scholarly journals Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

2015 ◽  
Vol 3 (2) ◽  
pp. 154-163
Author(s):  
Ning Bin ◽  
Chengke Zhang ◽  
Huainian Zhu ◽  
Zan Mo
Keyword(s):  
Singularly Perturbed ◽  
Stackelberg Equilibrium ◽  
Order System ◽  
Fast Time ◽  
Slow Time ◽  
Stackelberg Strategy ◽  
Fast Time Scale ◽  
Equilibrium Strategies ◽  
Numerical Result ◽  
Coupled Algebraic Riccati Equations

AbstractBased on singularly perturbed bilinear quadratic problems, this paper proposes to decompose the full-order system into two subsystems of a slow-time and fast-time scale. Utilizing the fixed point iterative algorithm to solve cross-coupled algebraic Riccati equations, equilibrium strategies of the two subsystems can be obtained, and further the composite strategy of the original full-order system. It was proved that such a composite strategy formed ano(ε) (near) Stackelberg equilibrium, and a numerical result of the algorithm was presented in the end.

DYNAMICS OF COUPLED DAHL TYPE AND NONSMOOTH SYSTEMS AT DIFFERENT SCALES OF TIME

2013 ◽  
Vol 23 (07) ◽  
pp. 1350114 ◽  
Author(s):  
A. TURE SAVADKOOHI ◽  
C.-H. LAMARQUE
Keyword(s):  
Time Scale ◽  
Coupled Oscillators ◽  
Energy Exchange ◽  
Fast Time ◽  
System Behavior ◽  
Slow Time ◽  
Fast Time Scale ◽  
Nonsmooth Systems ◽  
Main System ◽  
Nonsmooth Potential

Vibratory behavior of two coupled oscillators is studied. The main system — Dahl type — is coupled to a very light system with a nonsmooth potential that can be endowed for passively controlling the main system. Invariant manifold of the system at the fast time scale is revealed and the system behavior at slow time scale around the infinity of the fast time scale is detected. This can give us the chance to forecast all possible attractors of the system during energy exchange between the two oscillators.

The Dance of the Interneurons: How Inhibition Facilitates Fast Compressible and Reversible Learning in Hippocampus

2018 ◽  
Author(s):  
Wilten Nicola ◽  
Claudia Clopath
Keyword(s):  
Time Scale ◽  
State Of The Art ◽  
Fast Time ◽  
Slow Time ◽  
Fast Time Scale ◽  
Slow Time Scale ◽  
Spike Sequences ◽  
Incoming Information ◽  
Spiking Networks ◽  
Inhibitory Networks

AbstractThe hippocampus is capable of rapidly learning incoming information, even if that information is only observed once. Further, this information can be replayed in a compressed format in either forward or reversed modes during Sharp Wave Ripples (SPW-R). We leveraged state-of-the-art techniques in training recurrent spiking networks to demonstrate how primarily inhibitory networks of neurons in CA3 and CA1 can: 1) generate internal theta sequences or “time-cells” to bind externally elicited spikes in the presence of septal inhibition, 2) reversibly compress the learned representation in the form of a SPW-R when septal inhibition is removed, 3) generate and refine gamma-assemblies during SPW-R mediated compression, and 4) regulate the inter-ripple-interval timing between SPW-R’s in ripple clusters. From the fast time scale of neurons to the slow time scale of behaviors, inhibitory networks serve as the scaffolding for one-shot learning by replaying, reversing, refining, and regulating spike sequences.

Near-contact motion of surfactant-covered spherical drops

1998 ◽  
Vol 366 ◽  
pp. 259-287 ◽  
Author(s):  
VITTORIO CRISTINI ◽  
J. BŁAWZDZIEWICZ ◽  
MICHAEL LOEWENBERG
Keyword(s):  
External Force ◽  
Time Scale ◽  
Contact Region ◽  
Fast Time ◽  
Force Parameter ◽  
Slow Time ◽  
Fast Time Scale ◽  
Rigid Particles ◽  
External Forces ◽  
Gap Width

