不确定系统的鲁棒优化方法及应用研究
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摘要
从哲学观点看，不确定性是所有事物所固有的。在系统科学与系统工程学科中，对系统和过程进行决策必须考虑系统的不确定性，这时的决策才能称得上是科学决策。不确定性包括系统的结构不确定性和参数的不确定性等。本论文主要是研究参数的不确定系统的优化问题及一些应用。
本论文的研究目标是解决模型参数为区间数的不确定系统的优化问题，以此为目的，结合一些智能的计算方法，提出解决本问题的一些有效优化算法，如混合基因优化算法，动力学优化算法，基于目标函数分类的交互式多目标优化算法等。并把其中的解决MINIMAX的混合优化算法，应用到控制系统的鲁棒控制器设计。提出了一个解决不确定优化问题的多目标优化算法。最后根据作者的在城市供水系统自动化的工程实践，在总结了成功工程的基础上，提出了行业的一些研究前景。
本文的主要研究工作与主要贡献如下：
1．对参数不确定系统的优化问题的研究范围和研究和应用现状进行了详尽的分析与综述。特别详述了参数不确定系统的一个重要分支，即用区间数描述的参数不确定性系统的优化命题的研究现状。
2．针对模型参数为区间数的不确定系统优化命题，在总结前人工作的基础上，本文基于序和后悔度的概念，受顾基发研究员的“物理—事理—人理(WSR)”「Gu J.，Zhu Z.，(1995)」的系统科学思想的启发，创造性的提出了一个结合目标函数期望，不确定度和后悔度的三目标鲁棒优化命题，本优化命题可作为原不确定系统优化命题的替代命题。并通过实例分析了本优化命题的合理性。目前，尚未见到有关研究报道。
3．三目标鲁棒优化命题的最后解决，离不开单目标优化算法的实现和最小后悔度目标MINIMAX优化等一些基本优化问题的解决。本文在综合前人研究的基础上，创造性的提出了几种有效的优化方法：
3．1混合基因优化算法用于解决可微或不可微的单目标优化命题。由于基因算法全局搜索能力强但局部收敛性较差，而单纯型法局部收敛性好但全局搜索能力差，本算法综合了基因算法和单纯型法的各自优点，给出
浙江大学博士学位论文
了一种混合的基因算法，仿真显示算法有很好的快速和收敛性能。
3．2动力学优化算法用于解决单目标的优化命题。应用李亚普诺夫
（Lyapwhov）函数，Lasalle不变原理采用微分动力学系统给出了一种动
。．力学优化算法解决了增广ragange法的子优化命题，最后给出了一种新
的增广LagrangC乘子算法，它可有效地解决目标和约束条件函数可微的
单目标优化命题。
3．3同时本文还给出了一种基于基因算法和传统优化算法相结合的途径解
决连续的MINIMAX优化问题。
4．参数不确定性和滞后特性在实际工业过程中广泛存在。针对这种工业过程，
本文基于一个LQR的性能指标（本性能指标和衰减系数和自然频率密切相
关），提出应用本文提出的MmlAAX优化算法，对不确定工业过程进行鲁
棒Pto控制器的设计，取得令人满意的效果。
5．针对目标函数有参数不确定的优化命题，本文具体描述了其三目标优化命
题，综合当前交互式多目标优化算法的研究成果，并提出了一种基于目标
函数分类的交互式优化算法，把目标函数进行分类符合决策者在交互决策
过程中的行为习惯，可实现友好人机交互。本优化算法可保证获得优化解
为PARETO最优解。
6．进行系统优化的目的是指导工业生产，本文针对城市供水行业，提出了供
水行业集成生产的概念，提出了供水管网的一种多目标优化命题，提出了
不确定优化及相关的优化方法在城市供水行业的一些应用。由于供水行业
的流程分布非常广，结合作者针对市政行业开发的一个产品，提出了本产
品在城市供水行业实现全市供水行业集成生产信息集成方面的应用潜力。
结合工程实际，介绍了作者负责实施的一个供水企业全厂自动化的成功实
例。
From the view of philosophy, uncertainty is the inherent phenomenon of everything. In the subject of system science and system engineering, it is necessary to be taken into accounted hi the process of making decision to system and process, otherwise, the decision making is not be called scientific decision making 0 Uncertainty includes system structural uncertainty and systems parameter uncertainty, et al. The system optimization problems with parameter uncertainty and some applications are studied in the dissertation.
