不确定离散模糊系统的保性能控制

对一类具有范数有界、时变参数不确定性的离散模糊时间系统和一个二次型性能指标的保性能状态控制律的设计问题进行研究。通过采用线性矩阵不等式的方法，导出了存在保性能控制律的一个充要条件，证明了该条件等价于一组线性矩阵不等式的可解性问题，并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。在此基础上，通过建立并求解一个凸优化问题，给出了保性能控制律的设计方法。     

基频约束结构优化设计的线性矩阵不等式方法

介绍了半定规划及线性矩阵不等式 (LMI)的基本概念 ,给出具有基频约束的桁架结构优化问题的半定规划形式。半定规划法 (或称线性矩阵不等式方法 )可以有效地求解该问题的全局最优解 ,最后以一个简单桁架结构为算例     

基于量子粒子群优化算法的机器人运动学标定方法

基于量子粒子群优化算法,提出一种同样适用于串联机器人和并联机器人的运动学标定方法。利用闭环矢量链方法和Denavit-Hartenberg矩阵法,分别建立并联机器人和串联机器人的运动学误差模型,将运动学误差模型内的几何误差源作为相应的机构参数修正量。由于机器人运动学误差模型表现有较强的非线性,因此确定模型内的机构参数修正量为优化变量,将机器人运动学参数标定问题转化为非线性系统的优化问题。采用量子粒子群优化算法对优化问题进行求解,利用优化获得的参数修正量更新运动学模型,以达到提高机器人运动精度的目的。以五轴并联机床的平面约束机构为研究对象,通过试验验证该标定方法的标定效果,并与模糊插值标定方法进行比较分析,结果表明在较大的工作空间内基于量子粒子群优化的运动学标定方法更为有效。     

时变多状态滞后不确定系统的保性能控制

针对时变多状态滞后不确定线性系统 ,研究了状态反馈保性能控制律的设计问题 ,采用线性矩阵不等式方法 ,导出了保性能控制律的存在条件和参数化表示。通过求解一个线性矩阵不等式约束的凸优化问题 ,提出了最优化保性能控制律的设计方法     

现场双经纬仪三维坐标测量系统

分析了经纬仪透视投影模型以及双经纬仪三维坐标测量模型。采用线性与非线性相结合的方法来求解双经纬仪坐标测量系统的参数,首先由8个以上空间点在两台经纬仪投影平面内对应的投影坐标计算出本质矩阵E,通过本质矩阵E的奇异值分解以及空间绝对距离的约束采用线性方法求出右经纬仪的投影矩阵,然后建立包含空间点在两台经纬仪投影平面内投影点固有约束以及空间点三维坐标在内的目标函数,并以线性方法求出的参数为初值,采用非线性优化的方法求解最优测量系统的参数。该方法保证了求解参数为全局最优,且求解速度快。试验结果表明,该方法切实可行。     

磁轴承多目标模糊控制系统的设计

针对非线性和开环不稳定的磁悬浮系统,建立了T-S模糊模型,利用并行分布补偿原理设计了整个系统的模糊状态反馈控制器,并利用线性矩阵不等式的方法对凸优化问题进行求解。通过试验仿真证明,该方法提高了磁悬浮系统的稳定性,可有效满足工作要求。     

基于量子遗传的机械故障非线性盲源分离方法研究

针对传统的机械故障非线性盲分离方法的不足,即将非线性盲源分离中分离矩阵和非线性去混合函数的参数分开来优化,这样容易顾此失彼,学习效率低。将量子遗传引入到机械故障非线性盲分离中,提出一种基于量子遗传的机械故障非线性盲源分离方法(简称QGA-NBSS方法),该方法能同时对分离矩阵和非线性去混合函数的参数进行优化,获得全局最优解并加快了算法的全局收敛性,克服了传统的机械故障源的非线性盲源分离方法的不足。仿真和实验结果验证了提出的方法的有效性。     

一种基于LMI的鲁棒PID控制回路优化及工业应用

根据控制器实际投运中遇到性能下降问题,设计一个控制回路参数优化系统,包括模型辨识、鲁棒PID控制器设计和LQG控制器性能评价。将控制器设计相关算法转化为线性矩阵不等式(LMI)求解,并通过Matlab实现。工程实例说明该设计方法可行、有效。     

基于LMI-SDP优化的机器人手眼关系精确求解

机器人手眼关系(X)的精确求解对于视觉导引的机器人操作及其重要，通常用方程AX=XB表示。现有方法通常采用旋转矩阵与平移分量分离方式分步标定X，从而导致标定误差的累积。同时，推导的线性方程中回归矩阵的最小奇异值影响标定结果的精度。为此，提出了一种新颖且通用的AX=XB标定方法，采用LMI-SDP(线性矩阵不等式与半正定规划)优化同步标定出方程AX=XB的最优解。在此方法中，通过Kronecker积获得标定方程的线性形式，结合回归矩阵的QR分解形式转化为关于未知变量X的凸约束优化问题，通过LMI-SDP工具箱得到精确的同步解。通过考虑到不同噪声水平和数据对的仿真分析以及标定试验，对提出的方法与迭代算法、对偶四元数方法进行比较。结果表明，所提出的方法相比传统方法表现出更好的准确性和有效性，对于实现机器人手眼系统的推广与应用具有重要意义。     

