State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method,this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form,and presents a number of new results.First,some new properties of Caputo fractional derivative are presented,and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties.Then,by introducing appropriate transformations of coordinates,the problem of controller design is converted into the problem of finding some parameters,which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities.Finally,based on the Lyapunov function method,state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed.A simulation example is given to demonstrate the effectiveness of the proposed design procedure.

Adaptive Backstepping Output Feedback Control for SISO Nonlinear System Using Fuzzy Neural Networks

In this paper, a new fuzzy-neural adaptive control approach is developed for a class of single-input and single-output （SISO） nonlinear systems with unmeasured states. Using fuzzy neural networks to approximate the unknown nonlinear functions, a fuzzy- neural adaptive observer is introduced for state estimation as well as system identification. Under the framework of the backstepping design, fuzzy-neural adaptive output feedback control is constructed recursively. It is proven that the proposed fuzzy adaptive control approach guarantees the global boundedness property for all the signals, driving the tracking error to a small neighbordhood of the origin. Simulation example is included to illustrate the effectiveness of the proposed approach.

Adaptive State-feedback Stabilization for More General High-order Stochastic Nonlinear Systems

适应州反馈的稳定为在的高顺序的随机的非线性的系统的一个类被调查函数 fi 的上面的界限(?? 铄吗？？

An Improvement on Data-Driven Pole Placement for State Feedback Control and Model Identification

The recently proposed data-driven pole placement method is able to make use of measurement data to simultaneously identify a state space model and derive pole placement state feedback gain. It can achieve this precisely for systems that are linear time-invariant and for which noiseless measurement datasets are available. However, for nonlinear systems, and/or when the only noisy measurement datasets available contain noise, this approach is unable to yield satisfactory results. In this study, we investigated the effect on data-driven pole placement performance of introducing a prefilter to reduce the noise present in datasets. Using numerical simulations of a self-balancing robot, we demonstrated the important role that prefiltering can play in reducing the interference caused by noise.

Effects of error feedback on a nonlinear bistable system with stochastic resonance

In this paper, we discuss the effects of error feedback on the output of a nonlinear bistable system with stochastic resonance. The bit error rate is employed to quantify the performance of the system. The theoretical analysis and the numerical simulation are presented. By investigating the performances of the nonlinear systems with different strengths of error feedback, we argue that the presented system may provide guidance for practical nonlinear signal processing.

Robust Feedback Controller for Exponential Stability of Nonlinear Systems with Mismatched Uncertainties

The robust stabilization of nonlinear systems with mismatched uncertainties is investigated. Based on the stability of the nominal system, a new approach to synthesizing a class of continuous state feedback controllers for uncertain nonlinear dynamical systems is proposed. By such feedback controllers, the exponential stability of uncertain nonlinear dynamical systems can be guaranteed. The approach can give a clear insight to system analysis. An illustrative example is given to demonstrate the utilization of the approach developed. Simulation results show that the method presented is practical and effective.

The Design of Output Feedback Distributed Model Predictive Controller for a Class of Nonlinear Systems

For a class of nonlinear systems whose states are immeasurable, when the outputs of the system are sampled asynchronously, by introducing a state observer, an output feedback distributed model predictive control algorithm is proposed. It is proved that the errors of estimated states and the actual system's states are bounded. And it is guaranteed that the estimated states of the closed-loop system are ultimately bounded in a region containing the origin. As a result, the states of the actual system are ultimately bounded. A simulation example verifies the effectiveness of the proposed distributed control method.

Three-dimensional nonlinear H_2/H_∞ guidance law based upon approach of solving the state feedback Nash balance point

Based upon the theory of the nonlinear quadric two-person nonzero-sum differential game,the fact that the time-limited mixed H2/H∞ control problem can be turned into the problem of solving the state feedback Nash balance point is mentioned. Upon this,a theorem about the solution of the state feedback control is given,the Lyapunov stabilization of the nonlinear system under this control is proved,too. At the same time,this solution is used to design the nonlinear H2/H∞ guidance law of the relative motion between the missile and the target in three-dimensional(3D) space. By solving two coupled Hamilton-Jacobi partial differential inequalities(HJPDI),a control with more robust stabilities and more robust performances is obtained. With different H∞ performance indexes,the correlative weighting factors of the control are analytically designed. At last,simulations under different robust performance indexes and under different initial conditions and under the cases of intercepting different maneuvering targets are carried out. All results indicate that the designed law is valid.

