Related papers: Stable interactions via proper deformations
A feedback stabilization scheme to stabilize a classical reacting Hamiltonian system is proposed. It is based on transforming a saddle-type equilibrium to an asymptotically stable one, and is given in a simple and algorithmic way. The…
We show that any globally asymptotically controllable system on any smooth manifold can be globally stabilized by a state feedback. Since we allow discontinuous feedbacks, we interpret the solutions of our systems in the ``sample and hold''…
We speculate on Dyson series for the $S$-matrix when the interaction depends on derivatives of the fields. We stick on two particular examples: the scalar electrodynamics and the renormalised $\phi ^4$ theory. We eventually give evidence…
We confirm the stability of Podolsky's generalized electrodynamics by constructing a series of two-parametric bounded conserved quantities which includes the canonical energy-momentum tensors. In addition, we evaluate the…
A novel method for stability and instability study of autonomous dynamical systems using the flow and divergence of the vector field is proposed. A relation between the method of Lyapunov functions and the proposed method is established.…
We analyze the dynamical equations obeyed by a classical system with position-dependent mass. It is shown that there is a non-conservative force quadratic in the velocity associated to the variable mass. We construct the Lagrangian and the…
Ostrogradsky instability generally appears in nondegenerate higher-order derivative theories and this issue can be resolved by removing any existing degeneracy present in such theories. We consider an action involving terms that are at most…
This paper proposes a methodology to stabilize relative equilibria in a model of identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group structure of the resulting dynamical system, the…
We find and solve a large class of integrable dynamical systems which includes Calogero-Sutherland models and various novel generalizations thereof. In general they describe $N$ interacting particles moving on a circle and coupled to an…
We obviate the use of observers for the purpose of output feedback tracking control of Lagrangian systems and solve some long-standing yet well-documented open problems. As often implemented in control practice, we replace unavailable…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
The theory of the effect of external fluctuation force on the stability and spatial distribution of mutually interacting and slowly evaporating charged drops, levitated in an electrodynamic balance, is presented using classical…
Interaction is so ubiquitous that imaging a world free from it is a difficult fantasy exercise. At the same time, in understanding any complex physical system, our ability of accounting for the mutual interaction of its constituents is…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
The present paper extends the classical second-order variational problem of Herglotz type to the more general context of the Euclidean sphere S^n following variational and optimal control approaches. The relation between the Hamiltonian…
We investigate the stability with respect to homogenization of classes of integrals arising in the control-theoretic interpretation of some Hamilton-Jacobi equations. The prototypical case is the homogenization of energies with a Lagrangian…
We show that a longitudinal gauge degree of freedom for a vector field is equivalent to a Pais-Uhlenbeck scalar field. With the help of this equivalence, we can determine natural interactions of this field with scalars and fermions. Since…
We study a process of pattern formation for a generic model of species anchored to the nodes of a network where local reactions take place, and that experience non-reciprocal long-range interactions, encoded by the network directed links.…
This paper studies the problem of stabilizing target formations specified by inter-neighbor bearings with relative position measurements. While the undirected case has been studied in the existing works, this paper focuses on the case where…