Found 1339 results, showing the newest relevant preprints. Sort by relevancy only.Update me on new preprints

Critical Clearing Time Sensitivity for Inequality Constrained **Systems**

For such

**systems**, the interplay of feasibility region (man-made limits) and stability region (natural**dynamical****system**response) results in a positively invariant region in state space known as the constrained stability region (CSR). Expand abstract. With the growth of renewable generation (RG) and the development of associated ride through curves serving as operating limits, during disturbances, on violation of these limits, the power

**system**is at risk of losing large amounts of generation. In order to identify preventive control measures that avoid such scenarios from manifesting, the power**system**must be modeled as a constrained**dynamical****system**. For such systems, the interplay of feasibility region (man-made limits) and stability region (natural**dynamical****system**response) results in a positively invariant region in state space known as the constrained stability region (CSR). After the occurrence of a disturbance, as it is desirable for the**system**trajectory to lie within the CSR, critical clearing time (CCT) must be defined with respect to the CSR instead of the stability region as is done traditionally. The sensitivity of CCT to**system**parameters of constrained**systems**then becomes beneficial for planning/revising protection settings (which impact feasible region) and/or operation (which impact dynamics). In this paper, we derive the first order CCT sensitivity of generic constrained power**systems**using the efficient power**system**trajectory sensitivity computation, pioneered by Hiskens in [1]. The results are illustrated for a single-machine infinite-bus (SMIB)**system**as well as a multi-machine**system**in order to gain meaningful insight into the dependence between ability to meet constraints,**system**stability, and changes occurring in power**system**parameters, such as, mechanical power input and inertia.89 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Porosity in conformal **dynamical** **systems**

We then narrow our focus to

**systems**associated to complex continued fractions with arbitrary alphabet and we provide a novel characterization of porosity for their limit sets. Expand abstract. In this paper we study various aspects of porosities for conformal fractals. We first explore porosity in the general context of infinite graph directed Markov

**systems**(GDMS), and we show that, under some natural assumptions, their limit sets are porous in large (in the sense of category and dimension) subsets, and they are mean porous almost everywhere. On the other hand, we prove that if the limit set of a GDMS is not porous then it is not porous almost everywhere. We also revisit porosity for finite graph directed Markov systems, and we provide checkable criteria which guarantee that limit sets have holes of relative size at every scale in a prescribed direction. We then narrow our focus to**systems**associated to complex continued fractions with arbitrary alphabet and we provide a novel characterization of porosity for their limit sets. Moreover, we introduce the notions of upper density and upper box dimension for subsets of Gaussian integers and we explore their connections to porosity. As applications we show that limit sets of complex continued fractions**system**whose alphabet is co-finite, or even a co-finite subset of the Gaussian primes, are not porous almost everywhere, while they are mean porous almost everywhere. We finally turn our attention to complex dynamics and we delve into porosity for Julia sets of meromorphic functions. We show that if the Julia set of a tame meromorphic function is not the whole complex plane then it is porous at a dense set of its points and it is almost everywhere mean porous with respect to natural ergodic measures. On the other hand, if the Julia set is not porous then it is not porous almost everywhere. In particular, if the function is elliptic we show that its Julia set is not porous at a dense set of its points.90 days ago

9/10 relevant

arXiv

9/10 relevant

arXiv

Central limit theorems for the $\mathbb{Z}^2$-periodic Lorentz gas

This paper is devoted to the study of the stochastic properties of dynamical systems preserving an infinite measure. Expand abstract.

This paper is devoted to the study of the stochastic properties of

**dynamical****systems**preserving an infinite measure. More precisely we prove central limit theorems for Birkhoff sums of observables of $\mathbb{Z}^2$-extensions of**dynamical****systems**(satisfying some nice spectral properties). The motivation of our paper is the $\mathbb{Z}^2$-periodic Lorentz process for which we establish a functional central limit theorem for H\"older continuous observables (in discrete time as well as in continuous time).91 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

Probabilistic potential theory and induction of **dynamical** **systems**

In this article, we outline a version of a balayage formula in probabilistic potential theory adapted to measure-preserving

**dynamical****systems**. Expand abstract. In this article, we outline a version of a balayage formula in probabilistic potential theory adapted to measure-preserving

**dynamical****systems**. This balayage identity generalizes the property that induced maps preserve the restriction of the original invariant measure. As an application, we prove in some cases the invariance under induction of the Green-Kubo formula, as well as the invariance of a new degree 3 invariant.91 days ago

10/10 relevant

arXiv

10/10 relevant

arXiv

Assembly along lines in boundary-driven **dynamical** **system**

Repeated application of this algorithm results in the formation of unusual

**dynamical**patterns: during the process of assembly the**system**self-organizes into slices of low particle density separated by lines of increasingly high particle density along which most particles move. Expand abstract. We introduce a simple

