不确定线性系统的可达集估计

本文针对线性不确定系统,研究了系统状态可达集估计问题.在已知参考输入,未知扰动有界的条件下,提出了一种新的可达集估计方法,并把所提方法推广到系统不稳定的情况,分别估计出不稳定系统的闭环可达集和开环可达集.通过分析动态系统的李雅普诺夫函数,将求取系统可达集的问题转化为线性矩阵不等式优化问题,并将可达集范围用椭球集形式表述.最后分别通过数值仿真分析,验证了所提出方法对线性系统可达集估计的有效性.     

基于可达集的鲁棒模型预测控制

设计了一种基于可达集的鲁棒模型预测控制算法.首先确定了一个鲁棒不变集,并将此不变集用作模型预测控制的终端约束集;接着采用终端约束集对可达集的包含度作为优化指标;最后,采用预测时域逐渐减小的控制策略以保证在线优化存在可行解.从理论上证明了吸引域内的任意点在有限时域内都会被引导至终端约束集并始终停留在此集之内,并由仿真算例验证了本文所设计鲁棒模型预测控制算法的可行性.     

基于Hamilton-Jacobi方程的飞行器机动动作可达集分析

为了给驾驶员完成标准机动动作提供决策支持, 提出一种使用哈密尔顿-雅克比(Hamilton-Jacobi)方程求解机动动作可行状态空间的研究方法.使用关键点将机动动作划分为不同阶段, 将各关键点的标准状态约束作为目标集, 逆时间求解目标集对应的可达集得到各阶段的边界状态范围, 目标集和可达集均由零水平集表示.使用该方法得到斤斗动作三维度运动模型下各阶段的可达集及斤斗动作的可行状态空间, 为了使运动模型的控制量与驾驶员实际操纵更为接近, 构建了以迎角变化率为控制量的四维度运动模型, 在此基础上对斤斗动作各阶段的可达集进行了分析.     

车辆跟随控制策略的状态可达集建模及验证方法

车辆动态行为的不确定性会造成跟随车辆控制的不确定性.传统的车辆跟随控制方法只是针对车辆的单一行为动态的不确定性进行建模,无法遍历车辆所有可能的控制输入,因而,既无法一次性提供跟随策略下完整的可行控制方案,也不足以在理论上保证对策略安全检测的可信性.为此,提出车辆跟随控制策略的状态可达集建模及验证方法.该方法将控制策略转...     

HGV平衡滑翔式轨迹可达区域计算方法研究

针对滑翔式高超声速飞行器(HGV)平衡滑翔轨迹可达区域的高精度快速计算问题,研究了一种基于降阶动力学模型和连续凸优化方法的可达区域计算方法。首先,根据“准平衡滑翔假设”条件,将再入飞行器三自由度动力学方程进行降阶处理,得到以速度为自变量的三阶动力学方程。然后,将可达区域计算问题描述为一系列满足再入走廊约束和初、末状态约束下的横程最大优化问题,将动力学方程进行线性化、离散化处理后,采用连续凸优化方法对该问题进行求解,得到了滑翔飞行器不同末端速度下的可达区域。最后,以CAV-H飞行器模型为例进行了仿真验证,结果表明,该方法具有较高的求解效率和可达区域计算精度。     

一种基于凸多面体的集员滤波故障诊断方法

针对含有未知但有界噪声的线性系统,利用基于凸多面体的集员滤波算法进行故障诊断策略研究;针对不同故障类型设计集员滤波器,通过求解基于无故障模型的集员滤波器状态可行集进行故障检测.采用模型去伪的思路进行故障隔离,即在故障发生后寻找唯一当前状态可行集不为空的集员滤波器,其对应的故障类型即为故障隔离结果.通过实例仿真分析得出,所提出方法可完成对不同类型故障的诊断,具有可行性.     

具有自适应噪声边界的Tube可达集鲁棒预测控制

针对过程噪声设定边界与真实噪声边界失配的有界干扰离散线性不确定系统,提出一种具有自适应噪声边界的Tube可达集鲁棒模型预测控制方法.首先,该算法引入基于MIT规则的自适应集员滤波在线估计系统状态和噪声边界.其次,基于估计值,通过迭代自适应集员滤波的时间更新部分计算出预测时域内闭环不确定系统状态的可达集.最后,用可达集代替不变集并根据Tube鲁棒模型预测控制策略,给出了实际不确定系统的控制律,确保系统状态鲁棒渐近稳定,并收敛于终端干扰不变集.仿真结果验证了该控制方法的有效性.     

基于反向可达集的影响力最大化算法

现有影响力最大化算法多数因时间复杂度较高或影响力传播范围有限,不适用于大规模社交网络。基于独立级联模型,结合反向可达集采样提出一种改进的影响力最大化算法D-RIS。在影响力传播函数满足单调性和子模性的前提下,通过自动调试确定反向可达集生成数量的临界值。在Slashdot和Epinions真实数据集上的实验结果表明,D-RIS算法在影响力传播范围上接近CELF算法且优于RIS、HighDegree、LIR和pBmH启发式算法,同时在运行时间上相比CELF算法减少近百倍,具有更好的通用性与稳定性,适用于拓扑结构变化和规模较大的社交网络。     

一种基于变量可达向量的链表抽象方法

提出了一种链表抽象表示方法.该方法隐式存储链表结点之间的边信息,并采用了一种紧致的链表状态表示,存储开销较低,且维护了链表长度信息,精确度较高.具体而言,根据变量对链表结点的可达性质定义了变量可达向量,采用带计数的变量可达向量集描述链表的形态及数量性质,并定义了基本链表操作的抽象语义.通过简单扩展,该方法可以建模包括环形链表在内的所有单向链表.最后,为了验证该链表抽象方法的正确性,在符号执行框架中进行实验,并对常见链表操作程序的运行时错误、长度相关性质等关键性质进行了分析与验证.     

