Safety by Invariance, Liveness through Refinement: Heterogeneous Contract Framework for Co-Design of Layered Control

Real-world control systems must balance long-term objectives (liveness) with continuous-time safety constraints, a challenge that motivates layered control architectures (LCAs). However, existing LCA research lacks a uniform specification language across discrete planning and continuous execution, formal guarantees when subsystems operate at different time scales, and compositional separation between layers. Takayama et al. address all three gaps by introducing a heterogeneous contract framework that decomposes safety and liveness: safety is enforced by invariance at the continuous-time layer, and liveness is achieved through refinement at the discrete-time layer. Inter-layer coordination is formalized via vertical refinement and timing-compatibility conditions, providing rigorous guarantees.

The framework is instantiated with a novel LCA combining an MPC planner, an input-to-state stabilizing (ISS) low-level controller, and a reference-governor bridge. Validation on a Hybrid Energy Storage System (HESS) comprising a battery and a supercapacitor demonstrates practical effectiveness. This work is particularly relevant for autonomous systems, robotics, and energy management, where both safety and long-horizon performance are critical. By providing formal guarantees, the framework reduces reliance on ad-hoc filtering and enables more reliable co-design of layered control systems across heterogeneous time scales.