Weighted Artificial Fish Swarm Algorithm with Adaptive Behaviour Based Linear Controller Design for Nonlinear Inverted Pendulum

The Linear Quadratic Regulator (LQR) performance depends largely on the design choice of state and control weighting matrices (Q and R). However, these matrices are usually selected by the designer through several trial and error iterative processes. This might not guarantee robustness and may increase computational time. This paper proposes a new approach for the optimal determination of the LQR weighting matrices based on weighted artificial fish swarm algorithm (wAFSA), which is then used to obtain an optimal controller for a dynamic nonlinear Inverted Pendulum. In this paper, we first introduce an approach called inertial weight into the standard Artificial Fish Swarm Algorithm (AFSA) to adaptively select its parameters (visual and step sizes) thereafter, the modified algorithm was used to determine the optimal values of LQR weighting matrices which was then used to stabilize a non-linear inverted pendulum. Simulation results showed that the proposed method is efficient in determining the weighting matrices of LQR in comparison with the conventional trial-and error approach.