非线性系统鲁棒吸收的动态补偿方法

考虑非线性不确定系统的鲁棒吸引问题，借助于动态输出反馈，构造了两类控制律，这两类控制律分别可使相应的闭环系统被一任意小的区域鲁棒吸引，或被一预先设置的区域有限吸引。     

离线鲁棒预测控制器综合方法的改进方案

对离线鲁棒预测控制器综合方法进行改进.离线鲁棒预测控制算法离线确定一个控制律序列,对应一组吸引域;在线根据当前状态位于哪个吸引域内部(或哪两个吸引域之间)选择相应的一个控制律(或相邻的两个控制律的线性插值).引入参数Lyapunov函数得到多包椭圆型吸引域和多包二次稳定的离线控制律,改进了控制器的可行性和最优性.改进的控制器保持了稳定性以及控制律关于系统状态的连续性.     

带扰动补偿的无抖振离散重复控制器设计

针对周期离散系统的跟踪控制问题,提出一种有限时间单调收敛的无抖振吸引律,讨论扰动补偿措施并将其嵌入吸引律形成理想误差动态用于设计离散重复控制器.通过分析补偿误差上界说明扰动补偿措施能抑制重复控制未能消除的扰动,通过推导控制器稳态误差带说明吸引律的收敛性可使系统具有鲁棒稳定性.针对伺服电机系统的仿真与实验验证了设计工作的有效性.     

不确定性系统的非因果鲁棒学习控制

针对不确定性系统提出一种非因果鲁棒学习控制方法。该学习控制律的非因果学习部分通过标称系统的优化指标得到,鲁棒部分通过设计鲁棒加权来实现。首先,不考虑鲁棒部分的具体形式,推导出标称系统描述的学习控制律的鲁棒收敛性条件;然后,设计与系统不确定性相关的鲁棒加权,由鲁棒收敛性条件得到鲁棒加权的设计原则;最后,通过仿真实验验证了所提出方法的有效性,并分析了不同形式不确定性系统鲁棒设计的保守性。     

飞行控制系统的鲁棒性评估方法研究

随着现代飞机气动布局的改进和控制方式的多样化,旧有的评价体系已经不能适应新兴的控制系统。针对目前国内外对飞行控制律鲁棒性评估方法的不足,发展了一种基于MonteCarlo方法的评价控制律鲁棒性能的方法。提出了鲁棒度的概念,给出了具体的系统鲁棒性量化指标及计算方法,通过对飞行控制律鲁棒度的比较,进而完成对飞行控制律鲁棒性的评估。它能直观并且定量地得到控制系统在任意给定性能水平下的鲁棒度数值,从而可对不同飞行控制律鲁棒性能的优劣做出比较,得到更为直观的的评价结果。     

约束分段仿射系统的鲁棒最小时间控制

针对一类有界附加扰动的分段仿射系统,提出了一种离线低复杂性的鲁棒预测控制方法-鲁棒最小时间控制.首先计算系统的最大鲁棒正不变集和相关的局部稳定控制律,然后基于最大鲁棒正不变集通过多参数规划离线迭代计算系统的鲁棒一步集,得到的最小时间控制器覆盖最大鲁棒可稳定集.提出的鲁棒最小时间控制确保系统状态在最小时间内进入鲁棒正不变...     

具有闭环极点和方差约束的不确定离散系统鲁棒控制

对一类具有范数有界不确定性的离散时间系统,研究了使得闭环系统的所有极点位于一给定圆盘,且稳定状态方差不超过给定上界的状态反馈鲁棒方差控制律设计问题,基于线性矩阵不等式的处理方法,导出了鲁棒方差控制律的存在条件,并用一组线性矩阵不等式的珂行解给出了鲁棒方差控制律的一个参数化表示,进而,通过建立和求解一个凸优化问题,给出了具有最泸控制能量的鲁棒方差控制律设计方法。     

一类结构不确定采样系统的鲁棒H∞控制

本文针对一类结构不确定线性采样系统,研究了鲁棒H∞控制问题,给出了系统鲁棒稳定的充分条件及响应的鲁棒H∞控制律和最优鲁棒H∞控制律,控制律的求取通过借助一类线性矩阵不等式(LMI),或通过求取满足线性矩阵不等式约束的优化问题.仿真结果表明,系统在受到扰动后仍然是稳定的,同时给出了最优性能指标随外部扰动加权矩阵的变化规律.     

