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In this paper, we introduce an angle notion called the singular angle for nonlinear systems from an input-output perspective. The proposed system singular angle, based on the angle between $L_2$-signals, describes an upper bound for the…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
The Cauchy problem for the system of equations of two-dimensional rotational gas dynamics is considered. It is assumed that the Cauchy data are a smooth compact perturbation of a constant state. Integral conditions for the data sufficient…
Quantum tracking control aims to identify applied fields to steer the expectation values of particular observables along desired paths in time. The associated temporal fields can be identified by inverting the underlying dynamical equations…
A novel MIMO homogeneous Super-Twisting Algorithm is proposed in this paper for nonlinear systems with relative degree one, having a time and state-varying uncertain control matrix. The uncertainty is represented by a constant but unknown…
Continuum manipulators offer intrinsic dexterity and safe geometric compliance for navigation within confined and obstacle-rich environments. However, their infinite-dimensional backbone deformation, unmodeled internal friction, and…
This paper presents a formulation of Lagrangian dynamics of constrained mechanical systems in terms of reduced quasi-velocities and quasi-forces that can be used for simulation, analysis, and control purposes. In this formulation, Cholesky…
In this paper we propose a process of lagrangian reduction and reconstruction for nonholonomic discrete mechanical systems where the action of a continuous symmetry group makes the configuration space a principal bundle. The result of the…
Isolated mechanical systems -- e.g., those floating in space, in free-fall, or on a frictionless surface -- are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers…
This paper provides a constructive passivity-based control approach to solve the set-point regulation problem for input-affine continuous nonlinear systems while considering saturation in the inputs. As customarily in passivity-based…
Passivity property gives a sense of energy balance. The classical definitions and theorems of passivity in dynamical systems require time invariance and locally Lipschitz functions. However, these conditions are not met in many systems. A…
In this paper, the notion of contraction is used to solve the trajectory-tracking problem for a class of mechanical systems. Additionally, we propose a dynamic extension to remove velocity measurements from the controller while rejecting…
We show that for isolated relativistic systems with spin the conservation of total angular momentum implies that, instead of the center of mass, it is a modified center of mass and spin which behaves inertially. This requires a change in…
This paper develops an input-output feedback linearization-based adaptive controller to stabilize and regulate a dual-rotor rotational system (DRRS), whose inertial properties as well as the geometric configuration of rotors are unknown.…
Aerial manipulators (AM) exhibit particularly challenging, non-linear dynamics; the UAV and the manipulator it is carrying form a tightly coupled dynamic system, mutually impacting each other. The mathematical model describing these…
The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…
Quantum nonrelativistic systems with $2\times2$ matrix potentials are investigated. Physically, they simulate charged or neutral fermions with non-trivial dipole momenta, interacting with an external electric field. Assuming rotationally…
Safe and compliant control of dynamic systems in interaction with the environment, e.g., in shared workspaces, continues to represent a major challenge. Mismatches in the dynamic model of the robots, numerical singularities, and the…
We study the bounce cosmology to construct a singularity-free $f(\mathcal{R})$ model using the reconstruction technique. The formulation of the $f(\mathcal{R})$ model is based on the Raychaudhari equation, a key element employed in…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…