Estimation of Complex Systems

在许多系统中，尽管信息不完善和不完全，但仍需要对状态进行估计。例如，确定湖温变化、桥梁振动、电网稳定性、电池电量估计、建筑供暖。估计器通常也是控制系统的一部分。通常，数学模型和测量数据都是可用的。两者都包含错误。估计中的基本问题是在存在不确定性的情况下使用数据来产生最佳估计。对于复杂系统，如上面的例子，当前的估值器设计依赖于复杂系统模型的简化。该研究项目将为提高复杂系统的估计水平做出根本性的贡献。更好的算法将是这项研究的结果。头五年将集中实现以下目标：O1。带约束系统的估计。许多物理系统具有依赖于空间和时间的动力学，并与平衡条件相结合。例子包括锂离子电池，以及机械/电磁场耦合的机电系统。将得到解存在和适定的可检查条件。这是后续开发估计算法所必需的。氧气。非线性系统的最优估计。现有的非线性系统估值器设计在很大程度上是启发式的。流行的方法有时表现良好，但在其他情况下，估计者会有所不同。得到了误差系统有界的更好的条件。此外，还将制定定义最优估计器的正式成本函数。将使用创新的估计器设计方法。一种工具将是机器学习，以实现复杂系统的实时估计器。臭氧。传感器的优化设计。更好的传感器放置和传感器形状设计提高了估计器的精度，而不需要额外的硬件成本。在设计算法之后，将发展一套完整的非线性系统传感器/估计器设计理论。将获得复杂系统估计的基本结果；特别是对非线性系统的估计，以及对被称为分布参数系统的依赖于空间和时间的系统的估计。其中一个进步是改进了非线性系统估计的稳定性估计。给出了分布参数系统适当离散化的条件。一个主要的进展将是基于最优性准则综合非线性系统的估计器。这将与最佳传感器位置和设计相结合，以进一步提高估计器的性能。由于估计在许多工业和环境系统中发挥着重要作用，其中一些在上面列出，因此这项研究将在控制系统领域之外产生影响。估计器设计和相关技能，如计算、应用领域之间的转换等，因此学生培训将对未来的工业和学术界职业生涯有价值。

In many systems, an estimation of the state is needed despite imperfect and incomplete information. Examples include determining lake temperature changes,  bridge vibrations, electrical network stability, battery charge estimation, building heating. An estimator is also often part of a control system. Typically both a mathematical model and measured data are available. Both contain errors. The fundamental issue in estimation is to use data to yield the best estimate in the presence of uncertainty. For complex systems, such as the above examples, current estimator design relies on simplifications of complex system models. The research program will make fundamental contributions to improving estimation of complex systems. Better algorithms will be a consequence of the research. The first five years will concentrate on the following objectives: O1. Estimation of systems with constraints. Many physical systems have dynamics that depend on space and time, coupled to equilibrium conditions. Examples include lithium -ion cells,  mechatronic systems with coupled mechanical/electro-magnetic fields. Checkable conditions for existence of a solution and well--posedness will be obtained. This is needed for subsequent development of estimation algorithms. O2. Optimal estimation of nonlinear systems. Existing design of estimators for nonlinear systems are largely heuristic. The popular methods sometimes perform well, but in other situations the estimator diverges. Better conditions for a bounded error system will be obtained. Also, formal cost functions that define an optimal estimator will be formulated. Innovative approaches to estimator design will be used. One tool will be machine learning to achieve real-time estimators for complex systems. O3. Optimal sensor design. Better sensor placement and sensor shape design improves estimator accuracy without additional hardware expenditure. An integrated theory for sensor/estimator design for nonlinear systems will be developed followed by design algorithms. Fundamental results in estimation of complex systems will be obtained; in particular for estimation of nonlinear systems and also to systems that depend on space and time, known as distributed parameter systems. One advance will be improved stability estimates for estimation of nonlinear systems. Conditions for the proper discretization of distributed parameter systems will be obtained. A major advance will be synthesis of estimators for nonlinear systems, based on an optimality criteria. This will be combined with optimal sensor location and design to further improve estimator performance. Because estimation plays a major role in many  industrial and environmental systems, some listed above, this research will have an impact outside of the control systems field. Estimator design and related skills, such as computation, transfer between application areas and so student training will be valuable to future careers in industry and academia.