多目标优化问题的有效Pareto最优集

多目标优化问题求解是当前演化计算的一个重要研究方向,而基于Pareto最优概念的遗传算法更是研究的重点,然而,遗传算法在解决多目标优化问题上的缺陷却使得其往往得不到一个令人满意的解。在对该类算法研究的基础上提出了衡量Pareto最优解集的标准,并对如何满足这个标准提出了建议。     

解决复杂Pareto解集问题的进化算法

针对各种进化算法在解决PS问题上表现出来的脆弱性，提出一种解决复杂PS问题的自适应多目标差分进化算法SA-MODE。根据随机选择的父个体X与当前种群中的个体Y的支配关系，通过改变缩放因子的大小来控制新个体和父个体的距离。当X支配Y则新个体接近X，反之远离X，当X与Y互相不支配则产生2个新个体，一个接近X一个远离X。实验结果表明，在处理复杂PS问题时，SA-MODE与GDE3和NSGA-II相比有更理想的效果。     

Optimality Conditions and Solution of a Class of Multicriteria Continuous Set Partitioning Problems

Multicriterion continuous problems of partitioning sets into subsets with fixed centers under constraints are considered. Two approaches to obtaining Slater optimality conditions are proposed. An algorithm for solution of these problems is developed on their basis. Steps of meshes approximating the partitioned set are estimated and a set of parameter convolution criteria is constructed. Numerical results are given for solution of test examples.     

Evolutionary Algorithms for Minimax Problems in Robust Design

Many robust design problems can be described by minimax optimization problems. Classical techniques for solving these problems have typically been limited to a discrete form of the problem. More recently, evolutionary algorithms, particularly coevolutionary optimization techniques, have been applied to minimax problems. A new method of solving minimax optimization problems using evolutionary algorithms is proposed. The performance of this algorithm is shown to compare favorably with the existing methods on test problems. The performance of the algorithm is demonstrated on a robust pole placement problem and a ship engineering plant design problem.     

＋不确定连续系统线性二次型次优控制问题的研究

基于静态输出反馈研究了不确定连续系统线性二次型（LQ）次优控制问题,应用线性矩阵不等式（LMI）给出了问题可解的充分条件,设计出了输出反馈控制器,保证了闭环系统的稳定。最后给出了仿数值算例说明该方法的有效性。     

Multicriteria Decision Making Based on a Set of Optimization Methods

The authors provide an approach to multicriteria decision making in the analysis of complex systems. It is based on the results obtained from a number of methods (ranking as well as forming of the kernel), which increases the substantiation of the results due to increasing the completeness of alternatives comparison.     

Polyhedral Feasible Set Computation of MPC-Based Optimal Control Problems

Feasible sets play an important role in model predictive control (MPC) optimal control problems (OCPs). This paper proposes a multi-parametric programming-based algorithm to compute the feasible set for OCP derived from MPC-based algorithms involving both spectrahedron (represented by linear matrix inequalities) and polyhedral (represented by a set of inequalities) constraints. According to the geometrical meaning of the inner product of vectors, the maximum length of the projection vector from the feasible set to a unit spherical coordinates vector is computed and the optimal solution has been proved to be one of the vertices of the feasible set. After computing the vertices, the convex hull of these vertices is determined which equals the feasible set. The simulation results show that the proposed method is especially efficient for low dimensional feasible set computation and avoids the non-unicity problem of optimizers as well as the memory consumption problem that encountered by projection algorithms.      

Robust Control System Design for an Uncertain Nonlinear System Using Minimax LQG Design Method

A systematic approach to design a nonlinear controller using minimax linear quadratic Gaussian regulator (LQG) control is proposed for a class of multi‐input multi‐output nonlinear uncertain systems. In this approach, a robust feedback linearization method and a notion of uncertain diffeomorphism are used to obtain an uncertain linearized model for the corresponding uncertain nonlinear system. A robust minimax LQG controller is then proposed for reference command tracking and stabilization of the nonlinear system in the presence of uncertain parameters. The uncertainties are assumed to satisfy a certain integral quadratic constraint condition. In this method, conventional feedback linearization is used to cancel nominal nonlinear terms and the uncertain nonlinear terms are linearized in a robust way. To demonstrate the effectiveness of the proposed approach, a minimax LQG‐based robust controller is designed for a nonlinear uncertain model of an air‐breathing hypersonic flight vehicle (AHFV) with flexibility and input coupling. Here, the problem of constructing a guaranteed cost controller which minimizes a guaranteed cost bound has been considered and the tracking of velocity and altitude is achieved under inertial and aerodynamic uncertainties.     

控制系统l~1优化设计最优解的存在性和次优解

本文初步研究了控制对象有z平面单位圆上零极点时l~2优化设计问题解的存在性,指出在此种情况下l~1优化问题的最优解不一定总是存在。提出了解存在性的判别定理。在最优解不存在时给出了次优解的求取方法。     

Hammerstein系统控制加权自适应次优控制

经典最小方差控制不能用于u(t)最高次幂u(t)p的系数多项式Bp(q-1)是不稳定的Hammerstein系统。基于经典二次型指标的控制加权一步最优控制亦难以推广到H系统。本文指出了文[3, 4]在研究此问题时的错误，提出采用对u(t)p加权的新性能指标，由此导出一种简单的直接自适应控制算法，证明了算法的局部收敛性。该算法可用于Bi(q-1), j=1, …, p稳定和非稳定的H系统的自适应控制。仿真结果证实了算法的优良性。     

