A synthesis procedure for parameter adaptive control systems

Given a plant with differential equations characterized by a parameter vector ω which is unknown and slowly varying with time and given a corresponding feedback controller with equations characterized by an adjustable parameter vector γ, a synthesis procedure is presented which leads to a closed-loop adaptive control system for adjusting γ in the face of drift variations in ω. The steps in the synthesis procedure involve 1) the structuring of the basic control system such that model matching is possible for an optimal choice in γ corresponding to every ω,
\gamma^{\ast} = \gamma^{\ast}(\omega)
, 2) the selection of a performance index
\rho(\gamma, \gamma^{\ast})
which has the properties of a metric function on every adjustment interval, and 3) the derivation of a modified gradient for updating the value of γ which can be implemented on-line during the normal course of system operation. An example of a pitch-rate orientational control system is used to illustrate the synthesis procedure, and the results of a computer simulation study of the overall adaptive system are discussed which include the effects of nonlinearities, disturbance and measurement noises, as well as time variations in the unknown ω-parameters.