Model Predictive Control of Nonlinear Systems: Stability Region and Feasible Initial Control

This paper proposes a new method for model predictive control （MPC） of nonlinear systems to calculate stability region and feasible initial control profile/sequence, which are important to the implementations of MPC. Different from many existing methods, this paper distinguishes stability region from conservative terminal region. With global linearization, linear differential inclusion （LDI） and linear matrix inequality （LMI） techniques, a nonlinear system is transformed into a convex set of linear systems, and then the vertices of the set are used off-line to design the controller, to estimate stability region, and also to determine a feasible initial control profile/sequence. The advantages of the proposed method are demonstrated by simulation study.

Stability Criterion with Less LMI Variables for Linear Discrete-time Systems with Additive Time-delays

In this correspondence paper, an equivalent stability criterion with minimal number of linear matrix inequality （LMI） variables is presented for a delay-dependent stability criterion reported recently in the International Journal of Automation and Computing for a class of linear discrete-time systems with additive time delays. The reported stability criterion for the additive timedelay systems has more number of matrix variables in the LMI and, hence, demand additional computational burden. The proposed equivalent stability criterion, unlike the reported one, does not involve free-weighing matrices and encompass only the matrix variables that are associated in the Lyapunov-Krasovskii functional, making the criterion mathematically less complex and computationally more effective.

Model predictive control synthesis algorithm based on polytopic terminal region for Hammerstein-Wiener nonlinear systems

An improved model predictive control algorithm is proposed for Hammerstein-Wiener nonlinear systems.The proposed synthesis algorithm contains two parts:offline design the polytopic invariant sets,and online solve the min-max optimization problem.The polytopic invariant set is adopted to replace the traditional ellipsoid invariant set.And the parameter-correlation nonlinear control law is designed to replace the traditional linear control law.Consequently,the terminal region is enlarged and the control effect is improved.Simulation and experiment are used to verify the validity of the wind tunnel flow field control algorithm.

LMI Approach to Robust H_∞/H_2 Controller Design with Regional Poles Constraint of a Pump-Motor System

The time domain guideposts requirements of a pump-motor system is transfered into a series of constraints which express the robust performance upper bound and regional poles limits of the closed loop system. Then the servo system control problem is transferred into the problem of robust performance optimizing under regional poles constrains described by linear matrix inequality （LMI）. These LMIs are easy to solve through the Matlab LMI-toolbox. Simulations indicate that the controller has excellent dynamic, static and disturbance rejection performance, and the control system is robust and has perfect H2 performance to the bounded external torque disturbance.

基于LMI的分段线性系统共存吸引子转迁控制研究

以一类两自由度含间隙分段线性系统为研究对象,利用线性矩阵不等式(linear matrix inequality,LMI)和线性反馈方法对系统共存的吸引子进行在预期目标轨道引导下的转迁控制。在状态平面上利用胞映射方法对系统随参数变化时的共存吸引子进行识别,并基于Poincaré映射和Lyapunov指数研究了系统共存吸引子的稳定性及转迁机理。基于LMI和Lyapunov理论,并利用系统的向量场信息和S-procedure,将系统施加线性反馈控制器后的稳定性和反馈增益矩阵的求解问题转化为LMI描述。利用数值方法验证了所应用的线性反馈控制器及其增益矩阵选取方法的可行性及正确性。

Robust D-stability LMI conditions of matrix polytopes via affine parameter-dependent Lyapunov functions

The problem of the robust D-stability analysis for linear systems with parametric uncertainties is addressed. For matrix polytopes, new conditions via the affine parameter-dependent Lyapunov function of uncertain systems are developed with the benefit of the scalar multi-convex function. To be convenient for applications, such conditions are simplified into new linear matrix inequality （LMI） conditions, which can be solved by the powerful LMI toolbox. Numerical examples are provided to indicate that this new approach is less conservative than previous results for Hurwitz stability, Schur stability and D-stability of uncertain systems under certain circumstances.

LMI_based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.

基于LMI的不确定随机时滞系统输出反馈保性能控制

针对一类范数有界的随机时滞系统,研究在一定性能指标下的保性能控制问题。本文为获得能够实现系统保性能控制的最优输出反馈控制器,采用Lyapunov稳定性理论与LMI技术相结合的方法,将保性能控制问题转化为LMIs约束下的可行解问题。提出的控制器设计方案能够实现系统是依概率全局渐近稳定的,同时满足对系统性能指标的要求。此外,通过数值算例说明所提出控制方案的可行性。

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.

