Artificial Intelligence
The composition and validation of heterogeneous control laws
Automatica (Journal of IFAC)
Qualitative reasoning: modeling and simulation with incomplete knowledge
Qualitative reasoning: modeling and simulation with incomplete knowledge
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Proving properties of continuous systems: qualitative simulation and temporal logic
Artificial Intelligence
Advanced Control System Design
Advanced Control System Design
Exploiting spatial and temporal flexibility for plan execution of hybrid, under-actuated systems
AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Automated symbolic reachability analysis: with application to delta-notch signaling automata
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Qualitative heterogeneous control of higher order systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
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Multiple model approaches to the control of complex dynamical systems are attractive because the local models can be simple and intuitive, and global behavior can be analyzed in terms of transitions among local operating regions. In this paper, we argue that the use of qualitative models further improves the strengths of the multiple model approach by allowing each local model to describe a large class of useful non-linear dynamical systems. In addition, reasoning with qualitative models naturally identifies weak sufficient conditions adequate to prove qualitative properties such as stability. We demonstrate our approach by building a global controller for the free pendulum. We specify and validate local controllers by matching their structures to simple generic qualitative models. This process identifies qualitative constraints on the controller designs, sufficient to guarantee the desired local properties and to determine the possible transitions between local regions. This, in turn, allows the continuous phase portrait to be abstracted to a simple transition graph. The degrees of freedom in the design that are unconstrained by the qualitative description remain available for optimization by the designer for any other purpose.