Incentive stackelberg games for stochastic systems

Abstract

Dynamic games with hierarchical structure have been identified as key components of modern control systems that enable the integration of renewable cooperative and/or non-cooperative control such as distributed multi-agent systems. Although the incentive Stackelberg strategy has been admitted as the hierarchical strategy that induces the behavior of the decision maker as that of the follower, the followers optimize their costs under incentives without a specific information. Therefore, leaders succeed in using the required strategy to induce the behavior of their followers. This concept is considered very useful and reliable in some practical cases. In this survey, incentive Stackelberg games for deterministic and stochastic linear systems with external disturbance are addressed. The induced features of the hierarchical strategy in the considered models, including stochastic systems governed by Itô stochastic differential equation, Markov jump linear systems, and linear parameter varying (LPV) systems, are explained in detail. Furthermore, basic concepts based on the H2∕H∞ control setting for the incentive Stackelberg games are reviewed. Next, it is shown that the required set of strategies can be designed by solving higher-order cross-coupled algebraic Riccati-type equations. Finally, as a partial roadmap for the development of the underdeveloped pieces, some open problems are introduced.