arXiv:2611.13719v1 Announce Type: new Abstract: Existing work on modeling destination-constrained dynamic systems has mainly focused on discrete-time formulations with linear destination constraints or Gaussian destination distributions. Since practical systems are more naturally modeled in continuous time and often subject to nonlinear/non-Gaussian constraints/distributions, this paper proposes a unified measure-transformation framework for continuous-time modeling of systems subject to deterministic or distributional constraints on a nonlinear function of the terminal state. The framework starts from an unconstrained It\^{o} stochastic differential equation, typically derived from physical laws to describe the system's forward evolution without destination information, and takes its induced path measure as unconstrained measure. Doob's $h$-transform is employed to transform this measure into a constrained path measure incorporating destination information through an injected drift. The resulting system is proved to satisfy the constraints while preserving the laws of the unconstrained state process conditioned on the destination information. The transition density is derived, and the path measure of the distributionally constrained system is proved to uniquely minimize Kullback--Leibler divergence from the unconstrained path measure among those satisfying the same distributional constraint. Its injected drift is further shown to converge pointwise to that of the deterministically constrained system as the destination distribution shrinks to the prespecified value. For linear time-varying unconstrained systems, a simplified form of the constrained systems is derived in terms of the conditional expectation of the terminal state, leading to the development of trajectory-generation algorithms. Numerical simulations evaluate the proposed framework under both types of destination constraints.