Diamond interchanges (DIs) allow movement of vehicles between surface streets and freeways for all types of vehicles, including normal non-connected human-driven vehicle (NHDV) traffic and the connected vehicles (CVs). Unlike simple intersections, DIs consist of a pair of closely spaced intersections that are controlled together with complicated traffic movements and heavy demand fluctuations. This paper reviews the movements being controlled at DIs and presents a dynamic programming (DP)-based real-time proactive traffic control algorithm called MIDAS, to control both NHDVs and CVs. Like seminal cycle-free adaptive control methods such as OPAC and RHODES, MIDAS uses a forward recursion DP approach with efficient data structures for any large set of phase movements being controlled at DIs, over a finite-time horizon that rolls forward, and then uses a backward recursion to retrieve the optimal phase sequence and duration of phases. MIDAS captures Eulerian measurements from fixed loop detectors for all vehicles, and also captures Lagrangian measurements like in-vehicle GPS from CVs to estimate link travel times, arrival times, turning movements, etc. For every time horizon MIDAS predicts future arrivals, estimates queues at the interchange, and then minimizes a user-defined metric like delays, stops, or queues at an interchange. The paper compares performances of MIDAS with those of an optimal fixed cycle time signal control (OFTC) scheme and RHODES control on a simulated DI. The simulation is of Phoenix, AZ, DI (on I-17/19th Ave.) that uses the VISSIM micro-simulation platform. Performance is evaluated for various traffic loads and various CV market penetrations. Results show that MIDAS control outperforms RHODES and OFTC.