A Fundamental Study for Multiobjective Optimization Problems in Nonlinear Dynamical Systems

Multiobjective optimization problems are important in analysis and application of nonlinear dynamical systems. As a first step, this paper studies a biobjective optimization problem 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 biobjective optimization problem, the first objective evaluates stability of circuit operation and the second objective evaluates average input power. A main task is analysis of a trade-off between the 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. Relationship between the trade-off and parameters is also considered. The results provide fundamental information to analyze multiobjective optimization problems in various nonlinear systems and to realize their engineering applications.