The aim of this paper is to study the chaos, optimal control, and adaptive control of the hyperchaotic Chen system. In this paper, applying the Pontryagin’s minimum principle (PMP), the optimal control inputs for the interested model are obtained with respect to the selected measure. A piecewise-spectral homotopy analysis method (PSHAM) is used for solving the hyperchaotic Chen system and the extreme conditions obtained from the PMP. Furthermore, an adaptive control approach and a parameter estimation update law are introduced for the hyperchaotic Chen system with completely unknown parameters. The control results are established using the Krasovskii–LaSalle principle. Finally, numerical simulations are included to demonstrate the effectiveness of the proposed control strategy.

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