L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given.     

Robust Stabilization for Uncertain Control Systems Using Piecewise Quadratic Lyapunov Functions

The sufficient condition based on piecewise quadratic simultaneous Lyapunov functions for robust stabilization of uncertain control systems via a constant linear state feedback control law is obtained. The objective is to use a robust stability criterion that is less conservative than the usual quadratic stability criterion. Numerical example is given, showing the advanteges of the proposed method.     

基于PLPF方法的车辆ABS控制方法

建立了四通道车辆防抱制动系统（ABS）的状态空间模型，考虑到其非线性特性，提出了用PLPF（分段线性多项式）函数对其进行分段线性化的方法，并提出了修正的PLPF方法，利用车辆系统的状态参数得出系统矩阵和控制矩阵。用最优控制方法得出在下一个采样点时的车辆状态，即可按照基于PLPF的最优控制方法得到控制序列。     

连续时间多面体不确定系统的鲁棒预测控制

运用线性矩阵不等式方法,研究连续时间多面体不确定系统的鲁棒预测控制问题。通过在线求解无穷时域二次型性能指标下的"最小-最大"优化问题,给出了分段连续的状态反馈控制器存在的充分条件。运用可控不变集理论,解决在线优化问题的可行性,证明了初始时刻的可行解可以保证闭环系统渐近稳定。仿真证明了控制算法的有效性。     

新分段分数阶混沌系统的同步控制

通过改变修正的Lorenz-Stenflo (modified Lorenz-Stenflo, MLS)混沌系统的分段函数项,得到了一个新的四维分段混沌系统。新系统较MLS混沌系统具有更低的分数阶维数,在3.44阶时仍具有混沌特性。根据分数阶系统的线性稳定性理论和非线性反馈控制方法,提出了新分数阶系统的状态同步方法。通过理论推导,得到了两个混沌系统的同步稳定条件。控制器能够自适应地根据误差大小调节反馈系数,缩短同步时间。最后对3.6阶的分数阶系统进行了同步仿真实验,仿真结果验证了改进算法能够加快同步速度。     

地空导弹杀伤区数值化模型研究

针对杀伤区在地空导弹射击指挥中的快速应用问题, 提出了一种杀伤区数值化建模技术. 采用最小二乘法对零航路捷径垂直杀伤区边界数据点进行分段曲线拟合, 获得垂直杀伤区拟合数学模型. 然后用分段线性插值技术对拟合杀伤区进行处理, 用折线函数对拟合曲线进行分段逼近, 获得用封闭形表示的垂直杀伤区数值模型. 根据零航路捷径的垂直杀伤区数值模型, 设计了一种快速生成不同航路捷径上垂直杀伤区数值模型的算法. 最后, 对与杀伤区有关的目标射击诸元参数的计算问题进行了探讨, 给出了发射区远、近界等参数的计算模型. 通过仿真实例分析表明, 构建的模型和算法合理有效, 对地空导弹指挥控制系统的研制具有较大的应用价值.     

Pseudo-Random Sequences Generator Based on Discrete Hyperchaotic Systems

We first design a discrete hyperchaotic system via piece-wise linear state feedback. The states of the closed loop system are locally expanding in two directions but absolutely bounded on the whole, which implies hyperchaos. Then, we use three suchlike hyperchaotic systems with different feedback gain matrices to design a pseudo-random sequence generator (PRSG). Through a threshold function, three sub-sequences generated from the output of piecewise linear functions are changed into 0-1 sequences. Then, followed by XOR operation, an unpredictable pseudo-random sequence (PRS) is ultimately obtained. The analysis and simulation results indicate that the PRS, generated with hyperchaotic systems, has desirable statistical features.     

混沌系统的一种新型模糊控制方法

基于T-S模糊动态模型,针对气象学中的Lorenz混沌系统设计出一种新型的模糊控制器和模糊观测器,均采用分段Lyapunov函数法进行设计,即对每一个子系统选一个Lyapunov函数,系统总的Lyapunov函数为各个子系统的加权和。避免了并行分配补偿法(PDC)中求解公共正定矩阵P的困难,进一步减少了设计中的保守性,扩大了解的范围。并就其稳定性问题进行了研究。得出了系统全局渐近稳定的条件。模糊观测器的设计解决了系统状态不能直接测量的问题。通过对Lorenz混沌系统的仿真,证明了该方法的有效性。该方案也适合其他类型的非线性系统,有实际应用价值。     

