Studying Multiobjective Optimization Problems in Nonlinear Dynamical Systems

Multiobjective Optimization Problems (MOPs) are important in analysis and application of nonlinear dynamical systems. As a first step, this paper studies a Biobjective Optimization Problem (BOP) in a simple nonlinear switched dynamical system: a piecewise linear system based on a boost converter with photovoltaic input. The piecewise linearity enables us to analyze the nonlinear dynamics exactly. In the BOP, the first objective evaluates the stability of circuit operation and the second objective evaluates the average input power. The main goal is to analyze a trade-off between two objectives. Using the piecewise exact solutions, the two objectives are formulated theoretically. Using the theoretical formulae, the existence of a trade-off between the two objectives is clarified exactly. The relationship between the trade-off and parameters is also considered. The results provide fundamental information for analyzing MOPs in various nonlinear systems and to realize their engineering applications.