Control of Autonomous Vehicles Via Multistage Linear Feedback Design

In this paper, we show how autonomous vehicles performing a certain task can be controlled from one command center in order to achieve certain goals. The command center provides individual feedback gains to each vehicle in the form of one compounded feedback gain that in fact carries feedback gain information for each individual vehicle. Vehicles may be of different nature: satellites, cars, tanks, drowns, robots, unmanned aircraft, underwater vehicles, and ships. It is assumed that their dynamic is weakly coupled, namely, dynamics of each individual vehicle is weakly coupled to dynamics of all other vehicles and that they have the same control input. The weak coupling among the vehicles is represented either by physical interactions among vehicles or coordinating or communication signals. The results obtained are applicable to vehicles having different mathematical linear/linearized state space models. In the case when no interaction/coordination/communication among vehicles is present, and all feedback signals come from the command center (central controller) controller, the vehicle mathematical models can be identical. An important feature of the presented results is that different local feedback controllers can be facilitated for different vehicles using a unique global feedback controller signal designed by the command center. In this paper, we will consider cases of two and three vehicles, but the presented multistage feedback design methodology can be potentially extended to N vehicles. The presentation is done in continuous time. Similar derivations hold in the discrete-time domain.