基于分段模糊Lyapunov函数的模糊系统分析与设计

在分析模糊系统前提规则结构信息的基础上,将模糊Lyapunov函数和分段Lyapunov函数结合,构造出一类连续模糊系统的分段模糊Lyapunov函数。采用并行分配补偿(PDC)结构,利用分段模糊Lyapunov函数进行了稳定性分析与控制律设计,得到了线性矩阵不等式(LMI)形式的连续系统镇定方法。该方法减少了模糊Lyapunov函数与分段Lyapunov函数的局限性,继承两者的优点,所得稳定性判据更为宽松,控制系统具有良好的控制性能。仿真实例表明了该方法的有效性。     

求解非光滑最优控制问题的自适应网格优化

针对传统直接配点法在求解非光滑最优控制问题时存在离散误差大、精度低的问题, 提出了一种自适应直接配点法。利用局部分段插值多项式逼近最优解, 将最优控制问题离散为非线性规划问题, 并给出了离散误差估计方法, 根据离散误差的大小确定区间内节点的加密量, 提出了自适应网格优化算法, 利用该算法将大部分节点配置在非光滑区域以降低离散误差。最后通过仿真算例将所提算法与传统直接配点法和文献中的拟谱自适应算法分别进行比较,验证了所提算法的高精度和有效性。     

Stability Analysis of Event-Triggered Networked Control Systems with Time-Varying Delay and Packet Loss

Networked control systems(NCSs) are facing a great challenge from the limitation of network communication resources. Event-triggered control(ETC) is often used to reduce the amount of communication while still keeping a satisfactory performance of the system, by transmitting the measurements only when an event-triggered condition is satisfied. However, some network-induced problems would happen inevitably, such as communication delay and packet loss, which can degrade the control performance significantly and can even lead to instability. In this paper, a periodic eventtriggered NCS considering both time-varying delay and packet loss is studied. The system is discretized into a piecewise linear system with uncertainty. Then the model is handled by a polytopic overapproximation method to be more suitable for stability analysis. Finally, stability conditions are obtained and presented in terms of linear matrix inequalities(LMIs). The result is illustrated by a numerical example.     

空空导弹敏捷转弯的分段线性滑模控制设计

研究了空空导弹越肩发射敏捷转弯的复合执行机构姿态控制问题。针对一个直接侧向力装置安装在弹体尾部的导弹建立俯仰通道运动的数学模型,引入非光滑Lipschitz连续滑模控制,并利用非光滑分析的方法给出了分段线性滑模面的稳定性证明,然后采用气动舵控制作为等效控制,直接力控制作为切换控制的思想设计滑模控制律。数值仿真结果验证了分段线性滑模控制能改善常规线性滑模控制的性能,使得指令跟踪误差减小,复合控制效率提高。     

能力限制条件下内河集装箱枢纽港选址问题研究:以长江为例

相比于海洋运输,内河运输中集装箱船舶较小,船舶装载能力受到一定的限制.本文研究能力限制条件下内河集装箱枢纽港选址问题,建立一个混合整数非线性规划模型.不同于传统的枢纽选址问题的研究大多是基于枢纽之间的运输折扣因子的假设,本文采用基于流量的非线性费用函数来表示规模经济.从而使得所研究的问题是一个凹函数优化问题.为简化本文的问题,将目标函数分段线性化.基于线性化后的模型,根据能力限制的条件,提出一个启发式求解算法,以及一个加速技巧.最后,通过以长江为例,进行算例分析,来说明模型和算法的效果.     

基于改进MPC的协同自适应巡航控制策略研究

针对环境干扰、传感器噪声和跟随时变车速稳定性较差等问题,提出一种基于KF(kalman filtering)的改进MPC(model predictive control)算法。搭建CACC(cooperative adaptive cruise control)车辆间纵向运动学模型,并建立离散状态空间方程;利用KF对状态变量降噪,同时对预测模型进行鲁棒性设计;对不同工况下CACC控制目标进行分析,分别建立目标优化函数。通过搭建Simulink与CarSim联合仿真模型进行验证,结果表明,改进MPC算法能够提高城市与市郊工况下车辆的燃油经济性与驾乘舒适性,实现公路工况下对时变车速的稳定跟随。     