一类非线性不确定动态系统的鲁棒稳定控制器设计及Benchmark问题求解

本文研究一类非线性不稳定动态系统的基于状态反馈的鲁棒稳定控制设计问题，提出了一种基于状态反馈的非线性控制律，该控制器使得闭环系统鲁棒稳定，对于Ｂｅｎｃｈｍａｒｋ问题验证了所提控制律的正确性和有效性。     

输入状态稳定的鲁棒预测控制

以有界干扰非线性系统为研究对象,设计一种基于近似可达集的鲁棒预测控制方法。该方法以鲁棒控制不变集作为终端约束集,采用一种简单的三次多项式逼近预测控制的待优化控制律,通过在线优化求解三次多项式的各项系数,并从理论上证明了所设计的鲁棒预测控制律可以使系统输入状态稳定。最后通过仿真实例验证了所提出的鲁棒预测控制方法的可行性和有效性。     

基于细菌趋化的果蝇优化算法

受细菌趋化行为的启发,将细菌趋化行为中的吸引与排斥转换操作引入到果蝇优化算法中,提出基于细菌趋化的果蝇优化算法。该算法通过判断群体适应度方差是否为零来决定执行排斥操作（逃离最差个体）还是吸引操作（向最优个体靠近）,解决果蝇优化算法中只向最优个体靠近,而导致种群多样性丢失引起的早熟收敛问题。对几种经典测试函数的仿真结果表明,新算法具有更好的全局搜索能力,在收敛速度、收敛可靠性及收敛精度上比果蝇优化算法有较大的提高。     

Analytic Estimates for the Boundary of the Region of Asymptotic Attraction

The paper presents a method of back propagating analytic surfaces to approximate the boundary of the region of asymptotic attraction of autonomous dynamical systems. Starting with an initial parametrically defined surface within the region we use a symbolic version of the Euler numerical integration scheme to produce a sequence of parametrically defined surfaces which approach the required boundary. One example shows that good approximations for the limit cycle of the Van der Pol oscillator can be obtained for intermediate values of the parameter. The technique can be applied to systems of any dimension.     

Guaranteed estimates of the domain of attraction for a class of hybrid systems

This paper addresses the estimation of the domain of attraction for a class of hybrid nonlinear systems where the state space is partitioned into several regions. Each region is described by polynomial inequalities, and the union of all the regions is a complete cover of the state space. The system dynamics are defined on each region independently from the others by polynomial functions. First, the problem of computing the largest sublevel set of a Lyapunov function included in the domain of attraction is considered. An approach is proposed for addressing this problem based on linear matrix inequalities, which provides a lower bound of the sought estimate by establishing negativity of the Lyapunov function derivative on each region. Second, a sufficient and necessary condition is provided for establishing optimality of the found lower bound, which requires to solve linear algebra operations in typical cases. Third, the problem of looking for Lyapunov functions that maximize the estimate of the domain of attraction is considered, describing several strategies where the proposed approach can be readily adopted. Copyright © 2014 John Wiley & Sons, Ltd.     

Maximizing regions of attraction via backstepping and CLFs with singularities

When a nonlinear control law contains a singularity (that is, becomes unbounded on a set of points in the state space), the region of attraction is often only a subset of the region of feasibility of this control law. A method which is well known to suffer from this difficulty is feedback linearization. We show that the backstepping design (in its standard form) has an inherent ability to make the regions of feasibility and attraction coincide, thus maximizing the latter. The key observation that this paper provides is that a standard backstepping-style control Lyapunov function, which grows unbounded on the set where the control law becomes unbounded, has level sets that always remain in the feasibility region, which makes the feasibility region positively invariant. A simulation comparison with a feedback linearization design shows a dramatic improvement of the region of attraction with backstepping. Since our theorem imposes a strong assumption that the feasibility region for the first subsystem in the backstepping problem is positively invariant, we present examples (ranging from simple to fairly difficult) which demonstrate how this condition can be satisfied.     

Nonlinear region of attraction analysis for flight control verification and validation

Current practice for flight control validation relies heavily on linear analyses and nonlinear, high-fidelity simulations. This process would be enhanced by the addition of nonlinear analyses of the flight control system. This paper demonstrates the use of region of attraction estimation for studying nonlinear effects. A nonlinear polynomial model is constructed for the longitudinal dynamics of NASA's Generic Transport Model aircraft. A polynomial model for the short period dynamics is obtained by decoupling this mode from the nonlinear longitudinal model. Polynomial optimization techniques are applied to estimate region of attractions around trim conditions.     

