<p>In this paper, we introduce and study a new system of differential inverse mixed variational inequalities (SDIMVI) in finite-dimensional spaces, which couples ordinary differential equations with two inverse mixed variational inequalities. Motivated by dynamic normative control problems in intelligent transportation systems, we demonstrate that the SDIMVI framework is well-suited to model centralized traffic regulation under physical and policy constraints. Under suitable assumptions, we first establish the linear growth property of the solution set for the inverse mixed variational inequalities. By employing an essential result on measurable selection, we prove the existence of Carathéodory weak solutions. Furthermore, under monotonicity and Lipschitz continuity conditions, we establish the uniqueness of the Carathéodory weak solution. To solve the system numerically, we reformulate the inverse mixed variational inequalities as an optimization-based framework and propose a proximal neurodynamic algorithm. Finally, we illustrate the practical viability of the proposed approach through a numerical example modeling dynamic traffic flow control, where the ODE governs the evolution of traffic density and the inverse mixed variational inequalities encode normative regulatory actions–such as ramp metering and speed limits–subject to capacity constraints. The simulation results exhibit stable and well-behaved solution trajectories, confirming that the framework captures essential features of realistic traffic control scenarios.</p>