Showing papers by "Paulo Tabuada published in 2001"

Feasible formations of multi-agent systems

Abstract: Formations of multi-agent systems, such as satellites and aircraft, require that individual agents satisfy their kinematic equations while constantly maintaining inter-agent constraints. In this paper, we develop a systematic framework for studying formations of multiagent systems. In particular, we consider undirected formations for centralized formations and directed formations for decentralized formations. In each case, we determine differential geometric conditions that guarantee formation feasibility given the individual agent kinematics. Our framework also enables us to extract a smaller control system that describes the formation kinematics while maintaining,all formation constraints.

Compositional abstractions of hybrid control systems

Abstract: ion is a natural way to hierarchically decompose the analysis and design of hybrid systems. Given a hybrid control system and some desired properties, one extracts an abstracted system while preserving the properties of interest. Abstractions of purely discrete systems is a mature area, whereas abstractions of continuous systems is a recent activity. We present a framework for abstraction that applies to abstract control systems capturing discrete, continuous, and hybrid systems. Parallel composition is presented in a categorical framework and an algorithm is proposed to construct abstractions of hybrid control systems. Finally, we show that our abstractions of hybrid systems are compositional.

Hybrid Abstractions that Preserve Timed Languages

Abstract: In this paper we consider the problem of extracting an abstraction from a hybrid control system while preserving timed languages. Such consistent abstractions are clearly useful as the abstracted, higher level model could be used for controller synthesis or verification of the more complicated lower level model. The class of abstracting maps we consider in this paper compress only the continuous states without aggregating any discrete states. Given such an abstracting map, we determine natural conditions that determine when trajectories of the original hybrid system can be generated by the abstracted hybrid system. Conversely, we determine conditions under which the two hybrid systems generate exactly the same timed language.

Cyclic directed formations of multi-agent systems

Abstract: Formations of multi-agent systems, such as satellites, aircrafts and mobile robots require that individual agents satisfy their kinematic equations while constantly maintaining inter-agent constraints. In previous work we introduced the concept of undirected formation graphs and directed formation graphs to model such formations and presented conditions to determine formation feasibility. However the directed formations were only analyzed in the absence of cycles in the formation graph. In this paper we extend our previous results to accommodate also the presence of cycles in directed formations. Differential geometric and algebraic conditions are presented to determine feasibility of directed formations with possible cycles.

Hybrid abstractions: A search and rescue case study

Abstract: Large-scale, multi-agent systems are becoming extremely complex due to the rapid advances in computation and communication. A natural approach to deal with the increased complexity of such systems is the use of abstractions: given a complicated model and some properties of interest, extract simpler models of the original system that propagate the desired properties to the abstracted model, while hiding details that are of no interest. In this paper, we review our methodology for extracting hybrid systems out of continuous control systems while preserving timed languages. This allows us to extract high level models that can be used for real time scheduling while ensuring that high level plans have feasible implementations at the lower level model. Our methodology, is then fully illustrated by a search and rescue case study.

Abstractions of Hamiltonian control systems

Abstract: Given a control system and a desired property, an abstracted system is a reduced system that preserves the property of interest while ignoring modeling detail. We consider the abstraction problem for Hamiltonian control systems, that is, we preserve the Hamiltonian structure during the abstraction process. We show how the mechanical structure of Hamiltonian control systems can be exploited to simplify the abstraction computations and we provide conditions under which the local accessibility properties of the abstracted Hamiltonian system are equivalent to the local accessibility properties of the original Hamiltonian control system.