The research object of the dissertation is system optimization for the uncertainty system with interval model parameter. Based Interval mathematics and regret, an alternative problem of the uncertainty problem with tri-objective optimization is proposed. For this ami, Integrated some intelligent methods , some efficient optimization methods are proposed in this dissertation such as hybrid genetic optimization method^ optimization based on dynamics and interactive multi-objective method based on unbundled objective functions, and so on . The hybrid optimization methods used to solve Minimax optimization in the dissertation is applied to Robust controller design. In the mean time, a interactive multi-objective optimization algorithm is proposed. Finally, based the successful practice in the field of water industrial system, some research prospects in the field are proposed.
The marn contributions and research work are as follows:
1. Based on the concept of order and regret, A new tri-multi-objective optimization model is developed which is alternative used to solve the uncertainty optimization system with interval model parameter ?In particular, the uncertainty optimization model exits in many fields, such as economic and Industrial fields. The Tri-multi-objective optimization model include three functions: the first function is used to express the mathematical expectation in the uncertainty environment, the second function is used to express the robust property through a uncertainty degree function, the final function is used to express the mind of the decision maker
through a regret function
2. The Tri-Multi-objective optimization is very important in order to solve the uncertainty optimization problem. And the basis of the multi-objective optimization is single objective optimization and MINIMAX optimization?In the dissertation, some effective optimization methods are developed for the single objective optimization?The effective methods are as follows:
2.1 Hybrid Simplex-Genetic optimization method 0 One of the main obstacles in applying genetic algorithms (GAs) to complex problems has been the high computational cost due to their slow convergence rate. To alleviate this difficulty, we developed a hybrid approach that combines GA with simplex method in function optimization. In the same way, the hybrid simplex-Genetic method is applied to solve the continuous minimax optimization. Some benchmark problems are tested in the real space and showed the results.
2.2 Dynamical optimization method. The Lyapunov theorem and Lasalle invariance principle are applied to optimization sub-problem in augmented Lagrange multiplier method. A dynamical system is built which is satisfied to Lyapunov function whose energy function is penalty function in augmented Lagrange multiplier method. The dynamical system is global stable, and its stable solution is the optimization solution of sub-problem in augmented Lagrange multiplier method according to Lasalle invariance principle. Finally a complete optimization algorithm is developed.
3. A new unbundled interactive multi-objective optimization method used to solve the Tri-multi-objective optimization is developed. In the new interactive multi-objective optimization, the functions are unbundled to three classes: the first is the
set whose value should be improved ; the second is the set whose value are allowed to relax(impair)( ) and the final is the set whose value are
accepted)(such that {the set of all the objective
本论文的研究目标是解决模型参数为区间数的不确定系统的优化问题，以此为目的，结合一些智能的计算方法，提出解决本问题的一些有效优化算法，如混合基因优化算法，动力学优化算法，基于目标函数分类的交互式多目标优化算法等。并把其中的解决MINIMAX的混合优化算法，应用到控制系统的鲁棒控制器设计。提出了一个解决不确定优化问题的多目标优化算法。最后根据作者的在城市供水系统自动化的工程实践，在总结了成功工程的基础上，提出了行业的一些研究前景。
本文的主要研究工作与主要贡献如下：
1．对参数不确定系统的优化问题的研究范围和研究和应用现状进行了详尽的分析与综述。特别详述了参数不确定系统的一个重要分支，即用区间数描述的参数不确定性系统的优化命题的研究现状。
2．针对模型参数为区间数的不确定系统优化命题，在总结前人工作的基础上，本文基于序和后悔度的概念，受顾基发研究员的“物理—事理—人理(WSR)”「Gu J.，Zhu Z.，(1995)」的系统科学思想的启发，创造性的提出了一个结合目标函数期望，不确定度和后悔度的三目标鲁棒优化命题，本优化命题可作为原不确定系统优化命题的替代命题。并通过实例分析了本优化命题的合理性。目前，尚未见到有关研究报道。
3．三目标鲁棒优化命题的最后解决，离不开单目标优化算法的实现和最小后悔度目标MINIMAX优化等一些基本优化问题的解决。本文在综合前人研究的基础上，创造性的提出了几种有效的优化方法：
3．1混合基因优化算法用于解决可微或不可微的单目标优化命题。由于基因算法全局搜索能力强但局部收敛性较差，而单纯型法局部收敛性好但全局搜索能力差，本算法综合了基因算法和单纯型法的各自优点，给出
浙江大学博士学位论文
了一种混合的基因算法，仿真显示算法有很好的快速和收敛性能。
3．2动力学优化算法用于解决单目标的优化命题。应用李亚普诺夫
（Lyapwhov）函数，Lasalle不变原理采用微分动力学系统给出了一种动
。．力学优化算法解决了增广ragange法的子优化命题，最后给出了一种新
的增广LagrangC乘子算法，它可有效地解决目标和约束条件函数可微的
单目标优化命题。
3．3同时本文还给出了一种基于基因算法和传统优化算法相结合的途径解
决连续的MINIMAX优化问题。
4．参数不确定性和滞后特性在实际工业过程中广泛存在。针对这种工业过程，
