Related papers: Newtonian Mechanics Based Transient Stability PART…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
A major limitation of the classical control theory is the assumption that the state space and its dimension do not change with time. This prevents analyzing and even formalizing the stability and control problems for open multi-agent…
Classical, Quantum, Relativistic and Statistical: the four branches of mechanics. However, the Quattro Donna of Physics disagree even about the entities that are supposed to be fundamental, such as space, matter and time. In order to search…
There are two paradigms to study nanoscale engines in stochastic and quantum thermodynamics. Autonomous models, which do not rely on any external time-dependence, and models that make use of time-dependent control fields, often combined…
This paper explores cooperative trajectory planning approaches within the context of human-machine shared control. In shared control research, it is typically assumed that the human and the automation use the same reference trajectory to…
We consider the problem of classifying trajectories generated by dynamical systems. We investigate a model-based approach, the common approach in control engineering, and a data-driven approach based on Support Vector Machines, a popular…
This paper presents a trajectory tracking control strategy that modulates the active power injected by geographically distributed inverter-based resources to support transient stability. Each resource is independently controlled, and its…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
In dynamic simulation of complete wheel loaders, one interesting aspect, specific for the working task, is the momentary power distribution between drive train and hydraulics, which is balanced by the operator. This paper presents the…
This paper derives a density matrix of the steady-state statistical mechanics compatible with the steady-state thermodynamics proposed by Oono and Paniconi [Prog. Theor. Phys. Suppl. {\bf 130}, 29 (1998)]. To this end, we adopt three…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Transient stability and critical clearing time (CCT) are important concepts in power system protection and control. This paper explores and compares various learning-based methods for predicting CCT under uncertainties arising from…
We derive general trade-off relations among the power, efficiency, and constancy for two-terminal thermoelectric systems in the linear response regime. Constancy, which quantifies the steadiness of the heat engine, is measured by its…
Different variants of hybrid kinetic-fluid models are considered for describing the interaction of a bulk fluid plasma obeying MHD and an energetic component obeying a kinetic theory. Upon using the Vlasov kinetic theory for energetic…
The Lorentz symmetry group entails physical equations whose solutions are retarded. This leads to the concept of a relativistic engine resulting from retardation of electromagnetic fields. We have shown that Newton'n third law cannot…
The preconditioned iterative solution of large-scale saddle-point systems is of great importance in numerous application areas, many of them involving partial differential equations. Robustness with respect to certain problem parameters is…
The relationship between physiological systems and modern electromechanical technologies is fast becoming intimate with high degrees of complex interaction. It can be argued that muscular function, limb movements, and touch perception serve…
We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be…
In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics…
Since Newton, all classical and quantum physics depends upon the "Newtonian Paradigm". Here the relevant variables of the system are identified. The boundary conditions creating the phase space of all possible values of the variables are…