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A current challenge with adaptive controllers is to define efficient tuning methods of the controller parameters. Unlike linear systems, nonlinear systems may need parameters that are continuously tuned at different operating points to provide stability and desired behaviours. This study aims to develop a solution for tuning proportional–integral–derivative (PID) controller parameters as opposed to changing the operating points of a nonlinear system. Most tuning methods calculate parameters according to the system's step or frequency response. However, adaptive controllers have self-tuneable parameters or control rules. The proposed algorithm in this paper contains a controller, an estimator, and a reference model, and uses the system model. Unlike the model reference adaptive control method, the proposed controller has tuneable controller parameters estimated by the extended Kalman–Bucy filter. The filter estimates the controller parameters to make the system perform like the auxiliary ideal reference model to ensure minimum-time consumption. Hence, this study aims to develop an algorithm that will automatically calculate controller parameters for each operating point of the controlled chaotic or nonlinear system to minimize settling time at each operating point. The proposed algorithm is implemented in a unified chaotic system in which the estimator and controller of the system run together. Simulation results confirm the performance of the proposed algorithm. In addition, the simulation results provide strong evidence that the proposed algorithm can be an effective tool for controlling nonlinear or chaotic systems. [ABSTRACT FROM AUTHOR]

In this study, the control of hyperchaotic Rabinovich system is applied by using three different single state controllers, namely linear feedback, sliding mode, and passive control. Routh–Hurwitz criterions are used for constructing the sufficient conditions of the linear feedback controller. An appropriate switching surface is designed based on the sliding mode control theory. In order to ensure the global asymptotic stability of the system with the passive controller, a Lyapunov function is used. Simulation results are demonstrated not only to validate all the theoretical analyses but also to compare the effectiveness of proposed control methods. By adding the controllers to the hyperchaotic Rabinovich system, it asymptotically stabilizes towards its zero equilibrium point in the state space. Numerical simulations have also shown that the proposed single state sliding mode controller is more effective than linear feedback and passive controllers on the control of hyperchaotic Rabinovich system. [ABSTRACT FROM AUTHOR]