Analysis, design, and estimation of linear equality-constrained dynamic systems

The state of many dynamic systems evolves subject to some equality constraints. Most existing work focuses on developing state estimation algorithms for an equality-constrained dynamic system assuming the system is given. How to design and analyze such a system is rarely addressed, even though it is critically important for application and performance evaluation. In this paper, we first analyze the underlying structural information of linear equality-constrained (LEC) dynamic systems through direct elimination. It is found that the process noise of such a system is state dependent in general. This means that existing formulations of such a system are quite limited. Based on the analysis, we then propose a new systematic way to design LEC systems. The key idea is to design only the unconstrained part of the system. Unlike existing system conversion-based design techniques, in our work the desired model class is given and only the distributions of the initial state and process noise need to be determined, which is comparatively easier. To handle state dependency of the process noise, a new constrained state estimation algorithm based on direct elimination is also proposed. Three examples are provided to illustrate the effectiveness of the proposed methods of analysis, design, and estimation, respectively.