Related papers: Control contraction metrics on Lie groups
Accuracy and stability are common requirements for Quadrotor trajectory tracking systems. Designing an accurate and stable tracking controller remains challenging, particularly in unknown and dynamic environments with complex aerodynamic…
Many chemical processes exhibit diverse timescale dynamics with a strong coupling between timescale sensitive variables. Model predictive control with a non-uniformly spaced optimisation horizon is an effective approach to multi-timescale…
Many relevant applications of group theoretical methods to physical problems are related, in some manner, to classification schemes by means of symmetry groups. In these schemes, irreducible representations of a Lie group have to be…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
This paper presents an overview of recent developments in the analysis of shapes such as curves and surfaces through Riemannian metrics. We show that several constructions of metrics on spaces of submanifolds can be unified through the…
Actions of Lie groups on presymplectic manifolds are analyzed, introducing the suitable comomentum and momentum maps. The subsequent theory of reduction of presymplectic dynamical systems with symmetry is studied. In this way, we give a…
This paper proposes a Model Predictive Control (MPC) algorithm for target tracking amongst static and dynamic obstacles. Our main contribution lies in improving the computational tractability and reliability of the underlying non-convex…
This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to…
In this paper, a machine learning based observer for systems evolving on manifolds is designed such that the state of the observer is restricted to the Lie group on which the system evolves. Conventional techniques involving machine…
Model Predictive Control (MPC) can efficiently control constrained systems in real-time applications. MPC feedback law for a linear system with linear inequality constraints can be explicitly computed off-line, which results in an off-line…
This paper presents a general framework for the design of linear controllers for linear systems subject to time-domain constraints. The design framework exploits sums-of-squares techniques to incorporate the time-domain constraints on…
In this paper, we analyze the chain control sets of linear control systems on connected Lie groups. Our main result shows that the compactness of the central subgroup associated with the drift is a necessary and sufficient condition to…
In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie…
Controlled Lagrangian and matching techniques are developed for the stabilization of relative equilibria and equilibria of discrete mechanical systems with symmetry as well as broken symmetry. Interesting new phenomena arise in the…
We propose an abstract framework for solving the constrained set-point tracking problem for impedance passive infinite-dimensional nonlinear systems. The class of systems considered is governed by monotone differential inclusions and allows…
This work explores a novel perspective on solving nonconvex and nonsmooth optimization problems by leveraging sampling based methods. Instead of treating the objective function purely through traditional (often deterministic) optimization…
Model predictive control (MPC) has become the most widely used advanced control method in process industry. In many cases, forecasts of the disturbances are available, e.g., predicted renewable power generation based on weather forecast.…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
This study addresses the centralized synthesis of distributed controllers using linear matrix inequalities (LMIs). Sparsity constraints on control gains of distributed controllers result in conservatism via the convexification of the…
We show the contractibility of spaces of invariant Riemannian metrics of positive scalar curvature on compact connected manifolds of dimension at least two, with and without boundary and equipped with compact Lie group actions. On manifolds…