Output Feedback Nonlinear General Integral Control

This paper proposes an output feedback nonlinear general integral controller for a class of uncertain nonlinear system. By solving Lyapunov equation, we demonstrate a new proposition on Equal ratio gain technique. By using Equal ratio gain technique, Singular perturbation technique and Lyapunov method, theorem to ensure regionally as well as semi-globally exponential stability is established in terms of some bounded information. Moreover, a real time method to evaluate the ratio coefficients of controller and observer are proposed such that their values can be chosen moderately. Theoretical analysis and simulation results show that not only output feedback nonlinear general integral control has the striking robustness but also the organic combination of Equal ratio gain technique and Singular perturbation technique constitutes a powerful tool to solve the output feedback control design problem of dynamics with the nonlinear and uncertain actions.

Asymptotic regulation of cascade systems with unknown control directions and nonlinear parameterization

A robust partial-state feedback asymptotic regulating control scheme is developed for a class of cascade systems with both nonlinear uncertainties and unknown control directions. A parameter separation technique is introduced to separate the time-varying uncertainty and the unmeasurable state from nonlinear functions. Then, the Nussbaum-type gain method together with the idea of changing supply functions is adopted in the design of a smooth partial-state regulator that can ensure all the signals of the closed-loop system are globally uniformly bounded. Especially, the system state asymptotically converges to zero. The design procedure is illustrated through an example and the simulation results show that the controller is feasible and effective.

Finite-time Sliding Mode Control Design for a Class of Uncertain Conic Nonlinear Systems

This paper studies the sliding mode controller design problems for a class of nonlinear system. The nonlinear function is considered to satisfy conic-type constraint condition. A novel finite-time boundedness(FTB) based sliding mode controller design theory is proposed. And then a sufficient condition is obtained in terms of linear matrix inequalities(LMIs), which guarantees the resulted sliding mode dynamics to be FTB wrt some predefined scalars. Thereafter, a FTB-based sliding mode control(SMC) law is synthesized to ensure the state of the controlled system is driven into a novel desired switching surface s(t) = c(c is a constant) in a finite time. Simulation results illustrate the validity of the proposed FTB-based SMC design theory.

Stabilizing controller design for nonlinear fractional order systems with time varying delays

To deal with stabilizing of nonlinear affine fractional order systems subject to time varying delays,two methods for finding an appropriate pseudo state feedback controller are discussed.In the first method,using the Mittag-Lefler function,Laplace transform and Gronwall inequality,a linear stabilizing controller is derived,which uses the fractional order of the delayed system and the upper bound of system nonlinear functions.In the second method,at first a sufficient stability condition for the delayed system is given in the form of a simple linear matrix inequality(LMI)which can easily be solved.Then,on the basis of this result,a stabilizing pseudo-state feedback controller is designed in which the controller gain matrix is easily computed by solving an LMI in terms of delay bounds.Simulation results show the effectiveness of the proposed methods.

基于自抗扰方法的无人机控制律设计

针对多平台、多任务的无人机飞行控制律的快速开发问题,提出一种基于自抗扰方法的无人机控制律架构,设计了可复用的扩展状态观测器及微分跟踪器,研究对比了其在3种具有较大差异的无人机平台中的应用,使7 000 kg的超音速UAV_A获得了更优的敏捷性结果,在60 kg的缩比UAV_B完成了5.8g的半滚倒转大过载机动飞行试验,基于10 kg的平直翼UAV_C实现了12架机紧编队的精确轨迹控制飞行试验。仿真及试飞结果表明:所提自抗扰控制结构响应快速、控制精度高、鲁棒性强,能够较好地适应多类无人机、面向多种任务场景的控制需求,且不需调参就能够获得较好的控制效果,为飞行控制算法设计提供了新的技术途径。

