scholarly journals Uncoupling Isaacs’equations in nonzero-sum two-player differential games : The example of conflict over parental care

2008 ◽  
Vol Volume 9, 2007 Conference in... ◽  
Author(s):  
Frédéric Hamelin ◽  
Pierre Bernhard
Keyword(s):  
Parental Care ◽  
Differential Games ◽  
Nash Equilibria ◽  
Closed Loop ◽  
Classical Problem ◽  
Complete Analysis ◽  
Behavioural Ecology ◽  
International Audience ◽  
Set Up

International audience We use a recently uncovered decoupling of Isaacs PDE’s of some mixed closed loop Nash equilibria to give a rather complete analysis of the classical problem of conflict over parental care in behavioural ecology, for a more general set up than had been considered heretofore. On utilise un découplage récemment mis en évidence des équations d’Isaacs d’un jeu différentiel pour des stratégies mixtes singulières particulières pour donner une analyse assez complète d’un problème classique en écologie comportementale concernant le conflit à propos des soins parentaux.

The application of compound proportional resonant control strategy in multiple PV inverters system

2018 ◽  
Vol 32 (34n36) ◽  
pp. 1840098
Author(s):  
Yuan Li ◽  
Huifang Shen ◽  
Chao Xiong ◽  
Yaofei Han ◽  
Guofeng He
Keyword(s):  
Control Strategy ◽  
Closed Loop ◽  
Control Strategies ◽  
Integrated Control ◽  
Reference Signal ◽  
Loop Model ◽  
Harmonic Compensation ◽  
Feed Forward ◽  
Feed Forward Control ◽  
Set Up

In order to eliminate the effect on the grid current caused by the background harmonic voltage and the reference signal on the grid connected multi-inverter, this paper adopts the double closed-loop feed-forward control strategy. This strategy is based on the inductor voltage and the grid-connected current, and the integrated control strategy of quasi-proportional resonance loop parallel to a specific harmonic compensation loop. Based on the closed-loop model of multiple inverters, the change curves of the transfer function of the two control strategies are compared with the feed-forward control and the composite proportional resonance. The two corresponding control methods are used to analyze the current quality of the multi-inverter impact. Finally, the MATLAB/Simulink simulation model is set up to verify the proposed control strategies. The simulation results show that the proposed method can achieve better tracking of the sinusoidal command signal at the fundamental frequency, and enhance the anti-interference ability of the system at the 3rd, 5th, and 7th harmonic frequency.

scholarly journals Operating diagram of a flocculation model in the chemostat

2020 ◽  
Vol Volume 31 - 2019 - CARI 2018 ◽  
Author(s):  
Radhouane Fekih-Salem ◽  
Tewfik Sari
Keyword(s):  
Local Stability ◽  
Stability Region ◽  
Steady States ◽  
Complete Analysis ◽  
Stable Limit ◽  
Control Parameters ◽  
Coexistence Region ◽  
Microbial Ecosystem ◽  
International Audience ◽  
Stable Limit Cycles

International audience The objective of this study is to analyze a model of the chemostat involving the attachment and detachment dynamics of planktonic and aggregated biomass in the presence of a single resource. Considering the mortality of species, we give a complete analysis for the existence and local stability of all steady states for general monotonic growth rates. The model exhibits a rich set of behaviors with a multiplicity of coexistence steady states, bi-stability, and occurrence of stable limit cycles. Moreover, we determine the operating diagram which depicts the asymptotic behavior of the system with respect to control parameters. It shows the emergence of a bi-stability region through a saddle-node bifurcation and the occurrence of coexistence region through a transcritical bifurcation. Finally, we illustrate the importance of the mortality on the destabilization of the microbial ecosystem by promoting the washout of species. L'objectif de cette étude est d'analyser un modèle du chémostat impliquant la dynamique d'attachement et de détachement de la biomasse planctonique et agrégée en présence d'une seule ressource. En considérant la mortalité des espèces, nous donnons une analyse complète de l'existence et de la stabilité locale de tous les équilibres pour des taux de croissance monotones. Le modèle pré-sente un ensemble riche de comportements avec multiplicité d'équilibres de coexistence, bi-stabilité et apparition des cycles limites stables. De plus, nous déterminons le diagramme opératoire qui dé-crit le comportement asymptotique du système par rapport aux paramètres de contrôle. Il montre l'émergence d'une région de bi-stabilité via une bifurcation noeud col et l'occurrence d'une région de coexistence via une bifurcation transcritique. Enfin, nous illustrons l'importance de la mortalité sur la déstabilisation de l'écosystème microbien en favorisant le lessivage des espèces.

