Set-Valued Modeling for Drop-Point Constrained Dynamic Systems

This paper addresses the problem of drop-point constrained state modeling in the set-valued framework, where only drop-point information of state trajectories is available. Due to the lack of complete trajectory information, existing estimation methods with linear equality constraints struggle to achieve effective state prediction. This paper primarily investigates the integration of drop-point constraint information into the entire system state evolution process via convex optimization projection in the set-valued framework, aiming to reconstruct a linear dynamic system model. Subsequently, by employing multiple affine transformations of ellipsoids and designing a weight matrix, the smoothness of state trajectories is enhanced to better align with real motion patterns. Finally, through simulation experiments, we validate the significant advantages of the reconstructed system model over traditional unconstrained system models under the set-valued framework. Additionally, we demonstrate the impact of drop-point constraints on state trajectory evolution under different initial point conditions with the same drop point.