This dissertation addresses the design and stability analysis of decentralized, cooperative control laws for multivehicle systems. Advances in communication, navigation, and surveillance systems have enabled greater autonomy in multivehicle systems, and there is a shift toward decentralized, cooperative systems for computational efficiency and robustness. In a decentralized control scheme, control inputs are determined onboard each vehicle; therefore, decentralized controllers are more efficient for large numbers of vehicles, and the system is more robust to communication failures and reconfiguration.
The design of decentralized, cooperative control laws is explored for a nonlinear vehicle model that can be represented in a double-integrator form. Cooperative controllers are functions of spacing errors with respect to other vehicles in the system, where the communication structure defines the information that is available to each vehicle. Control inputs are selected to achieve internal stability, or zero steady-state spacing errors, between vehicles in the system.
Closed-loop equations of motion for the cooperative system can be written in a structural form, where damping and stiffness matrices contain control gains acting on the velocity and positions of the vehicles, respectively. The form of the stiffness matrix is determined by the communication structure, where different communication structures yield different control forms. Communication structures are compared using two structural analysis tools: modal cost and frequency-response functions, which evaluate the response of the multivehicle systems to disturbances. The frequency-response information is shown to reveal the string stability of different cooperative control forms.
The effects of time delays in the feedback states of the cooperative control laws on system stability are also investigated. Closed-loop equations of motion are modeled as delay differential equations, and two stability notions are presented: delay-independent and delay-dependent stability.
Lastly, two additional cooperative control forms are investigated. The first control form spaces vehicles along an arbitrary path, where distances between vehicles are constant for a given spacing parameter. This control form shows advantages over spacing vehicles using control laws designed in an inertial frame. The second control form employs a time-based spacing scheme, which spaces vehicles at constant-time intervals at a desired endpoint. The stability of these control forms is presented.