OPEN ACCESS
The present paper studies a chaotic system with one cubic nonlinear term and deals with optimal control of this system. The problem analysis technique of this paper, which is a major issue in oscillators, robotics, lasers, etc., has not been proposed in previous studies. Modal Series technique was used to solve the problem of optimal control with infinite time horizon for chaotic system. Nonlinear boundary value obtained in this technique is converted to a sequence of time invariable linear boundary value using Pontryagin's minimum principle. By resolving this sequence, state trajectory and optimal control law are obtained in the form of series with uniform convergence. Moreover, this technique allows for selection of suitable number of answers to reach an appropriate approximation of the main answer. In addition, the number of series terms is not limited. A reverse algorithm for drawing approximate state trajectory and sub-optimal control law. The results of simulations confirmed efficiency and accuracy of the proposed algorithm.
optimal control, chaos, four-scroll chaotic system, pontryagin's minimum principle, modal series method
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