相关论文: Model Reduction Near Periodic Orbits of Hybrid Dyn…
In this work, we investigate a model order reduction scheme for high-fidelity nonlinear structured parametric dynamical systems. More specifically, we consider a class of nonlinear dynamical systems whose nonlinear terms are polynomial…
This paper considers the optimal control for hybrid systems whose trajectories transition between distinct subsystems when state-dependent constraints are satisfied. Though this class of systems is useful while modeling a variety of…
Transient stability is crucial to the reliable operation of power systems. Existing theories rely on the simplified electromechanical models, substituting the detailed electromagnetic dynamics of inductor and capacitor with their impedance…
We present a numerically tractable formulation for computing the optimal control of the class of hybrid dynamical systems whose trajectories are continuous. Our formulation, an extension of existing relaxed-control techniques for switched…
Soft robots offer remarkable adaptability and safety advantages over rigid robots, but modeling their complex, nonlinear dynamics remains challenging. Strain-based models have recently emerged as a promising candidate to describe such…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…
This paper is a survey of extensions to finite automata theory to model real-time systems as well as systems exhibiting mixed discrete-continuous behavior. Real-time systems maintain a continuous and timely interaction with the environment,…
Models such as those involving abrupt changes in the Earth's reflectivity due to ice melt and formation often use nonlinear terms (e.g., hyperbolic tangent) to model the transition between two states. For various reasons, these models are…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
We introduce a class of convex, higher-dimensional billiard models which generalise stadium billiards. These models correspond to the free motion of a point-particle in a region bounded by cylinders cut by planes. They are motivated by…
We investigate random complex dynamics of rational or polynomial maps on the Riemann sphere. We show that regarding random complex dynamics of polynomials, generically, the chaos of the averaged system disappears at any point in the Riemann…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
This paper presents a control methodology for achieving orbital stabilization with simultaneous time synchronization of periodic trajectories in underactuated robotic systems. The proposed approach extends the classical transverse…
We simulate the dynamics of a disordered interacting spin chain subject to a quasi-periodic time-dependent drive, corresponding to a stroboscopic Fibonacci sequence of two distinct Hamiltonians. Exploiting the recursive drive structure, we…
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by…
If one wants to explore the properties of a dynamical system systematically one has to be able to track equilibria and periodic orbits regardless of their stability. If the dynamical system is a controllable experiment then one approach is…
A one-parameter family of time-reversible systems on $\mathbb{T}^3$ is considered. It is shown that the dynamics is not conservative, namely the attractor and repeller intersect but not coincide. We explain this as the manifestation of the…