Nonlinear Semi-discrete Population Evolution System and Stability

This paper set up a class of nonlinear semi-discrete age-structured model of population evolution system, by using the concept of critical proliferation rate, it discussed the stability of linear and nonlinear population system, and it obtain the sufficiency conditions of the stable for nonlinear semi-discrete system.     

Model algorithm control using neural networks for input delayed nonlinear control system

The performance of the model algorithm control method is partially based on the accuracy of the system’s model. It is difficult to obtain a good model of a nonlinear system, especially when the nonlinearity is high. Neural networks have the ability to "learn"the characteristics of a system through nonlinear mapping to represent nonlinear functions as well as their inverse functions. This paper presents a model algorithm control method using neural networks for nonlinear time delay systems. Two neural networks are used in the control scheme. One neural network is trained as the model of the nonlinear time delay system, and the other one produces the control inputs. The neural networks are combined with the model algorithm control method to control the nonlinear time delay systems. Three examples are used to illustrate the proposed control method. The simulation results show that the proposed control method has a good control performance for nonlinear time delay systems.     

A Family of Reliable H_∞ State-Feedback Controllers for Nonlinear Systems with Strictly Redundant Actuators: the Full Information Case

1　 IntroductionInherited from state space linear H∞ control theory,a number of nonlinear H∞ solutionshave been presented in terms of various formulations.The nonlinear H∞ control problemcan be stated as follows:find a compensator,either state feedback ormore general outputfeedback such that( 1 ) the internal state of the closed-loop system is stable and( 2 ) the L2 -gain of the mapping from the exogenous input disturbance to the controlled output liketracking error or cost variables is mi…     

LEARNING CAUSAL GRAPHS OF NONLINEAR STRUCTURAL VECTOR AUTOREGRESSIVE MODEL USING INFORMATION THEORY CRITERIA

Detection and clarification of cause-effect relationships among variables is an important problem in time series analysis. Traditional causality inference methods have a salient limitation that the model must be linear and with Gaussian noise. Although additive model regression can effectively infer the nonlinear causal relationships of additive nonlinear time series, it suffers from the limitation that contemporaneous causal relationships of variables must be linear and not always valid to test conditional independence relations. This paper provides a nonparametric method that employs both mutual information and conditional mutual information to identify causal structure of a class of nonlinear time series models, which extends the additive nonlinear times series to nonlinear structural vector autoregressive models. An algorithm is developed to learn the contemporaneous and the lagged causal relationships of variables. Simulations demonstrate the effectiveness of the nroosed method.     

THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN OPERATOR IN L^s-SPACES

By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ L^s （Ω） of nonlinear boundary value problems involving the p-Laplacian operator, where 2≤ s〈＋∞, and 2N/N＋1 〈 p ≤ 2 for N（≥ 1） which denotes the dimension of R^N. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.     

Composite nonlinear feedback control for output regulation problem of linear discrete-time systems with input saturation

Transient performance for output regulation problems of linear discrete-time systems with input saturation is addressed by using the composite nonlinear feedback（CNF） control technique. The regulator is designed to be an additive combination of a linear regulator part and a nonlinear feedback part. The linear regulator part solves the regulation problem independently which produces a quick output response but large oscillations. The nonlinear feedback part with well-tuned parameters is introduced to improve the transient performance by smoothing the oscillatory convergence. It is shown that the introduction of the nonlinear feedback part does not change the solvability conditions of the linear discrete-time output regulation problem. The effectiveness of transient improvement is illustrated by a numeric example.     

Parameter estimation for dual-rate sampled Hammerstein systems with dead-zone nonlinearity

The identification of nonlinear systems with multiple sampled rates is a difficult task.The motivation of our paper is to study the parameter estimation problem of Hammerstein systems with dead-zone characteristics by using the dual-rate sampled data.Firstly,the auxiliary model identification principle is used to estimate the unmeasurable variables,and the recursive estimation algorithm is proposed to identify the parameters of the static nonlinear model with the dead-zone function and the parameters of the dynamic linear system model.Then,the convergence of the proposed identification algorithm is analyzed by using the martingale convergence theorem.It is proved theoretically that the estimated parameters can converge to the real values under the condition of continuous excitation.Finally,the validity of the proposed algorithm is proved by the identification of the dual-rate sampled nonlinear systems.     

