Adaptive Dynamic Programming for Cooperative Control with Incomplete Information

There is a trend towards interconnected and complex dynamical systems that are controlled by more than one controller. Due to the coupling of the controllers by means of the system, these interacting controllers need to consider not only the system dynamics but also the influence of each other. However, in realistic scenarios, they usually do not exchange all the information concerning their parameters and control laws and an exact model of the system dynamics is often hard to obtain. This is why we consider the challenging setting where the controllers have no access neither to the parameters of each other nor to the system dynamics. The controller design is quite difficult in this scenario, as the final system configuration is not known during the design process. In this complex scenario, we propose algorithms where each controller uses Adaptive Dynamic Programming to adapt its control law. Here, each controller strives for reaching its individual control objectives, a setting which can be formulated as a coupled optimization problem, respectively a dynamic game. As an example, we consider a vehicle model with two lateral controllers. With our proposed algorithms, the controllers converge successfully to a solution of the coupled optimization problem without knowing the parameters of each other and the system dynamics.