Estimation of Complex Systems

点击翻译按钮获取中文摘要

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.