Connections between port-controlled Hamiltonian systems and differential games and their applications to decentralised control of multi-agent systems

Connections between port-controlled Hamiltonian (PCH) systems and differential games are explored in this paper. First, it is shown that a given differential game can be associated with a family of PCH systems. Second, the converse is demonstrated namely that a given PCH system can be associated with a family of differential games. Third, combining these insights, we present a strategy for assigning cost matrices of a differential game, and the free parameters that arise in the context of PCH systems, to achieve a specific closed-loop behaviour, characterised by a desired closed-loop energy function. The construction of the resulting control laws only requires solving linear matrix inequalities. Finally, the latter “integrated approach” is extended to provide a method to design decentralised control laws for a class of networked multi-agent systems.