Optimal control and anti-control of the nonlinear dynamics of a rigid block

2006 ◽  
Vol 364 (1846) ◽  
pp. 2353-2381 ◽  
Author(s):  
Stefano Lenci ◽  
Giuseppe Rega
Keyword(s):  
Nonlinear Dynamics ◽  
Optimal Control ◽  
Upper Bounds ◽  
Rigid Block ◽  
Periodic Excitation ◽  
Heteroclinic Bifurcation ◽  
Lower And Upper Bounds ◽  
Good Agreement

This paper deals with control and anti-control of overturning of a rigid block subjected to a generic periodic excitation. Attention is focused on two relevant thresholds, corresponding to heteroclinic bifurcation and immediate overturning, and representing lower and upper bounds of the region where toppling can occur. The two opposite problems of increasing (control) or decreasing (anti-control) of these two curves by properly modifying the shape of the excitation are investigated in depth and the optimal excitations permitting their maximum variations are determined. The notions of ‘global’ and ‘one-side’ control (anti-control) are utilized and their different importance for the various cases is discussed. The effects of control (anti-control) of one curve on the uncontrolled (non-anti-controlled) curve are also investigated, both analytically and with numerical overturning charts. A good agreement is seen to occur.

Collapse Strength of Redundant Beams After Lateral Buckling

1957 ◽  
Vol 24 (2) ◽  
pp. 283-288
Author(s):  
E. F. Masur ◽  
K. P. Milbradt
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Postbuckling Behavior ◽  
Collapse Strength ◽  
Neutral Equilibrium ◽  
Slender Beams ◽  
End Restraint ◽  
Limiting Values ◽  
Increasing Load ◽  
Good Agreement

Abstract According to classical linear theory, slender beams buckle laterally under vertical loads which remain constant as the buckling amplitude increases. Unless prior yielding takes place, the loads corresponding to neutral equilibrium represent therefore the collapse strength of the beam. However, the inclusion of nonlinear terms in the strain-displacement relations modifies the predicted postbuckling behavior of redundant beams. If continued elasticity is postulated, increasing amplitudes are associated with increasing load magnitudes, which generally approach limiting values. These “ultimate loads” may be estimated by means of two principles establishing lower and upper bounds. Tests performed on a single-span beam of varying degrees of end restraint show good agreement with the proposed theory.

Stable manifolds for perturbations of exponential dichotomies in mean

2018 ◽  
Vol 18 (03) ◽  
pp. 1850022 ◽  
Author(s):  
Luis Barreira ◽  
Claudia Valls
Keyword(s):  
Nonlinear Dynamics ◽  
Banach Space ◽  
Exponential Dichotomy ◽  
Invariant Manifolds ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Exponential Behavior ◽  
Exponential Dichotomies ◽  
Stable Invariant Manifolds ◽  
Stable Invariant

We establish the existence of stable invariant manifolds for any sufficiently small perturbation of a cocycle with an exponential dichotomy in mean. The latter notion corresponds to replace the exponential behavior in the classical notion of an exponential dichotomy by an exponential behavior in average with respect to an invariant measure. We consider both perturbations of a cocycle over a map and over a flow that can be defined on an arbitrary Banach space. Moreover, we obtain an upper bound for the speed of the nonlinear dynamics along the stable manifold as well as a lower bound when the exponential dichotomy in mean is strong (this means that we have lower and upper bounds along the stable and unstable directions of the dichotomy).

HETEROCLINIC BIFURCATIONS AND OPTIMAL CONTROL IN THE NONLINEAR ROCKING DYNAMICS OF GENERIC AND SLENDER RIGID BLOCKS

2005 ◽  
Vol 15 (06) ◽  
pp. 1901-1918 ◽  
Author(s):  
STEFANO LENCI ◽  
GIUSEPPE REGA
Keyword(s):  
Nonlinear Dynamics ◽  
Optimal Control ◽  
System Response ◽  
Rigid Block ◽  
Stable And Unstable Manifolds ◽  
Small Perturbations ◽  
Numerical Investigations ◽  
Nonlinear Dynamics And Chaos ◽  
Heteroclinic Connection ◽  
Unstable Manifolds

A method for controlling nonlinear dynamics and chaos, previously developed by the authors, is applied to the rigid block on a moving foundation. The method consists in modifying the shape of the excitation in order to eliminate, in an optimal way, the heteroclinic intersections embedded in the system dynamics. Two different cases are examined: (i) generic block under small perturbations and (ii) slender block under generic perturbations, and they are investigated analytically either by a perturbation analysis (former case) or exactly (latter case). Two different strategies are proposed: (i) one-side control, which consists in eliminating the intersections of a single heteroclinic connection, and (ii) global control, which consists in simultaneously eliminating the intersections of both heteroclinic connections. The best excitations permitting the maximum distance between stable and unstable manifolds are determined in both cases. Finally, some numerical investigations aimed at highlighting meaningful aspects of system response under controlled (optimal) and noncontrolled (harmonic) excitations are performed.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number
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