Application of particle swarm optimization to parameter search in dynamical systems

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This paper proposes an application of the particle swarm optimization (PSO) to analysis of switched dynamical systems (SDS). This is the first application of PSO to bifurcation analysis. We consider the application to an example of the SDS which relates to a simplified model of photovoltaic systems such that the input is a single solar cell and is converted to the output via a boost converter. Our SDS includes a piecewise linear current-controlled voltage source that is a simplified model of the solar cell and the switching rule is a variant of peak-current-controlled switching. We derive two equations that give period-doubling bifurcation set and the maximum power point (MPP) for the parameter: they are objective of the analysis. The two equations are transformed into an multi objective problem (MOP) described by the hybrid fitness function consisting of two functions evaluating the validity of parameters and criteria. The proposed method permits increase (deteriorate) of some component below the criterion and the increase can help to exclude the bad component. This criteria effect helps an improvement of trade-off problems in existing MOP solvers. Furthermore, by using the piecewise exact solution and return map for the simulation, the MOP is described exactly and the PSO can find the precise (approximate) solution. From simulation results, we confirm that the PSO for the MOP can easily find the solution parameters although a standard numerical calculation needs huge calculation amount. The efficiency of the proposed algorithm is confirmed by measuring in terms of accuracy, computation amount and robustness.

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