**dynamical**rule in which each particle locates a particle that is farthest from it and moves towards it. Repeated application of this algorithm results in the formation of unusual**dynamical**patterns: during the process of assembly the**system**self-organizes into slices of low particle density separated by lines of increasingly high particle density along which most particles move. As the process proceeds, pairs of lines meet and merge with each other until a single line remains and particles move along it towards the zone of assembly. We show that this pattern is governed by particles (attractors) situated on the instantaneous outer boundary of the**system**and that both in two and in three dimensions the lines are formed by zigzag motion of a particle towards a pair of nearly equidistant attractors. This novel line-dominated assembly is very different from the local assembly in which particles that move towards their nearest neighbors produce point-like clusters that coalesce into new point-like clusters, etc.91 days ago

5/10 relevant

arXiv

5/10 relevant

arXiv

MPC-Net: A First Principles Guided Policy Search

We present an Imitation Learning approach for the control of

**dynamical****systems**with a known model. Expand abstract. We present an Imitation Learning approach for the control of

**dynamical****systems**with a known model. Our policy search method is guided by solutions from Model Predictive Control (MPC). Contrary to approaches that minimize a distance metric between the guiding demonstrations and the learned policy, our loss function corresponds to the minimization of the control Hamiltonian, which derives from the principle of optimality. Our algorithm, therefore, directly attempts to solve the HJB optimality equation with a parameterized class of control laws. The loss function's explicit encoding of physical constraints manifests in an improved constraint satisfaction metric of the learned controller. We train a mixture-of-expert neural network architecture for controlling a quadrupedal robot and show that this policy structure is well suited for such multimodal**systems**. The learned policy can successfully stabilize different gaits on the real walking robot from less than 10 min of demonstration data.92 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Ergodic decomposition

Ergodic systems, being indecomposable are important part of the study of

**dynamical****systems**but if a**system**is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic systems in such a way that the study of the former reduces to the study of latter ones? Expand abstract. Ergodic systems, being indecomposable are important part of the study of

**dynamical****systems**but if a**system**is not ergodic, it is natural to ask the following question: Is it possible to split it into ergodic**systems**in such a way that the study of the former reduces to the study of latter ones? Also, it will be interesting to see if the latter ones inherit some properties of the former one. This document answers this question for measurable maps defined on complete separable metric spaces with Borel probability measure, using the Rokhlin Disintegration Theorem.92 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Parallel in time **dynamic**s with quantum annealers

Here, we propose a parallel in time approach to simulate

**dynamical****systems**designed to be executed already on present-day quantum annealers. Expand abstract. Recent years have witnessed an unprecedented increase in experiments and hybrid simulations involving quantum computers. In particular, quantum annealers. Although quantum supremacy has not been established thus far, there exist a plethora of algorithms promising to outperform classical computers in the near-term future. Here, we propose a parallel in time approach to simulate

**dynamical****systems**designed to be executed already on present-day quantum annealers. In essence, purely classical methods for solving dynamics**systems**are serial. Therefore, their parallelization is substantially limited. In the presented approach, however, the time evolution is rephrased as a ground--state search of a classical Ising model. Such a problem is solved intrinsically in parallel by quantum computers. The main idea is exemplified by simulating the Rabi oscillations generated by a two-level quantum**system**(i.e. qubit) experimentally.92 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Synthesis of Boolean Networks from Biological **Dynamical** Constraints
using Answer-Set Programming

Boolean networks model finite discrete

**dynamical****systems**with complex behaviours. The state of each component is determined by a Boolean function of the state of (a subset of) the components of the network. This paper addresses the synthesis of these Boolean functions from constraints on their domain and emerging**dynamical**properties of the resulting network. The**dynamical**properties relate to the existence and absence of trajectories between partially observed configurations, and to the stable behaviours (fixpoints and cyclic attractors). The synthesis is expressed as a Boolean satisfiability problem relying on Answer-Set Programming with a parametrized complexity, and leads to a complete non-redundant characterization of the set of solutions. Considered constraints are particularly suited to address the synthesis of models of cellular differentiation processes, as illustrated on a case study. The scalability of the approach is demonstrated on random networks with scale-free structures up to 100 to 1,000 nodes depending on the type of constraints.93 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv

Efficient Iterative Linear-Quadratic Approximations for Nonlinear Multi-Player General-Sum Differential Games

Unfortunately, numerical solution techniques for general nonlinear

**dynamical****systems**scale poorly with state dimension and are rarely used in applications requiring real-time computation. Expand abstract. Differential games offer a powerful theoretical framework for formulating safety and robustness problems in optimal control. Unfortunately, numerical solution techniques for general nonlinear

**dynamical****systems**scale poorly with state dimension and are rarely used in applications requiring real-time computation. For single-agent optimal control problems, however, local methods based on efficiently solving iterated approximations with linear dynamics and quadratic costs are becoming increasingly popular. We take inspiration from one such method, the iterative linear quadratic regulator (ILQR), and observe that efficient algorithms also exist to solve multi-player linear-quadratic games. Whereas ILQR converges to a local solution of the optimal control problem, if our method converges it returns a local Nash equilibrium of the differential game. We benchmark our method in a three-player general-sum simulated example, in which it takes < 0.75 s to identify a solution and < 50 ms to solve warm-started subproblems in a receding horizon. We also demonstrate our approach in hardware, operating in real-time and following a 10 s receding horizon.93 days ago

4/10 relevant

arXiv

4/10 relevant

arXiv