Control Contraction Metrics on Finsler Manifolds

@article{Chaffey2018ControlCM,
  title={Control Contraction Metrics on Finsler Manifolds},
  author={Thomas Chaffey and Ian R. Manchester},
  journal={2018 Annual American Control Conference (ACC)},
  year={2018},
  pages={3626-3633}
}
Control Contraction Metrics (CCMs) provide a nonlinear controller design involving an offline search for a Riemannian metric and an online search for a shortest path between the current and desired trajectories. In this paper, we generalize CCMs to Finsler geometry, allowing the use of non-Riemannian metrics. We provide open loop and sampled data controllers. The sampled data control construction presented here does not require real time computation of globally shortest paths, simplifying… 

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References

SHOWING 1-10 OF 26 REFERENCES

Control Contraction Metrics: Convex and Intrinsic Criteria for Nonlinear Feedback Design

It is shown that sufficient conditions for exponential stabilizability of all trajectories of a nonlinear control system are necessary and sufficient for feedback linearizable systems and also derive novel convex criteria for exponential stabilization of anonlinear submanifold of state space.

Nonlinear stabilization via Control Contraction Metrics: A pseudospectral approach for computing geodesics

It is shown that a CCM controller using a pseudospectral approach for online computations is a middle ground between the simplicity of LQR and stability guarantees for NMPC.

On Existence of Separable Contraction Metrics for Monotone Nonlinear Systems

Decentralized nonlinear feedback design with separable control contraction metrics

Methods based on contraction theory are employed to render the controller-synthesis problem scalable and suitable to use distributed optimization, and the nature of the approach is constructive, because the computation of the desired feedback law is obtained by solving a convex optimization problem.

On Contraction Analysis for Non-linear Systems

Contractive Systems with Inputs

Contraction theory provides an elegant way of analyzing the behaviors of systems subject to external inputs. Under sometimes easy to check hypotheses, systems can be shown to have the incremental

A Differential Lyapunov Framework for Contraction Analysis

The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle and endows the state-space with a Finsler structure.

A Lyapunov-Like Characterization of Asymptotic Controllability

It is shown that a control system in ${\bf R}^n $ is asymptotically controllable to the origin if and only if there exists a positive definite continuous functional of the states whose derivative can