An effective modeling framework for equality-constrained dynamic systems

Due to physical laws or mathematical properties the parameters and/or the states of some dynamic systems satisfy certain constraints, and exploitation of such constraints generally is expected to produce more accurate system models. This paper is concerned with modeling of the dynamic systems with equality constraints. An effective framework of the constrained dynamics modeling is proposed by which the equality constraints and the auxiliary (unconstrained) dynamics are optimally fused. In particular, modeling of linear equality constrained dynamic systems and quadratic equality constrained dynamic systems is systematically investigated. Meanwhile, the effects of the auxiliary dynamics on the constructed dynamic model are analyzed. Finally, the proposed modeling is assessed on a benchmark scenario of road-based vehicle tracking.