Fig. 1. The proposed schematic of two-wheeled wheelchair in balancing mode. The characteristic of the wheelchair is similar to a double-inverted pendulum on two wheels. Abstract-In this paper, the state feedback control design problem for stabilizing a two-wheeled wheelchair in balancing mode is considered. The system is modeled as double-inverted pendulum on two wheels. The calculation of state feedback control gains is conventionally handled by LQR method via Riccati equation. Unfortunately, the method still possesses trial and error approach when choosing some parameters, in particular tuning the elements of Q and R weighting matrices. Therefore, an intelligent numerical method to resolve this problem is proposed by adopting PSO algorithm. The simulation work is carried out to evaluate the effectiveness of the proposed method. The result shows that the numerical method reduces tuning time and improves the performance of the system.