具有未知参数漂浮基双臂空间机器人惯性空间复合自适应控制

讨论了载体位置与姿态均不受控制情况下具有未知参数的漂浮基双臂空间机器人系统惯性空间的复合自适应控制问题。为了克服空间机器人系统控制方程关于惯性参数的非线性性质,空间机器人被表示为欠驱动形式的机器人系统,其优点在于保持了系统动力学方程关于惯性参数的线性性质。对系统的运动学分析表明,联系两个机械臂末端运动速度与机器人关节角速度的增广广义Jacobi关系亦可以表示为一组惯性参数的线性函数。以此为基础,针对系统参数不确定的情况,设计了空间机器人系统跟踪惯性空间期望运动轨迹的复合自适应控制方案。系统的数值仿真证实了控制方法的有效性。     

Proximal-point method for finite element model updating problem

The problem of finding the optimal approximation to analytical stiffness matrix modeled by the finite element method is considered in this paper. Desired matrix properties, including satisfaction of the dynamic equation, symmetry, positive semidefiniteness and physical connectivity, are imposed as side constraints of the minimization problem. To the best of the author's knowledge, the finite element model updating problem containing all these constraints simultaneously has not been proposed in the literature earlier. By partial Lagrangian multipliers technique, the optimization problem is transformed into a matrix linear variational inequality and the proximal-point method is first used to solve the equivalent problem. The results of numerical examples show that the proposed method works well even for incomplete measured data.     

Machining process parameters optimization for heavy-duty CNC machine tools in sustainable manufacturing

Machining process parameters (MPP) directly affect the machining quality and efficiency of heavy-duty CNC machine tools (HCMT). The selection of MPP is very important to effectively improve machining performance. Machining performance has been closely related to the HCMT running state. In order to maintain HCMT sustainably manufacturing with high accuracy and low consumption after machining performance degradation for a long time running, MPP should be re-optimized according to the current state of the machine tools. Thus, this paper proposed a MPP optimization method for running HCMT to obtain optimal MPP based on current running state. A multi-objective optimization model was built, considering both the linear factors such as machining time and machining cost and nonlinear factors such as chatter in machining process. The nonlinear factors were reflected by the nonlinear dynamic model of machining process. Furthermore, a grid optimization algorithm was introduced to search the optimal MPP from the multi-objective optimization model. Finally, a case study was implemented to verify the feasibility of the nonlinear dynamic model and the superiority of the multi-objective optimization method compared with single-objective optimization method.     

Adaptive nearly optimal control for a class of continuous-time nonaffine nonlinear systems with inequality constraints

The state inequality constraints have been hardly considered in the literature on solving the nonlinear optimal control problem based the adaptive dynamic programming (ADP) method. In this paper, an actor-critic (AC) algorithm is developed to solve the optimal control problem with a discounted cost function for a class of state-constrained nonaffine nonlinear systems. To overcome the difficulties resulting from the inequality constraints and the nonaffine nonlinearities of the controlled systems, a novel transformation technique with redesigned slack functions and a pre-compensator method are introduced to convert the constrained optimal control problem into an unconstrained one for affine nonlinear systems. Then, based on the policy iteration (PI) algorithm, an online AC scheme is proposed to learn the nearly optimal control policy for the obtained affine nonlinear dynamics. Using the information of the nonlinear model, novel adaptive update laws are designed to guarantee the convergence of the neural network (NN) weights and the stability of the affine nonlinear dynamics without the requirement for the probing signal. Finally, the effectiveness of the proposed method is validated by simulation studies.     

扩展拉格朗日乘子粒子群算法解决工程优化问题

工程上很多优化问题,如容器设计、波纹管、板翅式换热器的结构优化设计等,皆为非线性约束优化设计问题,常采用惩罚函数法处理约束条件;为获得问题最优解,该方法需要合理确定初始惩罚因子,且需要动态惩罚因子无穷大。扩展拉格朗日乘子法是一种改进的惩罚函数法,可以克服惩罚函数法的不足,获得全局最优解,但目前对其研究和应用有限。对拉格朗日乘子法与粒子群算法相结合处理非线性约束问题进行研究,提出惩罚因子更新策略,确定扩展拉格朗日乘子粒子群算法合理的操作过程。标准测试函数结果显示：提出的方法及策略实现了扩展拉格朗日乘子粒子群算法解决非线性约束问题,并得到了问题的全局最优解;其在容器及波纹管系列优化设计中的应用进一步显示,提出的方法在处理非线性约束工程实际问题时,运行稳定可靠,可快捷获得问题的全局最优解或近似最优解。     

