Combined direct and indirect approach to adaptive control

An approach to adaptive control is introduced using a combination of both direct and indirect methods. On the basis of estimates of the plant parameters and the current values of the control parameters, closed-loop estimation errors ε_θ(t) and ε_k(t) are defined. These in turn are used in the adaptive laws for updating both identification and control parameters. The global uniform stability of the overall system is shown by constructing a Lyapunov function. Only the control of a first-order plant is treated in detail, to get across the principal concepts involved. In particular, the dynamic adjustment of the control parameters based on the estimates of the plant parameters is introduced as an indirect method and is the precursor of the combined method