A lubrication analysis is presented for the near-contact axisymmetric motion of spherical drops covered with an insoluble non-diffusing surfactant. Detailed results are presented for the surfactant distribution, the interfacial velocity, and the gap width between the drop surfaces. The effect of surfactant is characterized by a dimensionless force parameter: the external force normalized by Marangoni stresses. Critical values of the force parameter have been established for drop coalescence and separation. Surfactant-covered drops are stable to rapid coalescence for external forces less than 4πkTac0, where c0 is the surfactant concentration at the edge of the near-contact region and a is the reduced drop radius.For subcritical forces, the behaviour of surfactant-covered drops is described by two time scales: a fast time scale characteristic of near-contact motion between drops with clean interfaces and a slow time scale associated with rigid particles. The surfactant distribution evolves on the short time scale until Marangoni stresses approximately balance the external force. Supercritical values of the external force cannot be balanced; coalescence and separation occur on the fast time scale. The coalescence time normalized by the result for drops with clean interfaces is independent of the viscosity ratio and initial gap width.Under subcritical force conditions, a universal long-time behaviour is attained on the slow time scale. At long times, the surfactant distribution scales with the near-contact region and the surface velocity is directed inward which impedes the drop approach and accelerates their separation compared to rigid particles. For drops pressed together with a sufficiently large subcritical force, a shrinking surfactant-free clean spot forms.Surfactant-covered drops exhibit an elastic response to unsteady external forces because of energy stored in the surfactant distribution.

Phase Change Materials - From Structures to Kinetics

2006 ◽  
Vol 918 ◽  
Author(s):  
Matthias Wuttig ◽  
Wojciech Welnic ◽  
Ralf Detemple ◽  
Henning Dieker ◽  
Johannes Kalb ◽  
...  
Keyword(s):  
Phase Change ◽  
Crystalline State ◽  
Phase Change Materials ◽  
Amorphous State ◽  
Structural Difference ◽  
Fast Time ◽  
Optical Contrast ◽  
Fast Time Scale ◽  
Kinetics Of ◽  
Structure Properties

AbstractPhase change materials possess a unique combination of properties which include a pronounced property contrast between the amorphous and crystalline state, i.e. a high electrical and optical contrast. In particular the latter observation is indicative for a considerable structural difference between the amorphous and crystalline state. At the same time the crystallization of the amorphous state proceeds on a fast time scale. This raises the question how structure, properties and kinetics are related in phase change alloys. It will be demonstrated that only a small group of covalent semiconductors with octahedral-like coordination has the required property combination. This is related to their thermodynamic properties which govern the kinetics of crystallization.

A New Model for Long-Term Stochastic Analysis and Prediction—Part I: Theoretical Background

1992 ◽  
Vol 36 (01) ◽  
pp. 1-16
Author(s):  
G. A. Athanassoulis ◽  
P. B. Vranas ◽  
T. H. Soukissian
Keyword(s):  
Time Scale ◽  
Random Function ◽  
Spectral Characteristics ◽  
Time History ◽  
Time Variable ◽  
Sea Surface ◽  
Surface Elevation ◽  
Fast Time ◽  
Slow Time

A new approach for calculating the long-term statistics of sea waves is proposed. A rational long-term stochastic model is introduced which recognizes that the wave climate at a given site in the ocean consists of a random succession of individual sea states, each sea state possessing its own duration and intensity. This model treats the sea-surface elevation as a random function of a "fast" time variable, and the time history of the spectral characteristics of the successive sea states as a random function of a "slow" time variable. By developing an appropriate conceptual framework, it becomes possible to express various probabilistic characteristics of the sea-surface elevation, which are sensible only in the fast-time scale, in terms of the statistics of sea-states duration and intensity, which is meaningful only in the slow-time scale. As an example, we study the random quantity MU(T) = "number of maxima of the sea-surface elevation lying above the level u and occurring during a long-term time period [0,T]." Exploiting the proposed framework, it is shown that, under certain clearly defined assumptions, Mu(T) can be given the structure of a renewal-reward (cumulative) process, whose interarrival times correspond to the duration of successive sea states. Thus, using renewal theory, the complete characterization of the probability structure of MU(T) is obtained. As a consequence, the long-term probability distribution function of the individual wave height is rigorously defined and calculated. The relation of the present results with corresponding ones previously obtained is thoroughly discussed. The proposed model can be extended twofold: either by replacing some of the simplifying assumptions by more realistic ones, or by extending the model for treating the corresponding problems for ship and structures responses.

