非确定性系统多维相关过程的Bayes最优估计与随机最优控制

非确定性系统多维相关过程的Bayes最优估计与随机最优控制是一个首创性的国际多学科共性理论难题，其研究对理论与工程应用都有极为重要的实际意义和科学价值。本项目综合应用非确定性结构系统随机动力学、概率与随机过程、非确定性系统识别、随机最优控制、人工智能数据处理技术等理论，以典型工程结构为背景，深入研究基于观测的非确定性系统随机样本过程的统计分析及相关性、基于观测的非确定性系统多维相关过程的Bayes最优估计、基于Bayes估计的非确定性系统随机最优控制等，揭示非确定性与随机激励对响应统计特征、系统识别与参数估计的影响规律、响应观测与系统识别对随机最优控制的影响规律等，发展基于观测的随机激励非确定性系统多维相关过程的Bayes最优估计与基于估计的非确定性系统随机最优控制的新理论方法，为非确定性系统概率估计或异常诊断与基于估计的非确定性系统随机最优控制的深入发展与切实应用提供新的可靠的理论基础。

The researches on Bayesian optimal estimation and stochastic optimal control of nondeterministic systems with multi-dimension correlation processes are a new and challenging problem in relevant fields and have theoretical and practical significances in structural engineering and probabilistic dynamics theory. In this proposal, the statistics and correlation analysis of random sample processes of nondeterministic systems based on observation, Bayesian optimal estimation of nondeterministic systems with multi-dimension correlation processes based on observation, and stochastic optimal control of nondeterministic systems based on Bayesian optimal estimation are studied in detail for important engineering structures such as bridge beams, by using the stochastic dynamics theory of nondeterministic systems, probability and stochastic processes theory, nondeterministic system identification theory, stochastic optimal control theory of nondeterministic systems, and data processing technology for artificial intelligence. The effects of system nondeterminacy and random excitations on response statistical characteristics, effects of system nondeterminacy and random excitations on system identification and parameter estimation, and effects of response observation and system identification on stochastic optimal control are explored. Then the novel methods on Bayesian optimal estimation of nondeterministic systems with multi-dimension correlation processes under random excitations based on observation and on stochastic optimal control of nondeterministic systems based on Bayesian optimal estimation are developed. The research results proposed will be an important theoretical foundation for the theoretical development and practical application in Bayesian estimation and abnormity detection of nondeterministic systems and stochastic optimal control of nondeterministic systems based on estimation.