An Improved Nonlinear Multistage Switch System of Microbial Fermentation Process in Fed-Batch Culture

This paper considers the fed-batch culture in microbial fermentation process, which consists of batch and continuous culture. The goal is to explore the properties of a novel model which can describe the characteristics of multistage for the population growth of microorganisms in nonlinear switch dynamic system. The improved model is developed based on the experimental data to describe the delayed, developmental and stationary stages well for the phases of batch culture. Then the existence, uniqueness and boundedness of solutions to the nonlinear multistage switch system and the Lipschitz continuity and differentiability of solutions with respect to the initial state is discussed as well. Finally, a numerical simulation is employed for the nonlinear multistage switch system.     

ON COMPLEX DYNAMIC CONTROL SYSTEMS

This paper presents some recent works on the control of dynamic systems,which have certain complex properties caused by singularity of the nonlinear structures,structure~varyings, or evolution process etc. First, we consider the structure singularity of nonlinear control systems. It was revealed that the focus of researches on nonlinear control theory is shifting from regular systems to singular systems. The singularity of nonlinear systems causes certain complexity. Secondly, the switched systems are considered. For such systems the complexity is caused by the structure varying. We show that the switched systems have significant characteristics of complex systems. Finally, we investigate the evolution systems. The evolution structure makes complexity, and itself is a proper model for complex systems.     

Sliding Mode Formation Control of Nonlinear Multi-agent Systems with Local Lipschitz Continuous Dynamics

In this paper, the multi-agent formation problem of networked nonlinear multi-agent systems with local Lipschitz continuous dynamics under directed interaction topology, is investigated.Based on the nonlinear dynamics satisfying locally Lipschitz continuous conditions, three kinds of sliding mode controllers are proposed to solve the problem of multi-agent formation control. Using integral sliding mode controller in first-order system, formation shape is achieved within finite time.For second-order system, on the one hand, non-singular terminal sliding mode function is adopted to accomplish the system asymptotic convergence. Furthermore, super-twisting algorithm is proposed to make multi-agent achieve the desired formation within finite time. Lyapunov functions are applied in the whole paper to ensure the system stability. Numerical simulation examples are provided to demonstrate the effectiveness of the proposed sliding mode control methods.     

非匹配时变不确定性时滞系统的Terminal滑模控制

针对具有非匹配时变不确定性和时滞的线性系统,提出了快速terminal滑模控制策略.采用非线性滑动平面的设计方法,使得系统状态可在有限时间内收敛至平衡点.滑动平面系数满足扩展匹配条件时,设计的terminal控制器确保了在滑动平面上系统对于非匹配时变不确定性和时滞具有不变性,并保证了滑动平面的到达和闭环系统的稳定.仿真结果验证了控制策略的有效性.     

基于滑模观测器的非线性系统迭代学习控制

针对相当广泛的一类非线性系统有限时间轨迹跟踪问题,提出了一种基于滑模观测器的迭代学习控制算法。根据系统的非线性特性,利用一种滑模观测器对系统的状态进行估计,根据估计信号设计了一种类D型开环迭代学习控制律。这种控制方法不需要对系统的跟踪误差信号进行微分,从而对系统的量测噪声不敏感。给出了控制算法的收敛性证明,通过仿真实验证明了这种算法的有效性。     

Homogeneous Finite-Time Consensus Control for Higher-Order Multi-Agent Systems by Full Order Sliding Mode

This paper investigates the distributed finite-time consensus tracking problem for higher-order nonlinear multi-agent systems (MAS_s). The distributed finite-time consensus protocol is based on full order sliding surface and super twisting algorithm. The nominal consensus control for the MASs is designed based on the geometric homogeneous finite time control technique. The chattering is avoided by designing a full order sliding surface. The switching control is constructed by integrating super twisting algorithm, hence a chattering alleviation protocol is obtained to maintain a smooth control input. The finite time convergence analysis for the leader follower network is presented by using strict Lyapunov function. Finally, the numerical simulations validate the proposed homogeneous full-order sliding mode control for higher-order MAS_s.     

