Related papers: Robustly transitive behavior in symplectic dynamic…
We describe some general results that constrain the dynamical fluctuations that can occur in non-equilibrium steady states, with a focus on molecular dynamics. That is, we consider Hamiltonian systems, coupled to external heat baths, and…
Hybrid dynamical systems are systems which undergo both continuous and discrete transitions. The Bolza problem from optimal control theory was applied to these systems and a hybrid version of Pontryagin's maximum principle was presented.…
Stability and safety are critical properties for successful deployment of automatic control systems. As a motivating example, consider autonomous mobile robot navigation in a complex environment. A control design that generalizes to…
A huge number of technological and biological systems involves the lubricated contact between rough surfaces of soft solids in relative accelerated motion. Examples include dynamical rubber seals and the human joints. In this study we…
Nonadiabatic behavior of metastable systems modeled by anharmonic Hamiltonians is reproduced by the Fokker-Planck and imaginary time Schrodinger equation scheme with subsequent symplectic integration. Example solutions capture ergodicity…
High-performance closed-loop control of truly soft continuum manipulators has remained elusive. Experimental demonstrations have largely relied on sufficiently stiff, piecewise architectures in which each actuated segment behaves as a…
When complex systems are driven to extinction by some external factor, their non-stationary dynamics can present an intermittent behaviour between relative tranquility and burst of activity whose consequences are often catastrophic. To…
The dynamics of many important high-dimensional dynamical systems are both chaotic and complex, meaning that strong reducing hypotheses are required to understand the dynamics. The highly influential chaotic hypothesis of Gallavotti and…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
Robust design of autonomous systems under uncertainty is an important yet challenging problem. This work proposes a robust controller that consists of a state estimator and a tube based predictive control law. The class of linear systems…
The purpose of the present work is to show that an adequate basis for understanding the essentially nonlinear phenomena must also be essentially nonlinear however still simple enough to play the role of a basis. It is shown that such types…
This paper appears as the confluence of hyperbolic dynamics, symplectic topology and low dimensional topology, etc. We show that composite symplectic Dehn twists have certain form of nonuniform hyperbolicity: it has positive topological…
In this paper, we derive a "hamiltonian formalism" for a wide class of mechanical systems, including classical hamiltonian systems, nonholonomic systems, some classes of servomechanism... This construction strongly relies in the geometry…
Metriplectic dynamical systems consist of a special combination of a Hamiltonian and a (generalized) entropy-gradient flow, such that the Hamiltonian is conserved and entropy is dissipated/produced (depending on a sign convention). It is…
This paper considers continuously differentiable functions of two vector variables that have (possibly a continuum of) min-max saddle points. We study the asymptotic convergence properties of the associated saddle-point dynamics…
We consider the concept of strong pluripotency of dynamical systems for a hyperbolic invariant set, as introduced in [KNS]. To the best of our knowledge, for the whole hyperbolic invariant set, the existence of robust strongly pluripotent…
Learning or identifying dynamics from a sequence of high-dimensional observations is a difficult challenge in many domains, including reinforcement learning and control. The problem has recently been studied from a generative perspective…
Exceptional points, the spectral degeneracy points in the complex parameter space, are fundamental to non-Hermitian quantum systems. The dynamics of non-Hermitian systems in the presence of exceptional points differ significantly from those…
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…