Related papers: Control and stabilization of geometrically exact b…
The problem of stabilization of a system of coupled PDEs of the forth-order by means of boundary control is investigated. The considered setup arises from the classical Euler-Bernoulli beam model, and constitutes a generalization of…
This paper presents a novel total Lagrangian cell-centred finite volume formulation of geometrically exact beams with arbitrary initial curvature undergoing large displacements and finite rotations. The choice of rotation parametrisation,…
In this small comment mathematical formulations concerning the nonlinear beam model published in [1] are analyzed. The beam is subjected to vertical and axial loading (at its right end). This nonlinear model can be used to study…
This thesis is devoted to the study of well-posedness properties of some geometric variational problems: existence, regularity and uniqueness of solutions. We study two specific problems arising in the context of geometric calculus of…
Two-wheeled inverted pendulum robots are designed for self-balancing and they have remarkable advantages. In this paper, a new configuration and consequently dynamic model of one specific robot is presented and its dynamic behavior is…
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 paper investigates the robust nonlinear close formation control problem. It aims to achieve precise position control at dynamic flight operation for a follower aircraft under the aerodynamic impact due to the trailing vortices…
A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of…
The dynamics of hexagon patterns in rotating systems are investigated within the framework of modified Swift-Hohenberg equations that can be considered as simple models for rotating convection with broken up-down symmetry, e.g.…
The three-body problem is famously chaotic, with no closed-form analytical solutions. However, hierarchical systems of three or more bodies can be stable over indefinite timescales. A system is considered hierarchical if the bodies can be…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such…
The study of elastic structures embedded with fluid-filled cavities received considerable attention in fields such as autonomous materials, sensors, actuators, and smart systems. This work studies an elastic beam embedded with a set of…
It is shown that the kinematic system describing planar non-steady motions of ideal fibre-reinforced fluids may be reduced to a single two-dimensional third-order partial differential equation in which time enters parametrically. A…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
The linear instability of a beam tensioned by its own weight is considered. It is shown that for long beams, in the sense of an adequate dimensionless parameter, the characteristics of the instability caused by a follower force do not…
This paper focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses heterogeneous sensing mechanism. Depending on the convenience and reliability of the local information, each robot utilizes the…
We design observer-based controllers to stabilise abstract linear boundary control systems on Hilbert spaces. Our main results introduce conditions for exponential, strong, and polynomial stability, and establish external well-posedness of…
Control of a hybrid dynamical system can manifest in one of two main ways: either through the continuous or the discrete dynamics. An example of controls influencing the continuous dynamics is legged locomotion, where the joints are…
Airy beams are known for displaying shape invariance and self-acceleration along the transverse direction while they propagate forwards. Although these properties could be associated with the beam coherence, it has been revealed that they…