本文基于一个LQR的性能指标（本性能指标和衰减系数和自然频率密切相
关），提出应用本文提出的MmlAAX优化算法，对不确定工业过程进行鲁
棒Pto控制器的设计，取得令人满意的效果。
5．针对目标函数有参数不确定的优化命题，本文具体描述了其三目标优化命
题，综合当前交互式多目标优化算法的研究成果，并提出了一种基于目标
函数分类的交互式优化算法，把目标函数进行分类符合决策者在交互决策
过程中的行为习惯，可实现友好人机交互。本优化算法可保证获得优化解
为PARETO最优解。
6．进行系统优化的目的是指导工业生产，本文针对城市供水行业，提出了供
水行业集成生产的概念，提出了供水管网的一种多目标优化命题，提出了
不确定优化及相关的优化方法在城市供水行业的一些应用。由于供水行业
的流程分布非常广，结合作者针对市政行业开发的一个产品，提出了本产
品在城市供水行业实现全市供水行业集成生产信息集成方面的应用潜力。
结合工程实际，介绍了作者负责实施的一个供水企业全厂自动化的成功实
例。
From the view of philosophy, uncertainty is the inherent phenomenon of everything. In the subject of system science and system engineering, it is necessary to be taken into accounted hi the process of making decision to system and process, otherwise, the decision making is not be called scientific decision making 0 Uncertainty includes system structural uncertainty and systems parameter uncertainty, et al. The system optimization problems with parameter uncertainty and some applications are studied in the dissertation.
The research object of the dissertation is system optimization for the uncertainty system with interval model parameter. Based Interval mathematics and regret, an alternative problem of the uncertainty problem with tri-objective optimization is proposed. For this ami, Integrated some intelligent methods , some efficient optimization methods are proposed in this dissertation such as hybrid genetic optimization method^ optimization based on dynamics and interactive multi-objective method based on unbundled objective functions, and so on . The hybrid optimization methods used to solve Minimax optimization in the dissertation is applied to Robust controller design. In the mean time, a interactive multi-objective optimization algorithm is proposed. Finally, based the successful practice in the field of water industrial system, some research prospects in the field are proposed.
The marn contributions and research work are as follows:
1. Based on the concept of order and regret, A new tri-multi-objective optimization model is developed which is alternative used to solve the uncertainty optimization system with interval model parameter ?In particular, the uncertainty optimization model exits in many fields, such as economic and Industrial fields. The Tri-multi-objective optimization model include three functions: the first function is used to express the mathematical expectation in the uncertainty environment, the second function is used to express the robust property through a uncertainty degree function, the final function is used to express the mind of the decision maker
through a regret function
2. The Tri-Multi-objective optimization is very important in order to solve the uncertainty optimization problem. And the basis of the multi-objective optimization is single objective optimization and MINIMAX optimization?In the dissertation, some effective optimization methods are developed for the single objective optimization?The effective methods are as follows:
2.1 Hybrid Simplex-Genetic optimization method 0 One of the main obstacles in applying genetic algorithms (GAs) to complex problems has been the high computational cost due to their slow convergence rate. To alleviate this difficulty, we developed a hybrid approach that combines GA with simplex method in function optimization. In the same way, the hybrid simplex-Genetic method is applied to solve the continuous minimax optimization. Some benchmark problems are tested in the real space and showed the results.
2.2 Dynamical optimization method. The Lyapunov theorem and Lasalle invariance principle are applied to optimization sub-problem in augmented Lagrange multiplier method. A dynamical system is built which is satisfied to Lyapunov function whose energy function is penalty function in augmented Lagrange multiplier method. The dynamical system is global stable, and its stable solution is the optimization solution of sub-problem in augmented Lagrange multiplier method according to Lasalle invariance principle. Finally a complete optimization algorithm is developed.
3. A new unbundled interactive multi-objective optimization method used to solve the Tri-multi-objective optimization is developed. In the new interactive multi-objective optimization, the functions are unbundled to three classes: the first is the
set whose value should be improved ; the second is the set whose value are allowed to relax(impair)( ) and the final is the set whose value are
accepted)(such that {the set of all the objective
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