Motivated by the growing requirements on the operation of complex engineering systems, we present contracts as specifications for continuous-time linear dynamical systems with inputs and outputs. A contract is defined as a pair of assumptions and gua
rantees, both characterized in a behavioural framework. The assumptions encapsulate the available information about the dynamic behaviour of the environment in which the system is supposed to operate, while the guarantees express the desired dynamic behaviour of the system when interconnected with relevant environments. In addition to defining contracts, we characterize contract implementation, and we find necessary conditions for the existence of an implementation. We also characterize contract refinement, which is used to characterize contract conjunction in two special cases. These concepts are then illustrated by an example of a vehicle following system.
We introduce contracts for linear dynamical systems with inputs and outputs. Contracts are used to express formal specifications on the dynamic behaviour of such systems through two aspects: assumptions and guarantees. The assumptions are a linear sy
stem that captures the available knowledge about the dynamic behaviour of the environment in which the system is supposed to operate. The guarantees are a linear system that captures the required dynamic behaviour of the system when interconnected with its environment. In addition to contracts, we also define and characterize notions of contract refinement and contract conjunction. Contract refinement allows one to determine if a contract expresses a stricter specifications than another contract. On the other hand, contract conjunction allows one to combine multiple contracts into a single contract that fuses the specifications they express.
Freight transportation is of outmost importance for our society and is continuously increasing. At the same time, transporting goods on roads accounts for about 26% of all energy consumption and 18% of all greenhouse gas emissions in the European Uni
on. Despite the influence the transportation system has on our energy consumption and the environment, road transportation is mainly done by individual long-haulage trucks with no real-time coordination or global optimization. In this paper, we review how modern information and communication technology supports a cyber-physical transportation system architecture with an integrated logistic system coordinating fleets of trucks traveling together in vehicle platoons. From the reduced air drag, platooning trucks traveling close together can save about 10% of their fuel consumption. Utilizing road grade information and vehicle-to-vehicle communication, a safe and fuel-optimized cooperative look-ahead control strategy is implemented on top of the existing cruise controller. By optimizing the interaction between vehicles and platoons of vehicles, it is shown that significant improvements can be achieved. An integrated transport planning and vehicle routing in the fleet management system allows both small and large fleet owners to benefit from the collaboration. A realistic case study with 200 heavy-duty vehicles performing transportation tasks in Sweden is described. Simulations show overall fuel savings at more than 5% thanks to coordinated platoon planning. It is also illustrated how well the proposed cooperative look-ahead controller for heavy-duty vehicle platoons manages to optimize the velocity profiles of the vehicles over a hilly segment of the considered road network.
