Related papers: Variational Synthesis of Controlled Dynamic Mappin…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
Generic Hamiltonian systems have a mixed phase space where regions of regular and chaotic motion coexist. We present a method for constructing an integrable approximation to such regular phase-space regions including a nonlinear resonance…
This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…
In this work we address the problem of the quantization of a simple harmonic oscillator that is perturbed by a time dependent force. The approach consists of removing the perturbation by a canonical change of coordinates. Since the…
This article presents a scalable implementation of nonlinear Gramian-based control synthesis for control-affine systems, including a minimum energy control construction. These synthesis advances are achieved by addressing key computational…
We present a formalism for which a dissipative system is given by a variational principle. The formalism applies to dynamical systems where its trajectory is monotonic. Subsequently, we derive its Lagrangian and Hamiltonian. From the…
Content creation and image editing can benefit from flexible user controls. A common intermediate representation for conditional image generation is a semantic map, that has information of objects present in the image. When compared to raw…
In many synthesis problems, it can be essential to generate implementations which not only satisfy functional constraints but are also randomized to improve variety, robustness, or unpredictability. The recently-proposed framework of…
Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the…
In recent years, formal methods have been extensively used in the design of autonomous systems. By employing mathematically rigorous techniques, formal methods can provide fully automated reasoning processes with provable safety guarantees…
Long-term stability studies of nonlinear Hamiltonian systems require symplectic integration algorithms which are both fast and accurate. In this paper, we study a symplectic integration method wherein the symplectic map representing the…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Recent conditional image synthesis approaches provide high-quality synthesized images. However, it is still challenging to accurately adjust image contents such as the positions and orientations of objects, and synthesized images often have…
In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact and cocontact geometry, the canonoid…
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space $\R^N$. For such optimal control…
This work presents the analysis of the properties of the shortest path control synthesis for the rigid body system. The systems we focus on in this work have only kinematic constraints. However, even for seemingly simple systems and…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
Let the adiabatic invariant of action variable in slow-fast Hamiltonian system with two degrees of freedom have two limiting values along the trajectories as time tends to infinity. The difference of two limits is exponentially small in…
We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential…