H-半变分不等式分布参数系统辨识与最优控制问题

This project studies mainly the identification and the optimal control problems in hemivariational inequalities, including the nonempty of admissible couples (admissible state-controls),the dependent relationships between the state functions and the control functions (identification parameters). Under different objective functionals,we consider the existence of solutions of state hemivariational inequalities and optimal solutions of the optimal control and the identification problems, optimality conditions,the algorithms of infinite-dimensional optimization problems deriving from the identification and the optimal control problems of distributed parameter systems.We also consider the identification and the optimal control problems governed by fractional hemivariational inequalities (in this project, we only deal with fractional derivatives with time t) . Develop well-known methods solving this kind of problems and seek new computational methods. Some practical iterative algorithms for solving the identification problems are presented, the feasibility and validity of the algorithms are verified by the numerical experiments. At last, we try to apply our results to mechanical models so that people could have a sound grip of mechanical problems.

研究带状态和控制约束的H-半变分不等式所确定的分布参数系统参数辨识与最优控制问题，包括允许对（允许状态-控制）集合的非空性、相对应状态（集）与控制（识别参数）的连续依赖关系。在不同目标泛函下，最优控制问题最优解的存在性、最优性必要条件及求解基于辨识与最优控制问题而产生的无穷维最优化问题的算法。也将研究相应的分数阶（暂只考虑具有时间分数阶导数的）H-半变分不等式分布参数系统辨识和最优控制问题。拓展解决这些问题的已知解法和发展新的计算方法，给出实现问题解的迭代算法，通过数值试验证明算法的有效性。将我们获得的理论成果应用于力学模型。从而，更加深刻理解这类力学问题。

本课题主要研究带状态和控制约束的 H-半变分不等式所确定的分布参数系统参数辨识与最优控制问题，包括允许对（允许状态-控制）集合的非空性、相对应状态 （集）与控制（识别参数）的连续依赖关系。在不同目标泛函下，给出了最优控制问题最优解的存在性、最优性必要条件及求解基于辨识与最优控制问题而产生的无穷维最优化问题的算法。 与此同时，还研究相应的时间分数阶H-半变分不等式分布参数系统辨识和最优控制问题。建立了这些问题的已知解法和发展新的计算方法， 给出了实现问题解的迭代算法，通过数值试验证明算法的有效性。我们获得的理论成果应用于力学模型。从而，更加深刻理解了这类力学问题的本质。