Related papers: Controlled Rough Paths on Manifolds I
Let $M$ be any $n$ dimensional smooth manifold and $PM$ be the space of all smooth paths, then we showed that $PM$ is a smooth manifold modelled over a complete normable space. We discussed many geometric structure on Path spaces and its…
Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
A regularized version of Mixture Models is proposed to learn a principal graph from a distribution of $D$-dimensional data points. In the particular case of manifold learning for ridge detection, we assume that the underlying manifold can…
Automated driving has become more and more popular due to its potential to eliminate road accidents by taking over driving tasks from humans. One of the remaining challenges is to follow a planned path autonomously, especially when…
This paper is concerned with the problem of controlling a system of constrained dynamic subsystems in a way that balances the performance degradation of decentralized control with the practical cost of centralized control. We propose a…
Precise positioning and fast traversal times are crucial in achieving high productivity and scale in machining. This paper compares two optimization-based predictive control approaches that achieve high performance. In the first approach,…
Using dynamic models of tensegrity structures, we derive provable, distributed control laws for stabilizing and changing the shape of a formation of vehicles in the plane. Tensegrity models define the desired, controlled, multi-vehicle…
We address the problem of planning robot motions in constrained configuration spaces where the constraints change throughout the motion. The problem is formulated as a fixed sequence of intersecting manifolds, which the robot needs to…
In this paper, we present a geometric approach for computing controlled invariant sets for hybrid control systems. While the problem is well studied in the ellipsoidal case, this family is quite conservative for constrained or switched…
Control of multi-level quantum systems is sensitive to implementation errors in the control field and uncertainties associated with system Hamiltonian parameters. A small variation in the control field spectrum or the system Hamiltonian can…
We present an algorithm which combines recent advances in model based path integral control with machine learning approaches to learning forward dynamics models. We take advantage of the parallel computing power of a GPU to quickly take a…
We introduce `atomic flows': they are graphs obtained from derivations by tracing atom occurrences and forgetting the logical structure. We study simple manipulations of atomic flows that correspond to complex reductions on derivations.…
Controlling structural complexity, particularly the number of holes, remains a fundamental challenge in topology optimization, with significant implications for both theoretical analysis and manufacturability. Most existing approaches rely…
Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity…
Automated Vehicle Path Following Control (PFC) is an advanced control system that can regulate the vehicle into a collision-free region in the presence of other objects on the road. Common collision avoidance functions, such as forward…
A new geometric procedure to construct symplectic methods for constrained mechanical systems is developed in this paper. The definition of a map coming from the notion of retraction maps allows to adapt the continuous problem to the…
This paper addresses the problem of a boundary control design for traffic evolving in a large-scale urban network. The traffic state is described on a macroscopic scale and corresponds to the vehicle density, whose dynamics are governed by…
Constructing useful representations across a large number of tasks is a key requirement for sample-efficient intelligent systems. A traditional idea in multitask learning (MTL) is building a shared representation across tasks which can then…
Manifolds without boundary, and manifolds with boundary, are universally known in Differential Geometry, but manifolds with corners (locally modelled on [0,\infty)^k x R^{n-k}) have received comparatively little attention. The basic…