基于混合生物地理学优化的多目标优化算法

提出一种基于混合生物地理学优化算法的多目标进化算法(multi-objective optimization based on hybrid biogeography based optimization, MOBBO)。针对生物地理学优化算法(biogeography based optimization, BBO)自身的机制,建立适用于BBO的多目标进化模型。在模型中,结合栖息地个体间的Pareto支配关系对栖息地适应度指数进行了重新定义;为了保持栖息地种群的分布性,提出一种新的基于动态距离矩阵的分布性保持机制;同时,根据多目标优化的特点,提出了新的自适应迁入迁出率确定方式,动态迁移策略及分段logistic混沌变异策略。通过对测试函数ZDT和DTLZ的仿真实验表明,与现有多种多目标优化算法相比,MOBBO在解集的收敛性和分布的均匀性上均有明显改善,能够有效且高效地进行复杂多目标优化问题的求解。     

Existence and Uniqueness Results for Quaternion-Valued Nonlinear Impulsive Differential Systems

This paper studies the existence and uniqueness conditions for the quaternion-valued nonlinear impulsive system. Firstly, a space of quaternion-valued piecewise functions is constructed and completeness of the space is also proved. Then by taking advantage of the Bielecki norm and fixed point theorem, existence and uniqueness criteria of quaternion-valued nonlinear impulsive system are obtained. At last, an example is given to illustrate our theoretical results.     

基于信息素正态分布的连续蚁群优化系统

受生物蚂蚁觅食行为的启发,拓展蚁群系统的性能,以正态分布模拟信息素的密度分布,并以此进行随机数抽样,构成蚁群的状态转移规则。系统将随着蚂蚁的移动调整分布函数,实施信息素更新,蚁群在信息素的引导下逐步向最优食物源聚集。系统还引入优进策略和变异策略,加强局部挖掘和全局探索机制,提高蚁群的寻优能力,构建为混合连续蚁群系统(hybrid continuous ant colony system,HCACS)。经多种经典函数的测试,表明HCACS适用于连续优化问题,性能良好,对于维数较高和搜索空间较宽广的问题,更具优势。HCACS算法的参数较少,设置简单,实用性较强。     

离散模糊双线性关联大系统的广义H2分散控制

基于分段二次Lyapunov函数稳定性理论,研究了一类离散模糊双线性关联大系统广义H₂分散控制问题。模糊双线性关联大系统由J个相互关联的离散T-S模糊双线性系统组成。通过构造分段Lyapunov函数,给出了系统二次稳定的充分性条件。在此基础上,设计了广义H₂分散状态反馈控制器,使闭环系统广义H₂稳定,控制器的设计可以通过序列线性规划矩阵方法求解得到。仿真结果表明所提方法的有效性。     

可重复使用运载器自动着陆分段制导策略

针对可重复使用运载器无动力自动着陆问题,提出一种非轨迹跟踪式的分段制导策略。首先根据能量管理段和自动着陆段交接班要求以及着陆末端约束条件,分别设计了纵向轨迹和侧向轨迹的分段方案,然后针对各阶段特点设计了分段制导律,最后为了保证全程动压满足约束条件,提出了阻力板控制策略。数学仿真表明,该制导策略能够有效地实现自动着陆,且各项指标均满足规定的约束条件,并且抗风干扰及抗拉偏能力强,便于工程实现。     

Predictive control for mechanical system with backlash based on hybrid model

The mechanical system with backlash is distinguished between a “backlash mode” and a “contact mode”. The inherent switching between the two operating modes makes the system a prime example of hybrid system. For eliminating the bad effect of backlash, a piecewise affine (PWA) model of the mechanical servo system with backlash is built. The optimal control of constrained PWA system is obtained by taking advantage of model predictive control (MPC) method, and the explicit solution of MPC in a look-up table form is figured out by combining the dynamic programming and multi-parametric quadratic programming, thereby establishing an explicit hybrid model predictive controller. Furthermore, a piecewise quadratic (PWQ) function for guaranteeing the stability of closed-loop control is found by formulating the search of PWQ function as a semi-definite programming problem. In the tracking experiments, it is demonstrated that the explicit hybrid model predictive controller has a good traction control effect on the mechanical system with backlash. The error meets the demands of real system. Further, compared to the direct on-line computation, the computation burden is reduced by the explicit solution, thereby being suitable for real-time control of system with short sampling time.