Determination of Stresses in Cemented Lap Joints

1953 ◽  
Vol 20 (3) ◽  
pp. 355-364
Author(s):  
R. W. Cornell
Keyword(s):  
Differential Equations ◽  
Infinite Number ◽  
Lap Joints ◽  
The Other ◽  
Complete Analysis ◽  
Stress Distributions ◽  
Lap Joint ◽  
Analogy Method ◽  
Set Up

Abstract A variation and extension of Goland and Reissner’s (1) method of approach is presented for determining the stresses in cemented lap joints by assuming that the two lap-joint plates act like simple beams and the more elastic cement layer is an infinite number of shear and tension springs. Differential equations are set up which describe the transfer of the load in one beam through the springs to the other beam. From the solution of these differential equations a fairly complete analysis of the stresses in the lap joint is obtained. The spring-beam analogy method is applied to a particular type of lap joint, and an analysis of the stresses at the discontinuity, stress distributions, and the effects of variables on these stresses are presented. In order to check the analytical results, they are compared to photoelastic and brittle lacquer experimental results. The spring-beam analogy solution was found to give a fairly accurate presentation of the stresses in the lap joint investigated and should be useful in analyzing other cemented lap-joint structures.

A Digital Computer Model for Optimal Programming of Hemodialytic Treatment

1988 ◽  
Vol 11 (4) ◽  
pp. 235-242 ◽  
Author(s):  
C. Lamberti ◽  
E. Sarti ◽  
A. Santoro ◽  
M. Spongano ◽  
P. Zucchelli ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Closed Loop ◽  
Clinical Results ◽  
Pressure Regulation ◽  
Clinical Tests ◽  
Experimental Protocol ◽  
Dialysis Unit ◽  
Optimal Programming ◽  
Set Up ◽  
Arterial Pressure Regulation

A mathematical model of hydroelectrolyte exchanges and arterial pressure regulation in the human body during dialysis has been set up. It is conceived as a tool for a new dialysis unit which will be able to “interpret” the signals supplied by suitable instruments connected to the patient and modify the machine set-points in real time in order to obtain clinical results defined by the physician. The main aim is the prevention of hypotensive episodes during treatment. An experimental protocol has been developed for parameter estimation of each patient during a single dialysis. Clinical tests illustrated the model's ability to fit the patient's state during dialysis. This is the first step in the more general task of validation of the model, necessary for the achievement of a closed-loop dialysis unit.

Sampled-Data Nash Equilibria in Differential Games with Impulse Controls

2021 ◽  
Vol 190 (3) ◽  
pp. 999-1022
Author(s):  
Utsav Sadana ◽  
Puduru Viswanadha Reddy ◽  
Tamer Başar ◽  
Georges Zaccour
Keyword(s):  
Differential Games ◽  
Nash Equilibria ◽  
Sampled Data ◽  
Impulse Controls

scholarly journals Distance-Based Formation Control for Quadrotors with Collision Avoidance via Lyapunov Barrier Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
Jawhar Ghommam ◽  
Luis F. Luque-Vega ◽  
Maarouf Saad
Keyword(s):  
Collision Avoidance ◽  
Tracking Control ◽  
Formation Control ◽  
Closed Loop ◽  
Group Formation ◽  
Closed Loop System ◽  
Relative Localization ◽  
Formation Pattern ◽  
Set Up ◽  
The Stability

In this paper, group formation control with collision avoidance is investigated for heterogeneous multiquadrotor vehicles. Specifically, the distance-based formation and tracking control problem are addressed in the framework of leader-follower architecture. In this scheme, the leader is assigned the task of intercepting a target whose velocity is unknown, while the follower quadrotors are arranged to set up a predefined rigid formation pattern, ensuring simultaneously interagent collision avoidance and relative localization. The adopted strategy for the control design consists in decoupling the quadrotor dynamics in a cascaded structure to handle its underactuated property. Furthermore, by imposing constraints on the orientation angles, the follower will never be overturned. Rigorous stability analysis is presented to prove the stability of the entire closed-loop system. Numerical simulation results are presented to validate the proposed control strategy.

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