Optimal-tuned Parameters for ℒ1 Adaptive Control

Disturbance and noise exerted to the systems are two challenging problems in both classical and modern control approaches due to their unknown nature. While there are different theories to tackle disturbance and noise problems, ℒ
₁
adaptive control theory is a promising approach to guarantee the robust performance of the system. In this paper, ℒ
₁
control theory with output feedback of the system is presented. Then, an inverted pendulum system is considered to implement the ℒ
₁
controller in the presence of the disturbance applied to the actuator of the pendulum. Finally, control parameters of the system are optimized with respect to the output and control effort of the system. Results of the simulation of the optimal-tuned ℒ
₁
controller for the inverted pendulum system is presented and discussed.