一种线性动态模型参数估计方法

本文提出一种线性动态模型参数估计方法,该算法改进并推广了Durbin算法.它能在噪声过程结构未知时,给出实际过程和噪声过程参数的全局P相容估值.五个数字仿真例子表明了算法的有效性.     

Under-estimates of reachable sets for linear control systems

A new algorithm is presented for providing under-estimates of the reachable set from the origin for a class ofn-dimensional linear systems with bounded controls. This algorithm is based on the novel approach of choosing a feedback control which makes all the eigenvalues of the closed loop system unstable. Results from feedback control and Liapunov stability theory are then used to formulate the problem as the minimization of a nonlinear function subject to constraints on certain matrices. The solution of this optimization problem provides an under-estimate of the reachable set in the form of ann-dimensional ellipsoid. Examples of both continuous and discrete-time systems are presented to illustrate the method. Comparison with existing exact results for some 2-dimensional systems shows that the method provides good approximations in these cases.     

Asymptotics of reachable sets of linear dynamical systems with impulsive control

Explicit asymptotic formulas for the reachable sets of linear dynamical systems with constraints on the total impulse of control action under different assumptions concerning the spectrum of the system’s matrix are obtained. It is shown that for large time, the reachable sets can be approximately represented in the form of the product of the scaling matrix and the normalized reachable set, where the matrix is an elementary function of time, and the normalized reachable set depends on time quasi-periodically. Analysis of asymptotic formulas has shown that, generally speaking, there exists a continuum of limit shapes, the aggregate of which produces a multidimensional attractor.     

A complete characterization of reachable sets for constrained linear time-varying systems

We consider linear time-varying systems with linear constraints on both control and state variables. The reachable set is a convex polyhedron that we completely characterize in terms of its boundary hyperplanes.     

Boundary regularity of reachable sets of control systems

The reachable set of a differential inclusion has nonsmooth boundary in general. Now we give sufficient conditions on the compact initial set and the differential inclusion (a.e.) so that this topological boundary has “positive erosion”, i.e. it satisfies a uniform interior sphere condition. The proof is based on the close relation between the semiconcave value function of a suitable Mayer problem and its epigraph with positive erosion.     

Improved ellipsoidal bound of reachable sets for time-delayed linear systems with disturbances

We consider the problem of finding an ellipsoidal reachable set that bounds the states of time-delayed linear systems with bounded peak disturbances. The considered time-delay is time-varying but it has an upper bound in magnitude and rate. Based on the modified Lyapunov-Krasovskii(L-K) type functional, we derive a delay-dependent result expressed in the form of matrix inequalities containing only one non-convex scalar. The result is extended to uncertain time-delayed linear systems. Finally, we show the usefulness of our result by a comparative numerical example.     

A simple method for determining the reachable set for linear discrete systems

A simple method is described for determining the reachable set RNof annth-order linear discrete systemN > nfor a single bounded input. The method proposed reduces the problem from solving a set of (n - 1) simultaneous equations to a simpler one, requiring only the evaluation of two inner products.     

On reachable sets for linear systems with delay and bounded peak inputs

Linear systems with constant coefficients and time-varying delays are considered. We address the problem of finding an ellipsoid that bounds the set of the states in the Euclidean space that are reachable from the origin, in finite time, by inputs with peak value that is bounded by a prechosen positive scalar. The system may encounter uncertainties in the matrices of its state space model and in the delay length. The Lyapunov-Razumikhin approach is applied and a bounding ellipsoid is obtained by solving a set of linear matrix inequalities that depend on the upper-bound of the delay length.     

Comparative analysis of the asymptotic dynamics of reachable sets to linear systems

Explicit asymptotic formulas for reachable sets of linear dynamic systems with two types of control bounds, geometric constraints and constraints on the total impulse of the control action, are compared. A detailed proof of asymptotic formulas for the case of geometric constraints was first given. It was shown that, despite the similarity of the problem statement and methods to study the asymptotics of reachable sets for the considered types of constraints, the results obtained are essentially different. For example, for the impulsive case in the space of shapes of reachable sets, a multidimensional attractor may arise, while, in the case of geometric constraints, the corresponding attractor is reduced to a single point.     

An algorithm of the method of sections and program tools for constructing reachable sets of nonlinear control systems

The method of sections for constructing reachable sets of nonlinear control systems with constraints on the control and system state is considered. The proposed algorithms are based on the application of complexes of programs whose functional content contains methods for calculating an optimal control for various constraints on control and system coordinates. The problems of many-processor computing technology are discussed and the results of numerical experiments are presented.     

On the reachable set for third-order linear discrete-time systems with positive control

In this paper we study the geometrical properties of the set of reachable states of a single-input third-order discrete-time linear system with positive controls. This set is a cone and we give a complete geometrical characterization of this set when the system has all real eigenvalues. More in detail, we give necessary and sufficient conditions for properness and polyhedrality of the cone and provide the number of its edges in terms of eigenvalue locations. Moreover, we provide necessary and sufficient conditions for finite time reachability of every reachable state and characterize the minimum number of steps needed to reach every state in terms of eigenvalue locations.