On the Generalization and Stability Analysis of Pareto Seeking Control

In this letter, we address a multi-objective on-line optimization problem for unknown dynamical systems by providing a generalization of the Pareto seeking controller (PSC). The idea of the PSC is to drive the system to the Pareto front in the absence of knowledge of the values of the objectives or the input values to achieve Pareto optimality. Two special cases are presented, for two objectives and three objectives. A stability analysis is presented for the case of two objectives and two inputs, which shows that the controller practically drives the system into the neighborhood of the Pareto front, for any initial condition. Two simulation examples for the special cases are also presented.