Legged robots that balance
Proceedings of the 4th international symposium on Robotics Research
Extracting and representing qualitative behaviors of complex systems in phase space
Artificial Intelligence
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Universal computation and other capabilities of hybrid and continuous dynamical systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
An invariant based approach to the design of hybrid control systems containing clocks
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Nonlinear Control Systems: An Introduction
Nonlinear Control Systems: An Introduction
On Dynamically Consistent Hybrid Systems
Hybrid Systems II
Spatial aggregation: theory and applications
Journal of Artificial Intelligence Research
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We describe the Phase-Space Nonlinear Control Toolbox, a suite of computational tools for synthesizing and evaluating control laws for a broad class of nonlinear dynamical systems. The Toolbox comprises computational algorithms for identifying optimal control reference trajectories in the phase space of dynamical systems and experimental methods for evaluating performance of the control laws. These algorithms combine knowledge of the geometric theory of modern nonlinear dynamical systems with effcient computational methods for geometric reasoning and graph search; they define the properties of controllability and robustness in terms of phase-space geometric structures and exploit the phase-space neighborhood adjacencies to obtain computational efficiency. Compared to the traditional analytic control design methods, the phase-space based control synthesis and evaluation rely on high-performance computational techniques and are applicable to physical systems operating in large nonlinear regimes. Using a proof-of-concept physical experiment for stabilizing a nonlinear magnetic levitation system, we have successfully demonstrated the feasibility of the phase-space control technology.