Sixty Years of the Maximum Principle in Optimal Control: Historical Roots and Content Classification

Abstract

This study examines the scientific production focused on the Maximum Principle between 1962 and 2021. Results indicate a consistent increase in the absolute number of publications over time. In relative terms, there is a resurgence of interest in this research field after the period between 2004 and 2009. Overall, these findings support the idea of strategic complementarity between the Maximum Principle and optimal control. However, there is a notable exception during the period 2010–2015, characterised by a decline in scientific production focused on the Maximum Principle and a simultaneous increase in focus on optimal control. Academic journals that play a role in promoting this research field tend to have high impact factors and interesting cite scores. Using a modified Boston Consulting Group matrix, the results reveal the persistence of two researchers labelled as stars and three as cash cows. A multiple linear regression analysis confirms that reputation significantly influences the clustering trends. A critical discussion is provided to highlight the dichotomy between popularity and effective contributions in this research field.