Games, Decisions, and Control: Fifty Years Back, Fifty Years Forward

Abstract

Fifty years ago, when control was emerging as a scientific discipline fueled by developments in dynamic, recursive decision making, dynamical systems and stability theory, a separate discipline, differential games, was being born in response to the need to develop a framework and associated solution tools for strategic dynamic decision making in adversarial environments, as an outgrowth of game theory. The evolution of the two disciplines-control theory, and particularly optimal control, and the theory of differential games-initially followed somewhat different paths, but soon a healthy interaction between the two developed. Differential games, in both zero-sum and nonzero-sum settings, enabled the embedding of control into a broader picture and framework, and enriched the set of conceptual tools available to it. One of its essential ingredients-information structures (who knows what and when)-became a mainstay in control research, particularly in the context of large-scale systems. In the other direction, the rich set of mathematical tools developed for control, such as viscosity solutions, directly impacted progress in solvability of differential games. Such interactions between the two disciplines reached a climax when robustness became a prevalent issue in control, leading among others to a comprehensive treatment of H¥ control of both linear and nonlinear uncertain systems.

This Bode Lecture will dwell on the parallel developments in the two fields to the extent they influenced each other over the past half century, talk about the present, and embark on a journey into the future.