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Feedback control methods for stabilizing unstable equilibrium points in a new chaotic system. (English) Zbl 1181.34067

Consider the autonomous system

dx dt=20(y-x),dy dt=14x+10·6y-xz,dz dt=x 2 -2·8z,(*)

which has a chaotic attractor and three unstable equilibria. Together with (*), the author considers the control system

dx dt=2-(y-x)+u,dy dt=14x+10·6y-xz+v,dz dt=x 2 -2·8z

and presents the controls u=0, v=-kx; u=-kx, v=-ky, which stabilize the origin for k>k i . Applying the control u=0, v=-kx ˙, another equilibrium point becomes stable.

MSC:
34H05ODE in connection with control problems
34C28Complex behavior, chaotic systems (ODE)
93D15Stabilization of systems by feedback