# 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…

## 8 Citations

### Robust Control Contraction Metrics: A Convex Approach to Nonlinear State-Feedback ${H}^\infty$ Control

- MathematicsIEEE Control Systems Letters
- 2018

RCCM is a Riemannian metric that verifies differential L^{2} -gain bounds in closed-loop, and guarantees robust stability of arbitrary trajectories via small gain arguments, and can be transformed to a convex optimization problem.

### On Necessary Conditions of Tracking Control for Nonlinear Systems via Contraction Analysis

- Mathematics, Engineering2020 59th IEEE Conference on Decision and Control (CDC)
- 2020

A differentially detectable output is identified, based on which a simple differential controller for trajectory tracking is designed via damping injection, which shows the links to the well developed control contraction metric, as well as its invariance under dynamic extension.

### Contraction Analysis on Primal-Dual Gradient Optimization.

- Mathematics
- 2019

This paper analyzes the contraction of the primal-dual gradient optimization via contraction theory in the context of discrete-time updating dynamics. The contraction theory based on Riemannian…

### Robust Contraction Analysis of Nonlinear Systems via Differential IQC

- Mathematics2019 IEEE 58th Conference on Decision and Control (CDC)
- 2019

This work considers the uncertain system consisting of a feedback interconnection of a nonlinear nominal system and uncertainties satisfying differential integral quadratic constraints, and formulation of a pointwise linear matrix inequality condition is formulated to verify the closed-loop differential L2 gain.

### Distributed Model Predictive Control Under Inexact Primal-Dual Gradient Optimization Based on Contraction Analysis

- Mathematics, Engineering
- 2019

A distributed model predictive control strategy for a class of discrete-time linear systems with consideration of globally coupled constraints and the constraint tightening method is utilized to provide a capability of premature termination with guaranteeing the convergence of the DMPC optimization.

### Invariance and Contraction in Geometrically Periodic Systems with Differential Inclusions

- MathematicsArXiv
- 2021

The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and…

### Inexact Primal-Dual Algorithm for DMPC With Coupled Constraints Using Contraction Theory

- MathematicsIEEE Transactions on Cybernetics
- 2022

A primal-dual algorithm based on the Laplacian consensus to solve a class of discrete-time linear systems subject to globally coupled constraints in a distributed manner by introducing the local estimates of the dual variable is proposed.

### Event-triggered robust distributed nonlinear model predictive control using contraction theory

- EngineeringJ. Frankl. Inst.
- 2022

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