数连续。将低通滤波器引入控制器设计过程,避免了“微分爆炸”现象。通过构造适当形式的控制Lyapunov函数进行稳定性分析,证明了系统输出能被依概率地调节至参考信号的邻域范围。仿真结果验证了所提控制器设计方案的有效性。     

一类非线性随机系统的自适应控制

本文在文献「１，２」的基础上，对一类仿射非线性随机系统的最小二乘（ＬＳ）自适应控制问题进行了分析，给出了稳定性及收敛速度结果，在这里，我们仅要求非线性函数具有线性增长速度，而无需任何其它结构假设。     

一类非线性系统的动态补偿

本文考察一类非线性控制系统的调节问题。在一些常见的假设条件下,文中给出了动态补偿器的设计方法,这是一种基于状态观测器的补偿装置。结果表明:本文给出的动态补偿器的构造方法便于实际系统设计采用。     

非线性时变随机系统状态及参数的实时联合估计

在文[1]中,我们给出了一种用于一类非线性时变随机系统的带次优渐消因子的扩展卡尔曼滤波器,可以估计出快速变化的系统状态.本文推广了文[1]的结果,使其可处理一般的非线性测量.同时,给出了一种状态及参数的联合估计方法.所做大量仿真研究表明,本文方法具有良好的实时性及动态跟踪性.     

不确定随机非线性系统自适应观测器设计

考虑带非参数不确定项的随机非线性系统自适应观测器设计问题.不同于已有结果,系统的不确定项无需满足Lipschitz连续性条件,也不必要仅仅是系统输出的函数.通过设计一个带参数自适应律的非线性观测器来重构系统状态,该观测器结构简单目易于实现.应用Lyapunov稳定性理论和随机微分理论证明该观测器是最终有界的,并且它的界可以通过选取适当的参数进行调节.最后,数值仿真结果表明了该观测器的有效性.     

Observer-based adaptive neural dynamic surface control for a class of non-strict-feedback stochastic nonlinear systems

The problem of adaptive output feedback stabilisation is addressed for a more general class of non-strict-feedback stochastic nonlinear systems in this paper. The neural network (NN) approximation and the variable separation technique are utilised to deal with the unknown subsystem functions with the whole states. Based on the design of a simple input-driven observer, an adaptive NN output feedback controller which contains only one parameter to be updated is developed for such systems by using the dynamic surface control method. The proposed control scheme ensures that all signals in the closed-loop systems are bounded in probability and the error signals remain semi-globally uniformly ultimately bounded in fourth moment (or mean square). Two simulation examples are given to illustrate the effectiveness of the proposed control design.     

Global stabilisation for a class of switched high-order stochastic nonlinear systems

This paper is devoted to the problem of global stabili sation for a class of switched high-order stochastic nonlinear systems under arbitrary switchings. By extending the adding -a -power -integrator technique and choosing an appropriate common Lyapunov function, a common state-feedback controller is explicitly constructed to render the closed-loop system globally asymptotically stable in probability. The effectiveness of the proposed approach is demonstrated by a simulation example.     

On the simultaneous stabilization of stochastic nonlinear systems

In this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.     

Output feedback for stochastic nonlinear systems with unmeasurable inverse dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.     

Stability analysis of distributed-order nonlinear dynamic systems

The problem of asymptotic stability analysis of equilibrium points in nonlinear distributed-order dynamic systems with non-negative weight functions is considered in this paper. The Lyapunov direct method is extended to be used for this stability analysis. To this end, at first, a discretisation scheme with convergence property is introduced for distributed-order dynamic systems. Then, on the basis of this tool, Lyapunov theorems are proved for asymptotic stability analysis of equilibrium points in distributed-order systems. As the order weight function assumed for the distributed-order systems is general enough, the results are applicable to a wide range of nonlinear distributed-order systems such as fractional-order systems with multiple fractional derivatives. To verify the applicability of the obtained results, these results are applied for the stability analysis of a distributed-order diffusion system and control of a fractional-order Lorenz system with multiple fractional derivatives.     

Identification of systems containing linear dynamic and static nonlinear elements

Identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered. Previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems. It is shown that systems composed of cascade, feedforward, feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only.     

一类高阶次随机非线性系统的输出反馈镇定

针对一类高阶次随机非线性系统,研究其输出反馈镇定问题．通过选择有效的观测器和李雅普诺夫函数,所设计的光滑输出反馈控制器保证了闭环系统的平衡点是依概率全局渐近稳定的,输出几乎处处调节到零．数值仿真验证了控制方案的有效性．     

Adaptive neural network dynamic event-triggered control for strong interconnected stochastic nonlinear systems with output constraint

This paper proposes a dynamic event-triggered mechanism based command filtered adaptive neural network (NN) tracking control scheme for strong interconnected stochastic nonlinear systems with time-varying output constraints. By designing a state observer, the unmeasured states of the systems can be estimated. The NNs are utilized to handle the unknown intermediate functions. In the controller design process, the asymmetric time-varying barrier Lyapunov functions are used to guarantee that the systems outputs do not violate the constraint regions. By integrating the command filter with variable separation technique, the controller design process is more simple, and the problem of algebraic-loop can be solved which caused by interconnected functions. According to the Lyapunov stability theory, it can be ensured that all signals of the systems are bounded in probability. Finally, the availability of the developed control scheme can be showed by the simulation example.