Motivated by the challenge of developing control software provably meeting specifications for real world problems, this paper applies formal methods to adaptive cruise control (ACC). Starting from a Linear Temporal Logic specification for ACC, obtained by interpreting relevant ACC standards, we discuss in this paper two different control software synthesis methods. Each method produces a controller that is correct-byconstruction, meaning that trajectories of the closed-loop systems provably meet the specification. Both methods rely on fixed-point computations of certain set-valued mappings. However, one of the methods performs these computations on the continuous state space whereas the other method operates on a finitestate abstraction. While controller synthesis is based on a lowdimensional model, each controller is tested on CarSim, an industry-standard vehicle simulator. Our results demonstrate several advantages over classical control design techniques. First, a formal approach to control design removes potential ambiguity in textual specifications by translating them into precise mathematical requirements. Second, because the resulting closed-loop system is known a priori to satisfy the specification, testing can then focus on the validity of the models used in control design and whether the specification captures the intended requirements. Finally, the set from where the specification (e.g., safety) can be enforced is explicitly computed and thus conditions for passing control to an emergency controller are clearly defined.

A plethora of driver convenience and safety automation systems are being introduced into production vehicles, such as electronic stability control, adaptive cruise control, lane keeping, and obstacle avoidance. Assuring the seamless and safe integration of each new automation function with existing control functions is a major challenge for vehicle manufacturers. This challenge is compounded by having different suppliers providing software modules for different control functionalities. In this paper, we report on our preliminary steps to address this problem through a fresh perspective combining formal methods, control theory, and correct-by-construction software synthesis. In particular, we begin the process of synthesizing the control software module for adaptive cruise control from formal specifications given in Linear Temporal Logic. In the longer run, we will endow each interacting software module with an assume-guarantee specification stating under which environment assumptions the module is guaranteed to meet its specifications. These assume-guarantee specifications will then be used to formally prove correctness of the cyber-physical system obtained where the integrated modules interact with the physical dynamics.

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