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When the disturbance input matrix is nonlinear, existing disturbance observer design methods rely on the solvability of a partial differential equation or the existence of an output function with a uniformly well-defined disturbance relative degree, which can pose significant limitations. This note introduces a systematic approach for designing an Immersion and Invariance-based Disturbance Observer (IIDOB) that circumvents these strong assumptions. The proposed IIDOB ensures the disturbance estimation error is globally uniformly ultimately bounded by approximately solving a partial differential equation while compensating for the approximation error. Furthermore, by integrating IIDOB into the framework of control barrier functions, a filter-based safe control design method for control affine systems with disturbances is established where the filter is used to generate an alternative disturbance estimation signal with a known derivative. Sufficient conditions are established to guarantee the safety of the disturbed systems. Simulation results demonstrate the effectiveness of the proposed method. 

The latest developments in vehicle-to-infrastructure (V2I) and vehicle-to-anything (V2X) technologies enable all the entities in the transportation system to communicate and collaborate to optimize transportation safety, mobility, and equity at the system level. On the other hand, the community of researchers and developers is becoming aware of the critical role of roadway infrastructure in realizing automated driving. In particular, intelligent infrastructure systems, which leverage modern sensors, artificial intelligence, and communication capabilities, can provide critical information and control support to connected and/or automated vehicles to fulfill functions that are infeasible for automated vehicles alone due to technical or cost considerations. However, there is limited research on formulating and standardizing the intelligence levels of road infrastructure to facilitate the development, as the SAE automated driving levels have done for automated vehicles. This article proposes a five-level intelligence definition for intelligent roadway infrastructure, namely, connected and automated highway (CAH). The CAH is a subsystem of the more extensive collaborative automated driving system (CADS), along with the connected automated vehicle (CAV) subsystem. Leveraging the intelligence definition of CAH, the intelligence definition for the CADS is also defined. Examples of how the CAH at different levels operates with the CAV in the CADS are also introduced to demonstrate the dynamic allocation of various automated driving tasks between different entities in the CADS.