Parameter Estimation in a Nonlinear Vibrating System Using an Observer for an Extended System

1999 ◽  
Author(s):  
Anindya Chatterjee ◽  
Joseph P. Cusumano
Keyword(s):  
Parameter Estimation ◽  
Time Scale ◽  
Asymptotic Methods ◽  
System Response ◽  
Parameter Estimates ◽  
Fast Time ◽  
State Variables ◽  
Slow Time ◽  
Unknown Parameters ◽  
Lipschitz Continuous

Abstract We present a new observer-based method for parameter estimation for nonlinear oscillatory mechanical systems where the unknown parameters appear linearly (they may each be multiplied by bounded and Lipschitz continuous but otherwise arbitrary, possibly nonlinear, functions of the oscillatory state variables and time). The oscillations in the system may be periodic, quasiperiodic or chaotic. The method is also applicable to systems where the parameters appear nonlinearly, provided a good initial estimate of the parameter is available. The observer requires measurements of displacements. It estimates velocities on a fast time scale, and the unknown parameters on a slow time scale. The fast and slow time scales are governed by a single small parameter ϵ. Using asymptotic methods including the method of averaging, it is shown that the observer’s estimates of the unknown parameters converge like e−ϵt where t is time, provided the system response is such that the coefficient-functions of the unknown parameters are not close to being linearly dependent. It is also shown that the method is robust in that small errors in the model cause small errors in the parameter estimates. A numerical example is provided to demonstrate the effectiveness of the method.

The effect of fast-time-scale turbulence on magnetohydrodynamical behaviour

1984 ◽  
Vol 31 (1) ◽  
pp. 81-92 ◽  
Author(s):  
R. O. Dendy ◽  
D. Ter Haar
Keyword(s):  
Time Scale ◽  
Normal Modes ◽  
Dispersion Relations ◽  
Magnetized Plasma ◽  
Fast Time ◽  
Fast Time Scale ◽  
Scale Turbulence ◽  
The Ideal

We show what corrections have to be made to the equations of ideal magneto-hydrodynamics when there is fast-time-scale turbulence present in a magnetized plasma. We show how the dispersion relations for the ideal Alfvén and magnetoacoustic MHD normal modes are modified when such turbulence is present. Finally, we discuss the relation of our work to that of other authors.

Comparative effects of vasodilator drugs on flow distribution and venous return

1985 ◽  
Vol 63 (11) ◽  
pp. 1345-1355 ◽  
Author(s):  
R. I. Ogilvie
Keyword(s):  
Blood Flow ◽  
Blood Volume ◽  
Time Constant ◽  
Venous Return ◽  
Flow Distribution ◽  
Fast Time ◽  
Central Blood Volume ◽  
Slow Time ◽  
Arterial Resistance ◽  
Slow Time Constant

Systemic vascular effects of hydralazine, prazosin, captopril, and nifedipine were studied in 115 anesthetized dogs. Blood flow [Formula: see text] and right atrial pressure (Pra) were independently controlled by a right heart bypass. Transient changes in central blood volume after an acute reduction in Pra at a constant [Formula: see text] showed that blood was draining from two vascular compartments with different time constants, one fast and the other slow. At three dose levels producing comparable reductions in systemic arterial pressure (30–40% at the highest dose), these drugs had different effects on flow distribution and venous return. Hydralazine and prazosin had parallel and balanced effects on arterial resistance of the two vascular compartments, and flow distribution was unaltered. Captopril preferentially reduced arterial resistance of the compartment with a slow time constant for venous return (−26 ± 6%, −30 ± 6%, −50 ± 5% at 0.02, 0.10, and 0.50 mg∙kg−1∙h−1, respectively; [Formula: see text]) without altering arterial resistance of the fast time-constant compartment. Blood flow to the slow time-constant compartment was increased 43 ± 14% at the highest dose, and central blood volume was reduced 108 ± 15 mL. In contrast, nifedipine had a balanced effect on arterial resistance with the lowest dose (0.025 mg/kg) but caused a preferential reduction in arterial resistance of the fast time-constant compartment at higher doses (−38 ± 4% and −55 ± 2% at 0.05 and 0.10 mg/kg, respectively). Blood flow to the slow time-constant compartment was reduced 36 ± 5% at the highest dose of nifedipine, and central blood volume was increased 66 ± 12 mL. Total systemic venous compliance was unaltered or slightly reduced by each of the four drugs. These results add further evidence to the hypothesis that peripheral blood flow distribution is a major determinant of venous return to the heart.

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