Exploitation of Computational Control Theory

本研究项目的目的是开发控制理论的一个新领域，称为“计算控制理论”，它提供了利用计算能力获得理论难以解决的控制问题的次优解的数值方法。在这个项目期间，取得了以下成果：1。求解多目标控制问题次最优数值解的迭代方法：针对多目标控制问题，提出了子水平集法、外点法和双截面法，并通过数值算例说明了其有效性。灰盒模型的系统辨识方法：针对灰盒模型的参数估计问题，给出了基于平方和优化方法的数值方法，并给出了鲁棒性分析方法。双线性系统的鲁棒控制设计方法：从双线性系统L2增益优化问题的最优性条件出发，导出了包含状态变量的riccti型不等式。对于这类不等式，我们给出了一种基于平方和优化方法的数值求解方法。输入饱和系统的数值方法：对于输入饱和系统，我们提出了一种使用多项式的新表示形式，并给出了获得此类系统鲁棒分析/设计问题可行解的数值方法。并行计算：我们构建了一个并行计算的PC集群系统，并应用它解决了一些控制设计问题。

The objective of this research project is to exploit a new field for control theory called "Computational Control Theory" which gives numerical methods using computational power for obtaining sub-optimal solutions for control problems which are hardly solved theoretically. In this term of project the following results have been obtained.1. Iterative methods for obtaining sub-optimal numerical solutions to multi-objective control problems : For multi-objective control problems we have proposed a numerical method using sub-level sets, an exterior point method and a bi-section method, and show the effectiveness using some numerical examples.2. System identification methods for gray-box models : For parameter estimation problem for gray-box models we have given some numerical methods based upon SOS (sum of squares) optimization methods, and given a robustness analysis method.3. Robust control design methods for bi-linear systems : From the optimality condition for the L2 gain optimization problem in bi-linear systems Riccati-type inequalities including state variables are derived. For such inequalities we have given a numerical method based upon SOS (sum of squares) optimization methods to obtain a feasible solution.4. Numerical methods for input-saturated systems : For input-saturated systems we have proposed a new representation form using polynomials, and given numerical methods for obtaining feasible solutions to robust analysis/design problems for such systems.5. Parallel computing : We have constructed a PC cluster system for parallel computing, and applied it to solve some control design problems.