带有状态/输入量化的无人艇航向跟踪控制

[目的]针对水面无人艇(USV)的海上通信受限的问题,提出一种带有状态/输入量化的USV航向跟踪控制方法。[方法]基于反步法设计系统控制律,结合动态面技术降低虚拟控制律的计算量膨胀问题。对于控制系统中存在的不确定项及外界干扰,利用扩张状态观测器(ESO)进行估计。采用均匀量化器分别对控制系统中的状态变量和控制输入进行量化,且量化后的状态反馈信息仅用于跟踪控制。利用量化状态递归设计基于ESO的USV航向控制器,证明闭环控制系统中量化变量和非量化变量间误差的有界性。[结果]基于李雅普诺夫稳定性理论,提出了量化误差考量及闭环系统稳定性判定方法,严格证明了所设计的带有状态量化和输入量化的USV航向跟踪控制系统的稳定性,仿真实验验证了该控制策略的有效性。[结论]结果表明,所提方法可为USV航向跟踪控制提供借鉴。

三阶三次幂非线性混沌电路的自适应反馈控制和H_(∞)控制

针对三阶三次幂非线性混沌电路,研究其控制问题.首先,给出系统的Lyapunov指数和混沌吸引子,验证系统存在复杂的混沌现象;其次,用自适应反馈控制方法和H_(∞)状态反馈控制方法,设计参数已知和参数未知的自适应反馈控制器以及H_(∞)状态反馈控制器,将混沌系统状态稳定到平衡点上;最后,通过MATLAB软件进行数值仿真验证控制器的有效性,并对两种控制器的控制效果进行比较.

基于MIMO-ESO的高速飞行器自抗扰控制

针对高速飞行器无动力再入过程中具有强耦合、气动参数摄动及不确定性的非线性姿态模型,设计了高速飞行器MIMO-ESO自抗扰姿态控制器。考虑各通道间的耦合影响,结合自抗扰控制中的扩张状态观测器及非线性状态误差反馈律,将不确定性、耦合及参数摄动等干扰作为“总和干扰”,利用扩张状态观测器进行估计并动态反馈补偿,再利用非线性状态误差反馈律抑制补偿残差。仿真结果表明,MIMO-ESO自抗扰控制器能够克服干扰及气动参数大范围摄动的影响,在获取良好的动态品质和跟踪性能的同时,具有较强的鲁棒性,克服了实际工程中难以建立精确被控模型并获取参数摄动范围的困难,具有工程应用价值。

基于非线性状态空间控制的伺服液压执行器跟踪误差仿真研究

目前,伺服液压执行器控制系统不仅响应速度慢,而且执行器运动位移跟踪精度也相对较低。对此,本文设计了非线性状态空间控制方法,并对伺服液压执行器响应速度和跟踪误差进行仿真。建立了伺服液压执行器平面简图,推导出液压执行器运动方程式。针对传统线性控制方法进行改进,利用系统的非线性状态空间模型,通过非线性反馈和坐标变换转化为线性可控系统,给出了非线性状态空间控制流程。针对不同环境条件下的信号波形,采用Matlab软件对伺服液压执行器响应速度和跟踪误差进行仿真,并且与线性控制效果进行比较。仿真结果表明:采用线性控制的伺服液压执行器,执行器响应速度慢、运动位移跟踪误差大,容易受到外界波形的干扰。采用非线性状态空间控制的伺服液压执行器,执行器响应速度快、运动位移跟踪误差较小,能够抑制外界波形的干扰。该执行器能够有效地抑制外界波形的干扰,不仅可以提高伺服液压执行器的响应速度,而且还能降低位移跟踪误差。

具有未知增长率的一类上三角非线性多智能体系统的协同控制

基于有向领导者-追随者型的网络拓扑结构,研究了一类具有未知增长率的上三角非线性多智能体系统的协同控制问题。首先,通过引入坐标变换,将原系统转换为带有时间增益的等效系统;其次,针对标称系统进行控制器设计,获得原系统的分布式时变状态反馈控制器。所设计的控制器能够保证追随者与领导者的输出跟踪误差有界,且闭环系统所有信号有界。最后,利用仿真实例验证了控制方案的有效性。