Related papers: Geometric control theory of vertical rolling disc …
This letter studies a distributed collision avoidance control problem for a group of rigid bodies on a sphere. A rigid body network, consisting of multiple rigid bodies constrained to a spherical surface and an interconnection topology, is…
In this paper we continue our investigation of the global categorical symmetries that arise when gauging finite higher groups and their higher subgroups with discrete torsion. The motivation is to provide a common perspective on the…
Recent investigations on the longitudinal and lateral control of wheeled autonomous vehicles are reported. Flatness-based techniques are first introduced via a simplified model. It depends on some physical parameters, like cornering…
This paper participates in the development of a unified approach to the control of aerial vehicles with extended flight envelopes. More precisely, modeling for control purposes of a class of thrust-propelled aerial vehicles subjected to…
Geometric problems are usually formulated by means of (exterior) differential systems. In this theory, one enriches the system by adding algebraic and differential constraints, and then looks for regular solutions. Here we adopt a dual…
The motion of a disk spinning to rest after being tipped on its side is a classic example of a finite-time singularity, yet the dominant dissipation mechanism governing this process remains debated. Using stereoscopic high-speed imaging, we…
We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal…
In the formation control problem for autonomous robots a distributed control law steers the robots to the desired target formation. A local stability result of the target formation can be derived by methods of linearization and center…
In this paper we study, from a variational and geometrical point of view, second-order variational problems on Lie groupoids and the construction of variational integrators for optimal control problems. First, we develop variational…
This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be…
The paper deals with motion planning for a spin-rolling sphere when the sphere follows a straight path on a plane. Since the motion of the sphere is constrained by the straight line, the control of the sphere's spin motion is essential to…
We investigate a class of higher-order nonlinear dispersive equations posed on the circle, subject to additive forcing by a finite-dimensional control. Our main objective is to establish approximate controllability by using the…
A typical geometry extracted from the path integral of a quantum theory of gravity might be quite complicated in the UV region. Even if such a configuration is not physical, it may be of interest to understand the details of its nature,…
In this article we show the crucial role of elliptic regularity theory for the development of efficient numerical methods for the solution of some variational problems. Here we focus to a class of elliptic multiobjective optimal control…
This paper presents the design of an extremum seeking controller based on sliding modes and cyclic search for real-time optimization of non-linear multivariable dynamic systems. These systems have arbitrary relative degree, compensated by…
Geometric integration theory can be employed when numerically solving ODEs or PDEs with constraints. In this paper, we present several one-step algorithms of various orders for ODEs on a collection of spheres. To demonstrate the versatility…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [Comput. Methods…
We present control-oriented models for transient dynamics of isothermal one-dimensional gas flow through multiple pipes in series and intersecting pipe geometries. These composite models subsume algebraic constraints that would otherwise…
Controlled algebra plays a central role in many recent advances in geometric topology. This paper studies the iteration construction that was present from the very origins of the theory but started being exploited only recently. We develop…