摄动双积分系统的时间-燃料次优反馈控制

本文研究了摄动双积分系统的时间－燃料最优控制问题，用理想双积分系统时间－燃料最优切换线的改进形式，构造了摄动双积分系统的反馈控制律，证明了闭环系统的鲁棒收敛性。算例表明，反馈控制律与最优控制律具有相近的控制结果。     

基于多步控制集的鲁棒预测控制器设计

针对有约束多胞不确定系统, 本文提出多步控制集的概念, 并将其作为终端集进而设计鲁棒预测控制器. 由于设计了一系列可变的反馈律, 鲁棒预测控制器可以得到更好的控制性能和更大的初始可行域. 另外, 利用多步控制集的特性, 本文提出了一种将预测控制器的在线计算量转移到离线完成的算法. 通过该算法, 可以有效地平衡鲁棒预测控制器的控制性能、在线计算量和初始可行域. 仿真算例验证了这些算法的有效性.     

Properties of the Decision Methods in the Multicriteria Problems of Individual Choice

Quality-ordering of objects estimated by multiple criteria was considered. Standardized methods prescribing the rules of choice to the rational person were estimated from the standpoint of completeness and acyclicity of the relations on the set of alternatives, as well as sensitivity of the result to human errors. For different utilities of the alternatives for the decision maker, these requirements were shown not to be satisfied simultaneously.     

Real-time Stabilization of a Quadrotor UAV: Nonlinear Optimal and Suboptimal Control

In this paper a nonlinear suboptimal stabilizing control strategy based on Control Lyapunov Functions (CLF) is synthesized and applied to a quadrotor helicopter. Sufficient conditions are obtained for this control law to ensure the asymptotic stability of the closed loop system. Furthermore, a particular methodology to find a CLF candidate for nonlinear affine system is also presented, which is highly relevant because the dynamical model representing the VTOL aerial vehicles have this affine structure. Using this CLF candidate, we are able to synthesize a nonlinear stabilizing optimal control law which allows energy saving. Numerical simulations were developed for both control strategies and real time experiments have been performed using the nonlinear stabilizing control algorithm. The numerical simulations have shown a successful performance of the autonomous aerial vehicle.     

一类广义时滞系统的极小极大控制

研究一类广义时滞系统的极小极大控制问题,目的是利用构造局部检验函数的方法设计极小极大控制器,使得在最坏的干扰下系统的性能指标上界极小.利用线性矩阵不等式(LM I)给出了广义时滞系统极小极大控制器存在的充分条件,讨论了闭环系统的容许性,并将所得结果推广到含有不确定性的广义时滞系统.最后以数值算例说明了所提出的控制器设计方法的有效性和可行性.     

基于Pareto最优解集的多目标粒子群优化算法

本文结合Pareto支配思想、精英保留策略、锦标赛和排挤距离选择技术,对传统的粒子更新策略进行改进,给出了一种新的粒子淘汰准则,提出了一种基于Pareto最优解集的多目标粒子群优化算法。最后,通过7个多目标标准测试函数进行测试。测试结果表明,该方法有效可行,其性能优于如NSGAII、SPEA2等多目标优化算法。     

Control for Tractor-Semitrailer Vehicle Systems: A Lyapunov Minimax Approach

The problem of automated steering and independent braking control for a tractor-semitrailer vehicle system is addressed. The control is designed by combining the input/output linearization and Lyapunov minimax approach. The proposed design achieves, despite of the presence uncertainty, lane following and prevents the jack-knifing phenomenon of trailer yaw motion. This revised version was published online in July 2006 with corrections to the Cover Date.     

PAVED: Pareto Front Visualization for Engineering Design

Design problems in engineering typically involve a large solution space and several potentially conflicting criteria. Selecting a compromise solution is often supported by optimization algorithms that compute hundreds of Pareto-optimal solutions, thus informing a decision by the engineer. However, the complexity of evaluating and comparing alternatives increases with the number of criteria that need to be considered at the same time. We present a design study on Pareto front visualization to support engineers in applying their expertise and subjective preferences for selection of the most-preferred solution. We provide a characterization of data and tasks from the parametric design of electric motors. The requirements identified were the basis for our development of PAVED, an interactive parallel coordinates visualization for exploration of multi-criteria alternatives. We reflect on our user-centered design process that included iterative refinement with real data in close collaboration with a domain expert as well as a summative evaluation in the field. The results suggest a high usability of our visualization as part of a real-world engineering design workflow. Our lessons learned can serve as guidance to future visualization developers targeting multi-criteria optimization problems in engineering design or alternative domains.     

对DES实行优化控制的一种方法

对一类离散事件系统(DES),本文分析了其影响加工效率的因素,提出了优化控制的指标,并根据局部优化与全局优化相结合的原则提出了一种次优控制的方法,计算复杂度的分析表明了它的可行性和有效性,计算机仿真结果表明优化的闭环DES有一个从动态到静态最终稳定的过程,但只有当生产过程进入程序化生产后总加工效率才能随生产的进行而不断提高.     

摄动双积分系统的时间－燃料次优反馈控制

本文研究了摄动双积分系统的时间－燃料最优控制问题，用理想双积分系统时间－燃料最优切换线的改进形式，构造了摄动双积分系统的反馈控制律，证明了闭环系统的鲁棒收敛性．算例表明，反馈控制律与最优控制律具有相近的控制结果．