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Feedback Linearizable Discretizations of Second Order Mechanical Systems using Retraction Maps
Mechanical systems, in nature, are often described by a set of continuous-time, nonlinear, second-order differential equations (SODEs).
Exploiting Equivariance in the Design of Tracking Controllers for Euler-Poincare Systems on Matrix Lie Groups
In this paper, we propose a group structure on the cotangent bundle of a Lie group and leverage this to define momentum and configuration errors for trajectory tracking drawing on recent work on equivariant observer design.
Constructing Feedback Linearizable Discretizations for Continuous-Time Systems using Retraction Maps
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique.
Equivariant Filters are Equivariant
Observers for systems with Lie group symmetries are an active area of research that is seeing significant impact in a number of practical domains, including aerospace, robotics, and mechatronics.
Implicit Function Theorem: Estimates on the size of the domain
In this article, we present explicit estimates of the size of the domain on which the Implicit Function Theorem and the Inverse Function Theorem are valid.
Stabilizing a spherical pendulum on a quadrotor
In this article we design a backstepping control law based on geometric principles to swing up a spherical pendulum mounted on a moving quadrotor.
Scenario approach for minmax optimization with emphasis on the nonconvex case: positive results and caveats
Moreover, we perform a detailed study of both the asymptotic behaviour (consistency) and finite time behaviour of the scenario approach in the more general setting of nonconvex minmax optimization problems.
