Modeling Tools for Multi-modal Control Software

We propose to address the shortcomings of classical hybrid models by moving from the continuous-vs.-discrete focus to a more abstract input/output-vs.-state focus. We plan to pursue the following tasks:

Hybrid models

Formally relate and combine state-based models with I/O-based concurrency models. A hybrid automaton is just one example of such a combination, where finite-state machines are combined with analog computers. Other combinations will lead to a more general and modular view of hybrid systems. Other suitable state-based models include Petri nets; other suitable I/O-based concurrency models include dataflow, discrete-event systems, and synchronous/reactive models [LP95, C93, BB91].

Structuring mechanisms

Introduce Statecharts-like structuring mechanisms into hybrid models [H987]. This introduces hierarchical structuring into the traditionally flat structure of hybrid automata. The hierarchical structure will scale better since the number of levels and the interleaving of automata with I/O-based concurrency models is arbitrary. Moreover, state-space explosion is managed through the use of hierarchical and concurrent states. Hierarchy and concurrency can be exploited not only in design and specification, but also in efficient simulation and verification.

Semantics

Develop a theory of receptiveness and determinacy for hybrid models. Receptiveness ensures the existence of behaviors, determinacy the uniqueness. In a state-based model, these theories are most naturally set in a game-theoretic framework [AH97], whereas in an I/O-based model, they are most naturally studied in a fixed-point framework [LS97]. The hybrid combination promises to expose new insights into the relationship between both frameworks.

Simulation

Implement Ptolemy domains for hierarchically structured combinations of state-based and I/O-based domains. This will enable the simulation of hybrid systems, and provide a framework for specification and design. Ptolemy is a software architecture, developed at Berkeley largely with DARPA support, for heterogeneous modeling and design. Ptolemy has already been used to hierarchically combine automata with certain I/O-based concurrency models, namely, dataflow and discrete-event systems [GLL97]. Multi-way combinations become possible using, for example, analog computers to model physical devices, automata to model modes or regimes of operation, and dataflow to model embedded control software.

Implementation

Develop a theory of robustness and digital approximation for hybrid models. This will enable the validation of software implementations of discrete switching between control laws derived in continuous domains. While feedback can be used to regulate inaccuracies introduced in I/O models and implementations, inaccuracies may accumulate across transitions in state models and implementations. The beginnings of a theory that estimates the implementation error and guarantees conservative results have been developed for timed automata [GHJ97].