The chaotic dynamics along with the control of chaos in a half-car model with semi-active suspension system is considered in this paper. The time series responses, phase space trajectories, Poincaré sections, and Lyapunov exponent methods are used to analyze the chaotic behavior in the open-loop system. In order to suppress the chaotic responses in the system, a chaos controller is applied based on the development of Ott–Grebogi–Yorke algorithm. In this new control strategy, the Poincaré map of the system is estimated using the support vector machine innovatively. After linearization of the Poincaré map, the optimal discrete-time linear quadratic regulator is designed for the linear map as a main contribution. The discrete optimal Ott–Grebogi–Yorke controller improves the performance of the system along with the rejection of chaos in the responses. This improvement involves the reduction in settling time, control effort, and energy consumption in the suspension system.