APSO Based Weighting Matrices Selection of LQR Applied to Tracking Control of SIMO System

This paper employs an adaptive particle swarm optimization (APSO) algorithm to solve the weighting matrices selection problem of linear quadratic regulator (LQR). One of the important challenges in the design of LQR for real time applications is the optimal choice state and input weighting matrices (Q and R), which play a vital role in determining the performance and optimality of the controller. Commonly, trial and error approach is employed for selecting the weighting matrices, which not only burdens the design but also results in non-optimal response. Hence, to choose the elements of Q and R matrices optimally, an APSO algorithm is formulated and applied for tracking control of inverted pendulum. One of the notable changes introduced in the APSO over conventional PSO is that an adaptive inertia weight parameter (AIWP) is incorporated in the velocity update equation of PSO to increase the convergence rate of PSO. The efficacy of the APSO tuned LQR is compared with that of the PSO tuned LQR. Statistical measures computed for the optimization algorithms to assess the consistency and accuracy prove that the precision and repeatability of APSO is better than those of the conventional PSO.