By Sumit Chakraborty, Asim Kumar Pal
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Additional info for Algorithmic game : A cooperative game for multiagent collaborative planning
Kaufway, and H. D. I. Abrabanel. Correlations of periodic, areapreserving maps. Physica D, 6:375–384, 1983. R. Meucci, W. Gadomski, M. Ciofini, and F. T. Arecchi. Experimental control of chaos by means of weak parametric perturbations. Phys. Rev. E, 49:2528– 2531, 1994. E. Ott, C. Grebogi, and J. A. Yorke. Controlling chaotic dynamical systems. In D. Campbell, editor, CHAOS/XAOC, SovietAmer. Perspective on Nonlinear Science, pp. 153–172. Amer. Inst. , 1990. 27 28 1 Controlling Chaos 39 E. Ott, C.
11 Schematic representation of our complete targeting procedure. The system was evolving in a periodic orbit Xa . Our goal is to steer it to another periodic orbit Xb . The LQ controller drives the trajectory from Xa to a point Xnfa near Xfa. In Xnfa a small perturbation is applied, and the system moves to the state Xfa . Another perturbation is applied, and the system moves to the state Xfa . Our chaotic targeting procedure is then used to stir the system to Xtb . Another small perturbation drives the system to the point Xob , that belongs to the basin of attraction of Xb .
From there, the system dynamics will conduct the system evolution to a point pXt P Be xt in 2 Ã l iterates. With the use of this procedure, the average transport time to go from the source point to the target point typically scales logarithmically with the inverse of the size of the target region , which contrasts with the exponential increasing that takes place if this algorithm is not used. 2 Part II: Finding a Pseudo-Orbit Trajectory Part I of our method produces an orbit that goes from pXs to pXt .