Related papers: Projected Dynamical Systems on Irregular, Non-Eucl…
Projected gradient methods are widely used for constrained optimization. A key application is for partial differential equations (PDEs), where the objective functional represents physical energy and the linear constraints enforce…
Turbulent dynamical systems characterized by both a high-dimensional phase space and a large number of instabilities are ubiquitous among many complex systems in science and engineering. The existence of a strange attractor in the turbulent…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
The Cahn-Hilliard equation is a fundamental model that describes phase separation processes of two-phase flows or binary mixtures. In recent years, the dynamic boundary conditions for the Cahn-Hilliard equation have been proposed and…
Stable dynamical systems are a flexible tool to plan robotic motions in real-time. In the robotic literature, dynamical system motions are typically planned without considering possible limitations in the robot's workspace. This work…
Dynamical Systems (DS) are an effective and powerful means of shaping high-level policies for robotics control. They provide robust and reactive control while ensuring the stability of the driving vector field. The increasing complexity of…
This work investigates a dynamical system functioning as a nonsmooth adaptation of the continuous Newton method, aimed at minimizing the sum of a primal lower-regular and a locally Lipschitz function, both potentially nonsmooth. The…
We introduce a class of unconditionally energy stable, high order accurate schemes for gradient flows in a very general setting. The new schemes are a high order analogue of the minimizing movements approach for generating a time discrete…
Following Demidovich's concept and definition of convergent systems, we analyze the optimal nonlinear damping control, recently proposed [1] for the second-order systems. Targeting the problem of output regulation, correspondingly tracking…
This paper introduces a continuous-time constrained nonlinear control scheme which implements a model predictive control strategy as a continuous-time dynamic system. The approach is based on the idea that the solution of the optimal…
High-dimensional nonlinear systems pose considerable challenges for modeling and control across many domains, from fluid mechanics to advanced robotics. Such systems are typically approximated with reduced-order models, which often rely on…
A coupled computational approach to simultaneously learn a vector field and the region of attraction of an equilibrium point from generated trajectories of the system is proposed. The nonlinear identification leverages the local stability…
A general, variational approach to derive low-order reduced systems for nonlinear systems subject to an autonomous forcing, is introduced. The approach is based on the concept of optimal parameterizing manifold (PM) that substitutes the…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
We present a unified framework for embedding and analyzing dynamical systems using generalized projection operators rooted in local conservation laws. By representing physical, biological, and engineered systems as graphs with incidence and…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
We extend the theory of spectral submanifolds (SSMs) to general non-autonomous dynamical systems that are either weakly forced or slowly varying. Examples of such systems arise in structural dynamics, fluid-structure interactions and…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main…
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…