8. Cooperative Adaptive Control for Systems with First-Order Nonlinear Dynamics

In cooperative control systems, the control protocol for each agent is allowed to depend only on information about itself and its neighbors in the graph topology. We have confronted this problem for optimal cooperative control design in Part I of the book. In cooperative adaptive control systems, there is an additional problem. In adaptive control systems, the control law depends on unknown parameters that are tuned online in real time to improve the performance of the controller, whereas the challenge in cooperative adaptive control is to make sure that both the control protocols and the parameter tuning laws are distributed in terms of the allowed graph topology. That is, they are allowed to depend only on locally available information about the agent and its neighbors. We shall see in this chapter that the key to the design of distributed adaptive tuning algorithms is the selection of suitable Lyapunov functions that depend on the graph topology. This is closely connected to the selection of global performance indices that depend on the graph topology in Chap. 5. The basis for the selection of suitable graph-dependent Lyapunov functions was laid in the discussion on the graph Laplacian potential in Chap. 7.