Enlarging the domain of attraction of MPC controllers

This paper presents a method for enlarging the domain of attraction of nonlinear model predictive control (MPC). The usual way of guaranteeing stability of nonlinear MPC is to add a terminal constraint and a terminal cost to the optimization problem such that the terminal region is a positively invariant set for the system and the terminal cost is an associated Lyapunov function. The domain of attraction of the controller depends on the size of the terminal region and the control horizon. By increasing the control horizon, the domain of attraction is enlarged but at the expense of a greater computational burden, while increasing the terminal region produces an enlargement without an extra cost.In this paper, the MPC formulation with terminal cost and constraint is modified, replacing the terminal constraint by a contractive terminal constraint. This constraint is given by a sequence of sets computed off-line that is based on the positively invariant set. Each set of this sequence does not need to be an invariant set and can be computed by a procedure which provides an inner approximation to the one-step set. This property allows us to use one-step approximations with a trade off between accuracy and computational burden for the computation of the sequence. This strategy guarantees closed loop-stability ensuring the enlargement of the domain of attraction and the local optimality of the controller. Moreover, this idea can be directly translated to robust MPC.     

LMI stability conditions for uncertain rational nonlinear systems

This paper presents LMI conditions for local, regional, and global robust asymptotic stability of rational uncertain nonlinear systems. The uncertainties are modeled as real time varying parameters with magnitude and rate of variation bounded by given polytopes and the system vector field is a rational function of the states and uncertain parameters. Sufficient LMI conditions for asymptotic stability of the origin are given through a rational Lyapunov function of the states and uncertain parameters. The case where the time derivative of the Lyapunov function is negative semidefinite is also considered and connections with the well known LaSalle's invariance conditions are established. In regional stability problems, an algorithm to maximize the estimate of the region of attraction is proposed. The algorithm consists of maximizing the estimate for a given target region of initial states. The size and shape of the target region are recursively modified in the directions where the estimate can be enlarged. The target region can be taken as a polytope (convex set) or union of polytopes (non‐convex set). The estimates of the region of attraction are robust with respect to the uncertain parameters and their rate of change. The case of global and orthant stability problems are also considered. Connections with some results found in sum of squares based methods and other related methods found in the literature are established. The LMIs in this paper are obtained by using the Finsler's Lemma and the notion of annihilators. The LMIs are characterized by affine functions of the state and uncertain parameters, and they are tested at the vertices of a polytopic region. It is also shown that, with some additional conservatism, the use of the vertices can be avoided by modifying the LMIs with the S‐Procedure. Several numerical examples found in the literature are used to compare the results and illustrate the advantages of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

一类时延反馈神经网络的稳定性及吸引域的估计

反馈型神经网络由于具有极为丰富的动力学行为和整体计算能力（如优化、联想、振荡和混饨）而倍受关注，近几年的研究表明，当网络的时延足够小时，具有延时的对称Hopfield型神经网络和无时延情况一样也是全局稳定的．本文通过构造适当Lyapunov泛函的方法，对一类具有时延的反馈型神经网络平衡点的渐近稳定性进行了分析，得到了平衡点渐近稳定的充分条件：要检验一个有时间延迟的反馈型神经网络的稳定性，只要测试一个特定矩阵的定性性质或一个特定不等式即可．最后我们也提供了一种估计网络渐近稳定平衡点吸引域的方法．     

An observer for systems with nonlinear output map

A nonlinear observer, with the feedback gain weighted by the sensitivity of the output with respect to the state, is developed for systems with nonlinear output map. The observer can be obtained from the extended Kalman filter by a special choice of time-varying weighting matrices. It is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived. The observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal. Using plant data from the converter at SSAB Oxelösund AB, the observer is shown to provide accurate estimates of the carbon content.     

On the region of attraction of nonlinear quadratic systems

Quadratic systems play an important role in the modelling of a wide class of nonlinear processes (electrical, robotic, biological, etc.). For such systems, it is of mandatory importance not only to determine whether the origin of the state space is locally asymptotically stable but also to ensure that the operative range is included into the convergence region of the equilibrium. Based on this observation, this paper considers the following problem: given the zero equilibrium point of a nonlinear quadratic system, assumed to be locally asymptotically stable, and a certain polytope in the state space containing the origin, determine whether this polytope belongs to the region of attraction of the equilibrium. The proposed algorithm requires the solution of a suitable feasibility problem involving linear matrix inequalities constraints. An example illustrates the effectiveness of the proposed procedure by exploiting a population interaction model of three species.