Objective: Hybrid cardiovascular mock circuits (HMC), designed for dynamic testing of Ventricular Assist Devices (VAD), offer physiologic accuracy by sequestering model complexity in silico and ease of construction by reducing number of model elements in vitro. Despite superior response time and precision, pneumatic actuation is avoided in HMCs due to nonlinear dynamics and noise. We tested the hypothesis that a HMC consisting of a variable elastance-driven numerical circuit coupled to a pneumo-hydraulic physical circuit can be controlled without linearizing system dynamics. Methods: Reference left ventricular and aortic pressures generated in silico were tracked, respectively, in in vitro preload and afterload reservoirs by controlling non-linear pneumatic dynamics using the Lyapunov stability criterion. A centrifugal pump, the speed (i.e. flow) of which was adjusted using PID control, was interposed between the reservoirs and mimicked the VAD under evaluation. The flow of a recirculating gear pump was controlled by the backstepping method to equalize reservoir fluid volumes by rejecting pressure and flow disturbances. Sensor noise was reduced with discrete-time Kalman filtering. Results: Our results showed that normal, failing and assisted cardiovascular physiologies were numerically simulated and tracked at physical VAD terminals with high accuracy. Reservoir volumes remained stable at various combinations of heart rate, pressure, and VAD flow. Conclusion: The HMC described here offers a stable performance testing platform for VAD prototypes. Significance: This is the first proof that hybrid systems using pneumatic actuation at hydraulic interfaces can optimally be regulated with nonlinear controllers to achieve precise reference tracking and robust disturbance rejection.