Showing papers by "Paulo Tabuada published in 2002"

Composing Abstractions of Hybrid Systems

Abstract: The analysis and design of hybrid systems must exploit their hierarchical and compositional nature of in order to tackle complexity. In previous work, we presented a hierarchical abstraction framework for hybrid control systems based on the notions of simulation and bisimulation. In this paper, we build upon our previous work and investigate the compositionality of our abstraction framework. We present a composition operator that allows synchronization on inputs and states of hybrid systems. We then show that the composition operator is compatible with our abstraction framework in the sense that abstracting subsystems will the result in an abstraction of the overall system.

Bisimilar control affine systems

Abstract: The notion of bisimulation plays a very important role in theoretical computer science where it provides several notions of equivalence between models of computation. These equivalences are in turn used to simplify analysis and synthesis for these models. In system theory, a similar notion is also of interest in order to develop modular analysis and design tools for purely continuous or hybrid control systems. We introduce two notions of bisimulation for nonlinear systems. We present a differential-algebraic characterization of these notions and show that bisimilar systems of different dimensions are obtained by factoring out certain invariant distributions. Furthermore, we also show that all bisimilar systems of different dimension are of this form.

From nonlinear to Hamiltonian via feedback

Abstract: Mechanical control systems are a very important class of nonlinear control systems. They possess a rich mathematical structure which can be extremely important for the solution of various control problems. We expand the applicability of design methodologies developed for mechanical control systems by locally rendering nonlinear control systems, mechanical by a proper choice of feedback. In particular, we characterize control systems which can be transformed to Hamiltonian control systems by a local feedback transformation.

Discrete synchronization of hybrid systems

Abstract: Control theory is faced with new paradigms and challenges that fall beyond traditional problems. Nowadays applications tend to be distributed, and require partial synchronization among their various subsystems. We give initial steps towards discrete synchronization problems for systems which are compositions of several, possibly distributed, hybrid systems. Such problems arise frequently in the coordination of multi-agent systems, where each agent is modeled as a hybrid system. This results in control problems where the model is the composition of decoupled subsystems, but the specification is coupled across subsystems. A centralized solution to this problem requires computing the product hybrid system resulting in state explosion. We alternatively consider decentralized solutions to such discrete synchronization problems. Partially decentralized synchronization is achieved if each subsystem is allowed to communicate with the subsystems it needs to partially synchronize with. The required communication between agents is provided by modeling abstractions of the remaining agents. These abstractions. which are property-dependent, are then used to derive local controllers using global, but minimal, observations.