Adaptive Pso Based Lqr Tuning for Trajectory Tracking of Inverted Pendlum

The problem of state feedback control design is conventionally handled by pole assignment or Linear Quadratic Regulator (LQR) method via Algebraic Riccati Equation (ARE). However, these methods still suffer from the disadvantage of trial and error approach for parameter tuning. To be specific, selecting the weighting matrices Q and R of LQR has to be done by trial and error approach. Hence to address this problem, an evolutionary algorithm based optimization methods are employed for the design of optimal state feedback controller. Considering some important indices such as closed loop pole locations, speed of response and combining them into an objective function, an LQR optimization problem is formulated for trajectory tracking of single inverted pendulum. To solve the optimization problem, three evolutionary algorithms namely GA, PSO and Adaptive PSO are employed and the results of the optimization methods are compared.