  Directional motion towards a specified destination is a common occurrence in
physical processes and human societal activities. Utilizing this prior
information can significantly improve the control and predictive performance of
system models. This paper primarily focuses on reconstructing linear dynamic
system models based on destination constraints in the set-valued framework. We
treat destination constraints as inherent information in the state evolution
process and employ convex optimization techniques to construct a coherent and
robust state model. This refined model effectively captures the impact of
destination constraints on the state evolution at each time step. Furthermore,
we design an optimal weight matrix for the reconstructed model to ensure
smoother and more natural trajectories of state evolution. We also analyze the
theoretical guarantee of optimality for this weight matrix and the properties
of the reconstructed model. Finally, simulation experiments verify that the
reconstructed model has significant advantages over the unconstrained and
unoptimized weighted models and constrains the evolution of state trajectories
with different starting and ending points.
