基于LMI的参数随机变化系统的概率密度函数控制

针对模型参数在有界区域内随机变化的系统, 基于平方根 B 样条模型, 提出了输出概率密度函数 (Probability density function, PDF) 跟踪控制策略. 目标是控制系统输出的概率密度函数跟踪给定的概率密度函数. 通过 B 样条逼近建立了输出 PDF 和权值之间的对应关系, 把 PDF 的跟踪转化为权值的跟踪, 同时系统转化为 MIMO 系统,从而权值向量的跟踪就转化为 MIMO 系统的跟踪问题, 接着给出了系统输出概率密度函数跟踪给定概率密度函数的控制器存在的充分条件, 通过求解线性矩阵不等式完成状态反馈和输出反馈跟踪控制器的设计, 得到了系统具有 Hinfinity 范数界 Gamma 鲁棒镇定的结果. 仿真结果表明本文提出的控制算法是有效的.     

输出概率密度函数鲁棒弹性最优跟踪控制

研究了一类随机动态系统的鲁棒弹性最优跟踪控制问题。在采用B样条神经网络模型逼近随机动态系统的输出概率密度函数(PDF)的基础上,同时考虑系统模型和控制器增益不确定性,结合Lyapunov稳定性理论和线性矩阵不等式(LMI)技术,引入增广控制作用,设计基于广义状态反馈的鲁棒弹性最优跟踪控制器,目的是使系统的输出PDF跟踪给定PDF。通过求解LMI,所得控制器不仅能实现跟踪目的,而且能确保该随机动态系统全局稳定并满足一定的线性二次型性能指标上界。仿真结果表明该方法简单易行,且无需任何设计参数调整。     

磨矿粒度分布的概率密度函数跟踪控制研究

传统的磨矿粒度控制局限于百分比含量这一指标,未考虑粒度具体分布信息,而磨矿产品的粒度分布(PSD)对整个选矿系统能耗和精度的影响不容小视.为解决上述问题,用概率密度函数(PDF)表征PSD信息,对磨矿粒度的PDF进行跟踪控制,使其跟踪给定的最利于选别的粒度PDF.在每个采样时刻,首先测取磨矿产品的多个粒度样本,用核密度方法估算PDF;然后利用跟踪误差建立性能指标函数;最后,用粒子群算法优化性能指标函数,设计最优控制输入.仿真结果验证了所提方法的有效性,可为选矿系统的后续研究和实际应用提供参考.     

输出概率密度函数的最优跟踪控制:均方根B - 样条模型

在分析均方根B样条模型在实现输出概率密度函数最优跟踪控制时存在的问题的基础上,提出了将最优跟踪控制转化为非线性状态约束下的跟踪误差最优调节器,然后依据非线性状态约束和系统模型的特点分别设计了鲁棒变结构控制器及非线性观测器,并利用误差补偿控制来保证非线性观测器误差的有界性.仿真结果表明了提出的转换控制策略的有效性.     

一类非线性系统的奇异点克服控制

针对一类非线性系统, 研究存在奇异点时的跟踪控制问题. 在采用反馈线性化方法将对象转换成标准型后, 构造线性补偿器并结合期望轨迹的高阶导数构成伪控制量. 通过引入梯度动力学方法求解控制律, 以克服在控制过程中遇到的奇异点问题. 通过稳定性分析验证了闭环系统的稳定性和跟踪误差的收敛性. 仿真结果表明, 此类控制器具有良好的控制性能, 并且能有效克服奇异点问题.

     

一类输入饱和非仿射非线性系统的非线性动态逆控制

输入饱和是实际系统中经常遇到的问题,很多已有的控制方法要求被控系统具有仿射结构.本文针对一类具有输入饱和的非仿射纯反馈非线性系统提出了一种基于奇异值摄动理论的非线性动态逆控制方法.首先构建一个快变子系统,在慢时间尺度下将非仿射非线性系统转换为具有仿射结构的线性系统,从而应用已有的控制算法实现控制目的.为了消除输入饱和带...     

