Abstract
The Lorenz equations are well known for their ability to produce chaotic motion. We investigate here the Lorenz system subject to a control input. Two different controllers are the designed for this system, one based on linear methods and one based on nonlinear methods. The objective of the controller is to drive the system to one of the unstable equilibrium points associated with uncontrolled chaotic motion. Each controller is able to produce stable motion. However, the character of this motion may differ considerably, depending on adjustment of “gains” used in the controller. In particular, the motion may contain chaotic transients. It is possible to create a system with intermediate-term-senstive dependence on initial conditions, but with no such long-term dependence.
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Vincent, T.L., Yu, J. Control of a chaotic system. Dynamics and Control 1, 35–52 (1991). https://doi.org/10.1007/BF02169423
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DOI: https://doi.org/10.1007/BF02169423