Related papers: A New Hybrid Automaton Framework with Partial Diff…
Partial differential equation (PDE)-constrained optimization arises in many scientific and engineering domains, such as energy systems, fluid dynamics and material design. In these problems, the decision variables (e.g., control inputs or…
Hybrid systems are characterized by the hybrid evolution of their state: A part of the state changes discretely, the other part changes continuously over time. Typically, modern control applications belong to this class of systems, where a…
Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…
The solution of partial differential equations (PDEs) on complex domains often presents a significant computational challenge by requiring the generation of fitted meshes. The Diffuse Domain Method (DDM) is an alternative which reformulates…
This paper introduces a hierarchical framework that integrates graph search algorithms and model predictive control to facilitate efficient parking maneuvers for Autonomous Vehicles (AVs) in constrained environments. In the high-level…
We present a structure-preserving discretization of the hybrid magnetohydrodynamics (MHD)-driftkinetic system for simulations of low-frequency wave-particle interactions. The model equations are derived from a variational principle,…
This paper presents AFD-STA Net, a neural framework integrating adaptive filtering and spatiotemporal dynamics learning for predicting high-dimensional chaotic systems governed by partial differential equations. The architecture combines:…
Hybrid systems are dynamical systems with continuous evolution of states and discrete evolution of states and governing equations. We have worked on the design and implementation of HydLa, a constraint-based modeling language for hybrid…
Cyber-physical systems involve a network of discrete controllers that control physical processes. Examples range from autonomous cars to implantable medical devices, which are highly safety critical. Hybrid Automata (HA) based formal…
We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces---generalized by the term hypergraphs. To this end, we consider PDEs on…
In this paper, a computationally efficient data-driven hybrid automaton model is proposed to capture unknown complex dynamical system behaviors using multiple neural networks. The sampled data of the system is divided by valid partitions…
In scientific computation, it is often necessary to calculate higher-order derivatives of a function. Currently, two primary methods for higher-order automatic differentiation exist: symbolic differentiation and algorithmic automatic…
Hybrid systems are mostly modelled, simulated, and verified in the time domain by computer scientists. Engineers, however, use both frequency and time domain modelling due to their distinct advantages. For example, frequency domain…
One of the more prominent trends within Industry 4.0 is the drive to employ Robotic Process Automation (RPA), especially as one of the elements of the Lean approach. The full implementation of RPA is riddled with challenges relating both to…
Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder…
This paper introduces a hypothetical hybrid control framework for port-Hamiltonian (p$\mathcal{H}$) systems, employing a dynamic decomposition based on Data-Assisted Control (DAC). The system's evolution is split into two parts with fixed…
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,…
A characterization of a semilinear elliptic partial differential equation (PDE) on a bounded domain in $\mathbb{R}^n$ is given in terms of an infinite-dimensional dynamical system. The dynamical system is on the space of boundary data for…
Higher-dimensional automata (HDA) are a formalism to faithfully model the behaviour of concurrent systems. For ordinary automata, there is a correspondence between regular expressions, regular languages and finite automata, which provides a…
The diffuse-domain, or smoothed boundary, method is an attractive approach for solving partial differential equations in complex geometries because of its simplicity and flexibility. In this method the complex geometry is embedded into a…