Related papers: Newtonian Mechanics Based Transient Stability PART…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to…
We provide conditions under which trajectory outcomes in mechanical systems subject to unilateral constraints depend piecewise-differentiably on initial conditions, even as the sequence of constraint activations and deactivations varies.…
Keeping the power system stable is becoming more challenging with the growing share of renewable energy sources of low or negligible inertia. Inertia constants for individual power plants are generally not known and are roughly estimated by…
Terminal sliding mode (TSM) control algorithm and its non-singular refinement have been elaborated for two decades and belong, since then, to a broader class of the finite-time controllers, which are known to be robust against the matched…
Rotating the clamped ends of a buckled elastica induces a snap-through instability. Predicting the limit point and determining the equilibria at the start and end of the snap are routine computations in the quasi-static setting. The…
It has been proposed to investigate the equilibration properties of a small isolated quantum system by means of the matrix of asymptotic transition probabilities in some preferential basis. The trace $T$ of this matrix measures the degree…
In this note, a novel methodology that can extract a number of analysis results for linear time-invariant systems (LTI) given only a single trajectory of the considered system is proposed. The superiority of the proposed technique relies on…
Efficient skill acquisition, representation, and on-line adaptation to different scenarios has become of fundamental importance for assistive robotic applications. In the past decade, dynamical systems (DS) have arisen as a flexible and…
A new optimized extreme learning machine- (ELM-) based method for power system transient stability prediction (TSP) using synchrophasors is presented in this paper. First, the input features symbolizing the transient stability of power…
For constrained system which has several independent first integrals, we give a new stabilization method which named adjustment-stabilization method. It can stabilize all known constants of motion for a given dynamical system very well…
This paper derives a differential contraction condition for the existence of an orbitally-stable limit cycle in an autonomous system. This transverse contraction condition can be represented as a pointwise linear matrix inequality (LMI),…
We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…
Nonlinear dynamics of fluid conveying pipe, rotating with constant velocity about its longitudinal axis is analyzed. Considering boundary conditions and internal damping, the nonlinear equation of motion is derived, and it is discretized…
There is an increasing necessity to deploy autonomous systems in highly heterogeneous, dynamic environments, e.g. service robots in hospitals or autonomous cars on highways. Due to the uncertainty in these environments, the verification…
We consider non-stationary free and forced transverse oscillation of an infinite taut string on the Winkler foundation subjected to a discrete mass-spring system non-uniformly moving at a given sub-critical speed. The speed of the…
This paper aims to study the prediction of the bank stability index based on the Time Series Transformer model. The bank stability index is an important indicator to measure the health status and risk resistance of financial institutions.…
Given two distinct subsets $A,B$ in the state space of some dynamical system, Transition Path Theory (TPT) was successfully used to describe the statistical behavior of transitions from $A$ to $B$ in the ergodic limit of the stationary…
Event-B is a well known methodology for the verified design and development of systems that can be characterised as discrete transition systems. Hybrid Event-B is a conservative extension that interleaves the discrete transitions of Event-B…
Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove…