A proposed particle swarm optimization algorithm is analyzed to adapt the controller to an inverted pendulum system, where the physical parameters of the system will be changed throughout for iterations. The parameters to be changed will be the friction coefficients, the length of the pendulum rod, and the mass of the car at different times of the iterations. The five populations used to evaluate the performance of the algorithm in the adaptation of control vectors were generated in different ways using a random normal distribution, the linear-quadratic regulatory technique, and the description of the linear-quadratic regulatory technique in linear matrix inequality, thus occupying different regions of the search space and having different characteristics. The study shows that the proposed algorithm adapts the control vector independent of the origin of the populations and without knowledge of the changes in the system, thus demonstrating the contribution of this work.
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