Intelligent Transportation Systems (ITS) apply well-established technologies in communications, control, and computer hardware and software to increase safety and improve operational performance of the transportation network without expanding the current infrastructure. For many ITS applications, ensuring safety of the traffic participants, including drivers and pedestrians, is one of the most important research initiatives of the Intelligent Transportation Systems Society (ITSS). The ITS applications range from collision avoidance for autonomous or human-driven vehicles to cooperation of multiple vehicles to achieve common goals such as reduced fuel consumption or increased traffic throughput. The main challenges when designing controllers for such systems are the need to consider the close combination of, and coordination between, the system's computational and physical elements.
Most of the vehicles nowadays are controlled by tens of or even hundreds of microcontrollers, which communicate via a CAN bus, for electric steering, braking, chassis and body control. Moreover, vehicles interact with other traffic participants including (semi) autonomous vehicles and human-driven cars and also with roadside units through a Vehicle-to-Vehicle (V2V) or Vehicle-to-Infrastructure (V2I) communication, resulting in a large-scale Cyber-Physical System. Thus, traditional control theory that has been devoted to modeling continuous systems cannot adequately model such complex Cyber-Physical Systems, where both continuous (physical plant, e.g., vehicle) and discrete components (computing and communication) closely interacting each other.
This thesis studies the design of continuous control laws that satisfy the safety property of the systems and their interfaces with discrete components that abstract human's high-level, decision making process. Our primary goals are to design continuous controllers for ITS applications that by design guarantee the safety property without further verification. First of all, hybrid systems, a class of modeling frameworks which form the foundation for a mathematical approach to Cyber-Physical Systems will be introduced. Then the reachability analysis techniques are developed to compute the exact reachable sets which will then be manipulated to design control laws that satisfy the safety property of the system.
As a motivating application, we consider the Adaptive Cruise Control (ACC) system which becomes increasingly popular in commercial vehicles but lacks a fully-automated Collision Avoidance (CA) functionality, thus still leaving the responsibility to human drivers to apply proper braking force. Since the currently available ACC systems are developed mainly for providing drivers comfort and convenience riding, it cannot address the situation where safety should come first. Such situations may include sudden deceleration of a preceding vehicle and cut-in by a slower vehicle, where a rear-end collision is imminent or unavoidable. Thus, an active CA system needs to be developed and fully integrated into the ACC system in order to give more control authority to the vehicle when the driver cannot react fast enough to the imminent collision event.
In this regard, the CA problem between the ACC-equipped vehicle (follower) and the preceding vehicle (leader) is formulated as a pursuit-evasion game to take into account the worst case scenario. That is, the leader tries to cause a collision by full braking while the follower tries to avoid it. By solving this game under the assumption that the follower's braking force is larger than that of the leader, the unsafe region can be obtained as a union of sets reachable from a collision set. This means that if the follower is within this unsafe region it cannot avoid a collision regardless of its control effort, i.e., the unsafe region becomes a controlled-invariant set when the leader plays optimally. In other words, the follower can always avoid a collision if it stays outside of the unsafe region for all time. The resulting safe set, complement of the unsafe region, represents the minimum safe distances and serves as a lookup table so that the follower can refer to it and apply an appropriate level of braking. Moreover, the ACC with CA system will be further augmented with a communication capability so that vehicles can interact with other vehicles and maintain a very small gap, preferable several meters, to the preceding vehicles. This can implement Cooperative Adaptive Cruise Control (CACC) for multiple vehicles forming a platoon with a small inter-vehicle spacing in highway traffic, resulting in reduced fuel consumption and increased traffic throughput.