Discrete Control Barrier Proximal Dynamics: Quantized multi-actuator and sampled-data systems

We present a tractable safe control framework, referred to as discrete Control Barrier Proximal Dynamics (D-CBPD), for a class of quantized multi-actuator and sampled-data systems. We first characterize the tracking behavior of discretized parametric contracting dynamics. Next, we analyze discrete contracting dynamics as controllers and establish bounds on system evolution, shown to be linear for non-expansive systems. These bounds are then translated into control deviations at sampling instants and during inter-sample evolution using one-sided Lipschitz properties. Building on this, we introduce D-CBPD, which tracks the solution of a CBF-based QP controller, ensuring continuous safety with a bounded, tunable violation margin. We further propose discretization as a recurrent triggering mechanism for a generalizable approach to safe quantized control. The method is validated through simulations for thermal management of an air-cooled lithium-ion battery pack with multiple cooling fans, demonstrating its effectiveness in ensuring safety while remaining computationally scalable.