具有H_(∞)性能的输入受限三级倒立摆控制器设计

【目的】针对直线三级倒立摆控制输入受限下的稳摆控制问题,设计了具有H_(∞)性能的输入受限三级倒立摆控制器。【方法】利用线性矩阵不等式(LMI)方法,将控制输入约束问题转化为利用线性矩阵不等式求解优化值的优化问题,经Lyapunov稳定性推导出符合条件的LMI,利用MATLAB中的LMI工具箱求解得到有效的K。进一步在控制输入受限下引入H_(∞)性能指标,使所设计的控制输入受限下的算法具有H_(∞)性能。【结果】仿真结果表明,该控制器对于控制输入受限下的复杂高阶次不稳定系统具有很好的控制效果。【结论】控制输入信号在给定的受限范围内实现了三级倒立摆的稳摆要求,且引入H_(∞)性能指标后控制输入和摆杆波动更小。

基于LMI双故障动态输出反馈完整性控制

针对线性系统,基于线性矩阵不等式(LMI)给出了具有完整性的动态输出反馈控制器的设计方案,所得到的结论,不仅给出分别考虑执行器和传感器两类部件发生故障的完整性设计方案,而且给出了考虑执行器或传感器任何一类部件发生故障的完整性设计方案．本文使用了比离散故障模型更具有实际意义的连续故障模型．一个数值例子说明了所提方法的有效性．

一种基于LMI的非线性模型预测控制终端域优化方法

对于具有约束的非线性系统,提出了一种模型预测控制(Model predictive control,MPC)的终端域优化方法.基于线性矩阵不等式(Linear matrix inequality,LMI)优化和非线性系统的范数有界线性微分包含(Linear differential inclusion,LDI),给出了求解非线性MPC终端代价函数和局部稳定控制器的一种方法,在此基础上可方便地得到非线性模型预测控制终端域.一个具体的数值算例验证了算法的有效性.

低轨多星编队的相对运动差分气动控制

针对低轨纳卫星轨道机动能力不足的问题,本文研究了主动利用星间差分气动力的控制方法,创新性地提出了基于迎风姿态调整的多星编队拓展方案,并通过局部区域线性化方法实现系统的线性控制.本文研究了卫星姿态角与气动力的映射关系,建立了差分阻力和升力耦合控制的星间相对运动线性欠驱动模型,分析了此系统可控性和干扰形式,采用线性矩阵不等式(LMI)方法设计了考虑输入受限的反馈控制律.最后,针对包含两种队形的四星编队进行仿真,结果表明,卫星相对运动的稳定控制精度达到±0.4m,验证了所提出多星编队气动控制方案的可行性以及控制算法的有效性.

基于LMI的不确定混沌系统的模糊输出反馈控制

研究了基于 T-S 模糊模型描述的不确定混沌系统的静态输出反馈鲁棒控制问题,给出一种新的模糊静态输出反馈控制器设计方法。该方法充分考虑了模糊子系统间的相互作用,静态输出反馈控制器可通过求解一组线性矩阵不等式(LMI)获得。为说明问题,给出了 Chen 混沌系统模糊静态输出反馈控制设计和仿真结果。

基于LMI的结构振动鲁棒H∞控制

针对含有非线性环节与外部激励干扰的结构系统,提出了一种新型的基于LMI的鲁棒H∞振动主动控制算法。首先根据建筑结构动力学原理,建立了包含非线性不确定性的结构系统状态空间模型。然后基于动态输出反馈和线性矩阵不等式处理方法给出了鲁棒主动控制算法,可同时保证系统对模型参数摄动、控制器变化及干扰激励的鲁棒性。在EI Centro地震波作用下,对一个4自由度结构模型进行仿真,验证了该方法的有效性和较强的鲁棒性。

三电机卷绕系统的状态反馈鲁棒控制——LMI方法

针对具有强耦合、不确定性和非线性的三电机卷绕系统,提出一种基于线性矩阵不等式(linear matrix inequality,LMI)的全局鲁棒控制方法。首先,在三电机卷绕系统的数学模型的基础上给出了一种系统的稳态控制输入和参考速度的计算方法,得到了系统的动态误差模型。接着,考虑到卷绕过程中存在的参数不确定和时变性,引入区间矩阵进行描述,在此基础上,根据Lyapunov稳定性理论得到了使闭环系统鲁棒渐近稳定的LMI充分条件。最后,以实验室搭建的三电机卷绕系统为例进行了仿真和平台实验,实验结果证明了所提出的控制方法的有效性和鲁棒性。

感应电机速度和电阻自适应辨识的LMI方法(英文)

该文研究了一种感应电机无速度传感器模型参考自适应系统(model reference adaptive system,MRAS),提出一种新型的基于自适应磁链观测器的常数增益速度辨识方法。首先,运用李亚普诺夫(Lyapunov)稳定性理论设计出自适应磁链观测器及速度估算方法,通过MATLAB中的线性矩阵不等式(linear matrix inequality,LMI)工具箱求解线性矩阵不等式获得磁链观测器的增益矩阵,保证了此磁链观测器的稳定性,同时也克服了运用极点配置方法带来不稳定区域的问题。该文还研究了基于自适应观测器的电阻辨识问题。基于给出的自适应磁链估计方法,设计了感应电机无速度传感器直接转矩控制系统,并进行了MATLAB仿真和实验,结果表明,提出的无速度传感器速度方法在全速范围内具有很好的动态和静态性能。