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Robust Region-of-Attraction Estimation
We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics
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In this issue of IEEE Control Systems Magazine, Andy Packard and friends respond to a query on determining the region of attraction using sum-of-squares methods
Beyond Basins of Attraction: Quantifying Robustness of Natural Dynamics
Properly designing a system to exhibit favorable natural dynamics can greatly
simplify designing or learning the control policy. However, it is still unclear
what constitutes favorable natural dynamics and how to quantify its effect.
Most studies of simple walking and running models have focused on the basins of
attraction of passive limit-cycles and the notion of self-stability. We instead
emphasize the importance of stepping beyond basins of attraction. We show an
approach based on viability theory to quantify robust sets in state-action
space. These sets are valid for the family of all robust control policies,
which allows us to quantify the robustness inherent to the natural dynamics
before designing the control policy or specifying a control objective. We
illustrate our formulation using spring-mass models, simple low dimensional
models of running systems. We then show an example application by optimizing
robustness of a simulated planar monoped, using a gradient-free optimization
scheme. Both case studies result in a nonlinear effective stiffness providing
more robustness.Comment: 15 pages. This work has been accepted to IEEE Transactions on
Robotics (2019
Potentials and Limits to Basin Stability Estimation
Acknowledgments The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A.Peer reviewedPublisher PD
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