Adaptive control

[1][2] For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions.

Both of these methods provide update laws that are used to modify estimates in real-time (i.e., as the system operates).

Lyapunov stability is used to derive these update laws and show convergence criteria (typically persistent excitation; relaxation of this condition are studied in Concurrent Learning adaptive control).

[3] Hybrid methods rely on both estimation of parameters and direct modification of the control law.

[9][10] This body of work has focused on guaranteeing stability of a model reference adaptive control scheme using Lyapunov arguments.