一类非线性系统的自适应控制方法

非线性系统的模型参考自适应控制是自适应理论的一个新的发展方向,目前针对可反馈线性化的系统已经取得了很多研究成果.但以往采用的方法要求系统对未知参数是线性的,且计算复杂度随系统阶次或相对阶的升高而升高.给出一种新的非线性模型参考自适应跟踪控制方法,证明了无需未知参数以线性形式存在,而只要求回归向量对参数满足一定的Lipschitz条件即可保证系统具有期望的特性.     

基于神经网络的一类非线性系统自适应跟踪控制

提出一种非线性系统的自适应神经跟踪控制方案。通过利用RBF神经网络对未知非线性系统建模,并用一个滑模控制项消除网络建模误差和外部干扰的影响,从而能够保证闭环系统的全局稳定性和输出跟踪误差渐近收敛于零。     

一类广义非线性系统的无源控制

考虑一类广义非线性系统的无源控制问题，利用广义Lyapunov函数和线性矩阵不等式，给出广义非线性系统无源且零解渐近稳定的充分条件。并在一定条件下得到存在状态反馈无源控制器，使得闭环系统无源且零解渐近稳定的充分条件，同时给出相应的控制器构造方法。     

基于预设性能的非仿射非线性系统自适应有限时间控制

针对一类具有死区的非仿射非线性系统,将预设性能控制与有限时间控制相结合,提出一种具有预设性能的自适应有限时间跟踪控制方法.基于Backstepping技术、模糊逻辑系统及有限时间Lyapunov稳定理论,给出使系统半全局实际有限时间稳定(semi-globally practically finite-time stable,SGPFS)的充分条件和设计步骤.该控制策略不仅使系统的输出误差在有限时间内收敛到一个预先设定区域,同时保证其收敛速度、最大超调量和稳态误差均满足预先设定的性能要求.最后通过仿真示例验证了所提出设计方法的有效性.     

Feedback control of nonlinear stochastic systems for targeting a specified stationary probability density

In the present paper, an innovative procedure for designing the feedback control of multi-degree-of-freedom (MDOF) nonlinear stochastic systems to target a specified stationary probability density function (SPDF) is proposed based on the technique for obtaining the exact stationary solutions of the dissipated Hamiltonian systems. First, the control problem is formulated as a controlled, dissipated Hamiltonian system together with a target SPDF. Then the controlled forces are split into a conservative part and a dissipative part. The conservative control forces are designed to make the controlled system and the target SPDF have the same Hamiltonian structure (mainly the integrability and resonance). The dissipative control forces are determined so that the target SPDF is the exact stationary solution of the controlled system. Five cases, i.e., non-integrable Hamiltonian systems, integrable and non-resonant Hamiltonian systems, integrable and resonant Hamiltonian systems, partially integrable and non-resonant Hamiltonian systems, and partially integrable and resonant Hamiltonian systems, are treated respectively. A method for proving that the transient solution of the controlled system approaches the target SPDF as t→∞ is introduced. Finally, an example is given to illustrate the efficacy of the proposed design procedure.     

Optimal probability density function control for NARMAX stochastic systems

This paper presents a new control strategy for a class of non-Gaussian stochastic systems so that the output probability density function (PDF) of the system can be made to follow a desired PDF. The system considered is represented by an Nonlinear AutoRegressive and Moving Average with eXogenous (NARMAX) inputs with input channel time-delay and non-Gaussian noise. A multi-step-ahead nonlinear cumulative cost function is used to improve tracking performance. For this purpose, a relationship between the PDFs of all the inputs and the PDFs of multiple-step-ahead output is formulated by constructing an auxiliary multivariate mapping. By minimizing this performance function, a new explicit predictive controller design algorithm is established with less conservatism than some previous results. Furthermore, an improved approach is developed to guarantee the local stability of the closed-loop system by tuning the weighting parameters recursively. Simulations are given to demonstrate the effectiveness of the proposed control algorithm and desired results have been obtained.     

