On the Limitations of PSO in Cooperation with FPI-based Adaptive Control for Nonlinear Systems

Abstract

Essentially two kinds of adaptive controllers exist. To first-class belong those that commence their work with an available analytically known approximate system model and try to refine its parameters by using real-time observations. The elements of the second class do not wish to amend this initial model: rather they apply casual, not permanently maintained model corrections that rather depend on the observed situations that occur during the actual motion of the controlled system. Theoretically, it can be expected that an analytical model in the background can be refined, and placed in use even in this latter case. By the use of the van der Pol oscillator as a benchmark example of nonlinear systems and the Particle Swarm Optimization method for model correction, it is realized that our idea is too optimistic and the correction of the analytical model by learning may have limitations. This statement is substantiated via simulation examples.