Modular Adaptive Control of Chaos in Chua’s Circuit

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In this paper, a modular adaptive design is developed for the control of chaos in a Chuas circuit. The dynamics of the Chuas circuit are represented in a parametric strict feedback form. For the purpose of design, it is assumed that all the system parameters are unknown, but the sign of certain parameters and lower bounds on their absolute values are known. Then, an adaptive modular backstepping design approach is used to derive the control system for trajectory tracking of a selected output variable (node voltage). Unlike the direct adaptive controllers for the Chuas circuit available in literature, an input-to-state-stabilizing control law is used herein. The control law accomplishes input-to-state-stability with respect to parameter estimation errors and their derivatives as disturbance inputs. The control system includes a passive identifier (an observer and an adaptation law) for the parameter estimation. In the closed-loop system, control of the node voltage is accomplished, and the remaining state variables remain bounded. Simulation results are presented which show that the controller is effective in accomplishing the precise tracking of the reference trajectory and suppression of the chaotic motion.


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