The PDF shape control of the state variable for a class of stochastic systems

The shape control of probability density function (PDF) is an important subject in stochastic systems. The PDF-shaping control study has ranged from linear systems to non-linear systems. In this paper we present a PDF-shaping control technique which is useful for a class of non-linear stochastic systems. Controlling the PDF shape requires designing a controller to make the state PDF follow the goal PDF; it is actually to determine the gains of the controller. As we know, the stationary PDF of the state variable is equivalent to the solution of the Fokker–Planck–Kolmogorov (FPK) equation arising from the stochastic system driven with Gaussian white noise. After designing the controller, we derive the solution with some parameters to the corresponding FPK equation, and then solve out the parameters in the solution by the linear-least-squares method, therefore obtaining the gains of the controller. Finally, simulation experiments have been carried out to verify the effectiveness of the approach.     

Adaptive neural tracking control for a class of stochastic nonlinear systems

This paper investigates the problem of adaptive neural control design for a class of single‐input single‐output strict‐feedback stochastic nonlinear systems whose output is an known linear function. The radial basis function neural networks are used to approximate the nonlinearities, and adaptive backstepping technique is employed to construct controllers. It is shown that the proposed controller ensures that all signals of the closed‐loop system remain bounded in probability, and the tracking error converges to an arbitrarily small neighborhood around the origin in the sense of mean quartic value. The salient property of the proposed scheme is that only one adaptive parameter is needed to be tuned online. So, the computational burden is considerably alleviated. Finally, two numerical examples are used to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive control of a class of discrete-time affine nonlinear systems

The adaptive control problem is addressed in the paper for a class of discrete-time affine nonlinear input/output stochastic models with linear unknown parameters. The controller is a certainty equivalence weighted one-step-ahead control and is constructed by using the weighted-least-squares and random regularization methods. Global stability of the closed-loop systems is established, which shows that arbitrarily large growth rate is allowed for the multiplicative nonlinear part of the systems.     

随机非线性系统的输出反馈控制

针对满足线性增长条件的一类随机非线性系统, 本文研究了输出反馈镇定问题. 然而不同于现有的所有文献, 由于线性增长条件中含有不可量测的状态, 引入了一个待定的高增益观测器. 利用反推设计技术, 构造性地给出了一个输出反馈控制器的设计, 通过适当地选取高增益参数, 保证了闭环系统的零解是概率意义下全局渐近稳定的, 输出几乎处处调节于零.     

Neuro-adaptive cooperative tracking control of unknown higher-order affine nonlinear systems

In this paper we propose a practical design method for distributed cooperative tracking control of a class of higher-order nonlinear multi-agent systems. Dynamics of the agents (also called the nodes) are assumed to be unknown to the controller and are estimated using Neural Networks. Linearization-based robust neuro-adaptive controller driving the follower nodes to track the trajectory of the leader node is proposed. The nodes are connected through a weighted directed graph with a time-invariant topology. In addition to the fact that only few nodes have access to the leader, communication among the follower nodes is limited with some nodes having access to the information of their neighbor nodes only. Command generated by the leader node is ultimately followed by the followers with bounded synchronization error. The proposed controller is well-defined in the sense that control effort is restrained to practical limits. The closed-loop system dynamics are proved to be stable and simulation results demonstrate the effectiveness of the proposed control scheme.     

一类仿射非线性系统的自适应神经网络输出反馈变结构控制

本文研究了一类仿射非线性系统的输出反馈控制问题. 在介绍文献[4~6]的基础上, 提出一种基于神经网络参数化技术的自适应变结构输出反馈控制方案, 该方案能够避免使用严格正实(SPR)条件, 它不仅能够保证收缩条件的可行性, 而且还可以分析闭环系统的稳态和暂态的一致有界性, 并能够对观测增益和控制参数的选取进行清楚地分析.     

Stabilization of a class of uncertain nonlinear affine systems subject to control constraints

Practical and asymptotic stabilization is investigated for a class of uncertain nonlinear affine control systems subject to constraints on the control inputs. The uncertain systems are modelled as non‐linear perturbations to a known non‐linear idealized system and a problem formulation based on differential inclusions is adopted. A class of constrained generalized state‐feedback controls (containing both continuous and discontinuous selections) is developed, which guarantees stabilization with a specified region of attraction. In the presence of residual uncertainty, sufficient conditions for global stabilizability are presented, whilst local results are obtained by relaxing these conditions. Copyright © 2001 John Wiley & Sons, Ltd.