A symplectic pseudospectral method for nonlinear optimal control problems with inequality constraints

A symplectic pseudospectral method based on the dual variational principle and the quasilinearization method is proposed and is successfully applied to solve nonlinear optimal control problems with inequality constraints in this paper. Nonlinear optimal control problem is firstly converted into a series of constraint linear-quadratic optimal control problems with the help of quasilinearization techniques. Then a symplectic pseudospectral method based on dual variational principle for solving the converted constrained linear-quadratic optimal control problems is developed. In the proposed method, inequality constraints which can be functions of pure state, pure control and mixed state-control are transformed into equality constraints with the help of parameteric variables. After that, state variables, costate variables and parametric variables are interpolated locally at Legendre-Gauss-Lobatto points. Finally, based on the parametric variational principle and complementary conditions, the converted problem is transformed into a standard linear complementary problem which can be solved easily. Numerical examples show that the proposed method is of high accuracy and efficiency.     

一种考虑参数相关性的可靠性优化设计方法

在求解具有非线性相关性结构的可靠性设计优化问题时,现有的相关性处理方法在某些情况下可能会得到精度较低的优化结果。基于Copula函数提出了一种可靠性优化设计方法,用于求解存在非线性相关性结构的可靠性优化设计问题。该方法根据已知的样本对各备选Copula函数进行参数估计,并根据AIC准则选出最优Copula函数。根据最优Copula函数,构建联合概率分布函数,最后求解结构可靠性优化设计问题。通过两个数值算例验证了该方法的有效性,并讨论了不同Copula函数对优化结果的影响。     

基于非线性规划的间歇反应过程动态优化算法

采用对数障碍法和外点法将实际间歇反应过程中的约束条件转化为惩罚项生成新的目标函数,将有约束优化问题转化为无约束优化问题;采用非线性规划算法中的操作变量参数化方法,将操作变量的最优解转化为操作变量子函数的线性组合,将无限维最优解问题转化为有限维权值向量的最优估计问题;同时应用Lyapunov理论设计一种动态迭代优化算法,重点讨论了采样时间的取值对优化算法收敛性的影响.最终用于解决靛蓝生产中碱熔间歇反应过程中过程参数的最优分布,从而提高目标产物的最终收率和降低生产成本等.通过碱熔间歇反应动态优化问题作为实例进行仿真试验,实验结果表明所述算法的有效性和可靠性.     

基于禁忌制造特征动态调整的STEP-NC工艺路线蚁群优化方法

针对STEP-NC制造特征的加工工艺路线生成与优化问题,提出了一种以机床、夹具及刀具更换率最低为目标函数的禁忌制造特征动态更新的工艺路线蚁群优化方法。首先,根据加工工艺对制造特征进行分解,将工艺路线优化问题转化为对制造特征的排序;然后根据制造特征在加工过程中存在的加工遮挡关系以及刚性工艺性约束,提出禁忌制造特征动态更新的工艺路线生成方法;最后将禁忌制造特征动态更新方法与Ant-Cycle模型的蚁群算法相结合,求解制造特征工艺路线的优化问题。实例应用表明,提出的方法能较好解决加工工艺路线优化过程中的刚性约束处理问题。     

Observer-based reliable stabilization of uncertain linear systems subject to actuator faults,saturation, and bounded system disturbances

A matrix inequality approach is proposed to reliably stabilize a class of uncertain linear systems subject to actuator faults, saturation, and bounded system disturbances. The system states are assumed immeasurable, and a classical observer is incorporated for observation to enable state-based feedback control. Both the stability and stabilization of the closed-loop system are discussed and the closed-loop domain of attraction is estimated by an ellipsoidal invariant set. The resultant stabilization conditions in the form of matrix inequalities enable simultaneous optimization of both the observer gain and the feedback controller gain, which is realized by converting the non-convex optimization problem to an unconstrained nonlinear programming problem. The effectiveness of proposed design techniques is demonstrated through a linearized model of F-18 HARV around an operating point.     

A response surface based sequential approximate optimization using constraint-shifting analogy

When a traditional response surface method (RSM) is used as a meta-model for inequality constraint functions, an approximate optimal solution is sometimes actually infeasible in a case where it is active at the constraint boundary. The paper proposes a new RSM that ensures the constraint feasibility with respect to an approximate optimal solution. Constraint-shifting is suggested in order to secure the constraint feasibility during the sequential approximate optimization process. A central composite design is used as a tool for design of experiments. The proposed approach is verified through a mathematical function problem and engineering optimization problems to support the proposed strategies.