考虑布儒斯特角约束的复合积分制导律设计

雷达导引头下视探测超低空目标时,受多径效应的影响,严重降低了跟踪的精度。将弹目视线角约束在布儒斯特角附近,可有效降低多径干扰的影响。基于积分滑模控制的思想,设计出一种线性积分滑模制导律,该制导律相对于传统的滑模制导律而言,由于省去趋近滑模运动阶段,具有更快的渐进收敛特性。为了进一步提高视线角的收敛速率,设计了非线性积分滑模制导律,该制导律可保证弹目视线角在有限的时间内快速收敛至布儒斯特角。为了解决积分滑模开关项高增益系数引起的抖振问题,设计了滑模扰动观测器来估计目标的机动加速度。结合非线性积分滑模制导律,引入目标加速度的估计值,设计出一种复合制导律。结果表明,该复合制导律能有效地消除抖振现象,减小脱靶量,提高拦截的精度。     

不确定多变量线性系统的快速收敛滑模控制

讨论了一类不确定多变量线性系统滑模变结构控制的快速收敛问题,提出一种指数型快速终端滑模变结构控制方案。通过非奇异线性变换将不确定系统化为简约标准型,而后设计了非线性指数型快速终端滑模超曲面,给出了滑模面参数矩阵的选择方法。在此基础上设计了变结构控制律,使系统状态在有限时间内到达滑模面上,随后保持在滑模面上并按指数型终端滑模的规律运动,在有限时间内收敛到平衡点。与普通的快速终端滑模相比,系统状态能以更短的时间到达平衡点。该方法具有全局稳定性和鲁棒性,仿真结果证明其有效性。     

变体飞行器有限时间收敛LPV鲁棒控制

以一类翼展可变的飞行器模型为对象,研究了一种针对参数不确定的线性变参数(linear parameter varying, LPV)系统的滑模变结构鲁棒控制问题。首先,通过Jacobian线性化和模型张量积转化将变体过程中的非线性模型最终简化为多胞体LPV系统。然后将鲁棒滑模控制技术拓展到此LPV模型中,给出了以线性矩阵不等式(linear matrix inequality, LMI)为形式的降阶滑动模态的存在性及鲁棒稳定性定理,以此为基础所设计的参数依赖的趋近律控制器能够使具有不匹配不确定性的LPV系统在有限时间内收敛至滑模切换面。仿真结果表明,上述滑模控制器在模型存在不确定性的情况下能够保证变体过程的全局稳定性。     

一类非线性不确定系统自适应terminal滑模控制方法

针对一类非线性不确定系统设计了自适应terminal滑模控制器,使跟踪误差在有限时间内收敛到零,消除了通常滑模变结构控制的到达过程,因而闭环系统从t=0时刻就对干扰具有鲁棒性。采用RBF神经网络逼近系统未知的非线性函数,引入滑模误差对其权值进行在线自适应调整,改善动态性能。最后给出的仿真例子证明了算法的有效性。     

基于T-S模型的非线性系统离散时间滑模控制

基于T-S模糊模型,讨论了一类非线性离散时间系统的控制问题。采用T-S模糊模型来描述非线性系统的动态模型,再将非线性系统的全局T-S模糊模型转化为线性不确定系统的模型。这样复杂的非线性系统的稳定问题就转化为线性不确定系统的鲁棒镇定问题。采用离散时间滑模控制方法实现线性不确定系统的鲁棒镇定。利用用线性矩阵不等式技术设计稳定的滑动模面,以降低非匹配不确定对系统的影响。给出了线性矩阵不等式形式的稳定滑动模面存在的充分条件。此外还给出了滑模控制律的设计方法。所给设计方法可保证系统鲁棒镇定,并且在滑动模面附近的抖振可明显减弱。最后,给出了truck-trailer的仿真算例,证明了所给方法的可行性和有效性。     

椭圆轨道自主接近自适应滑模制导律设计

研究了一种适用于椭圆轨道航天器自主接近任务的滑模制导方法。针对自主接近模型中存在目标轨道不可知信息量问题,根据多输入系统滑模控制思想,设计了系统误差收敛时间有限的自主接近非线性滑模制导方法,解决了自主接近系统中存在的时变性和参数不确定问题。引入剩余飞行时间,改进定义误差的参数,使自主接近过程的距离和速度具备更好的协调收敛性。根据距离收敛特性,利用线性插值方法自适应地设定期望收敛时间进而确定切换系数,在较小延长接近时间的情况下,较好地保证了变结构制导的鲁棒性,并抑制了指令抖振问题。数值仿真验证了设计的制导策略对不同的初始条件表现出良好的适应能力,满足自主接近停泊点精度要求,且自主接近所需时间较短,尤其对较远距离自主接近任务表现出很好的快速性能。