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Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design | | Ian R. Manchester
; Jean-Jacques E. Slotine
; | | Date: |
11 Mar 2015 | | Abstract: | Contraction analysis uses differential dynamics and appropriate metrics to
show that all solutions of a particular system converge exponentially. In this
paper we generalize this approach to problems in control design, giving
sufficient conditions for exponential stabilizability of all trajectories of a
nonlinear control system. The conditions can be expressed in terms of a dual
metric as (convex) pointwise linear matrix inequalities. We show that for
feedback linearizable systems the conditions are necessary as well as
sufficient. We also show how computation can be greatly simplified through the
use of a virtual dynamical system admitting any solution of the actual system
as a particular trajectory. The results on virtual systems are used to derive
novel convex criteria for exponential convergence to a flow-invariant nonlinear
manifold. Extensions to approximate optimal and robust control are
straightforward, and generalize well-known linear results. The proposed
techniques are illustrated with several example problems. | | Source: | arXiv, 1503.3144 | | Services: | Forum | Review | PDF | Favorites | |
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