This paper extends the three-dimensional Bao system to the four-dimensional one by incorporating a smooth third-order nonlinear magnetic flux-controlled memristor as the feedback element. The four-dimensional Bao system is proved to be hyperchaotic and some of its dynamical characteristics are shown. The design of the system’s analog circuit is presented, and the results of circuit simulation aligns with numerical simulation ones. In addition, a predefined-time sliding mode filter controller is designed by employing an adaptive term to address the system’s unknown parameters to keep the system stable under external interference. Numerical simulation results demonstrate that the proposed controller exhibits faster convergence and less chattering compared to previous predefined-time sliding mode controller.
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