Related papers: Is there an optimal choice of configuration space …
Lie groups and their actions are ubiquitous in the description of physical systems, and we explore implications in the setting of model order reduction (MOR). We present a novel framework of MOR via Lie groups, called MORLie, in which…
Optimisation problems often have multiple conflicting objectives that can be computationally and/or financially expensive. Mono-surrogate Bayesian optimisation (BO) is a popular model-based approach for optimising such black-box functions.…
On a constraint manifold we give an explicit formula for the Hessian matrix of a cost function that involves the Hessian matrix of a prolonged function and the Hessian matrices of the constraint functions. We give an explicit formula for…
Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…
This paper introduces a novel robust closed-form control law to handle time-varying hard and soft constraints in uncertain high-relative-degree nonlinear MIMO systems. These constraints represent spatiotemporal specifications in mechanical…
This work develops a first Model Predictive Control for European Space Agencies 3-dof free-floating platform. The challenges of the platform are the on/off thrusters, which cannot be actuated continuously and which are subject to certain…
Space-times admitting a 3-dimensional Lie group of conformal motions $C_3$ acting on null orbits are studied. Coordinate expressions for the metric and the conformal Killing vectors (CKV) are provided (irrespectively of the matter content)…
Motion planning and control are crucial components of robotics applications like automated driving. Here, spatio-temporal hard constraints like system dynamics and safety boundaries (e.g., obstacles) restrict the robot's motions. Direct…
In this paper, a mixed integer linear formulation for problems considering time-of-use-type constraints for uninterruptible services is presented. Our work is motivated by demand response problems in power systems, in which certain devices…
Currently state estimation is very important for the robotics, and the uncertainty representation based Lie group is natural for the state estimation problem. It is necessary to exploit the geometry and kinematic of matrix Lie group…
Bayesian optimization (BO) is a flexible and powerful framework that is suitable for computationally expensive simulation-based applications and guarantees statistical convergence to the global optimum. While remaining as one of the most…
Basic idea presented in Parts (I) and (II) for the deformed boson scheme is applied to the case of the su(2,1)-algebra for describing many-body systems consisting of three kinds of boson operators. A possible form of the coherent state for…
This paper proposes a new class of mass or energy conservative numerical schemes for the generalized Benjamin-Ono (BO) equation on the whole real line with arbitrarily high-order accuracy in time. The spatial discretization is achieved by…
We demonstrate that the error dynamics of a thrusting spacecraft are nearly group affine on the $SE_2(3)$ Lie group, and the nonlinearity can be bounded, or removed with the application of a dynamic inversion control law. A numerical…
Quantum mechanical systems with position dependent masses (PDM) admitting two parametric Lie symmetry groups are classified. Namely, all PDM systems are specified which, in addition to their invariance w.r.t. a two parametric Lie group,…
Algorithms which compute the coarsest simulation preorder are generally designed on Kripke structures. Only in a second time they are extended to labelled transition systems. By doing this, the size of the alphabet appears in general as a…
We develop a discrete-time optimal control framework for systems evolving on Lie groups. Our work generalizes the original Differential Dynamic Programming method, by employing a coordinate-free, Lie-theoretic approach for its derivation. A…
In this paper, we efficiently compute overapproximating reachable sets for control systems evolving on Lie groups, building off results from monotone systems theory and geometric integration theory. We consider intervals in the tangent…
We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…
A type of prolongation structure for several general systems is discussed. They are based on a set of one-forms in which the underlying structure group of the integrability condition corresponds to the Lie-algebra of SL (2,R), O(3), or…