Bounded error adaptive control

Identification and control when plant output is corrupted with disturbance and when plant parameters vary with time are considered. It is shown how the error model can be described by a non-homogeneous differential equation. Subject to bounded disturbance and parameter variation and sufficiently rich input the parameter error vector remains bounded and explicit bounds are derived. For inputs that are not sufficiently rich some sufficient conditions for stability and some examples of instability are given. Finally, a non-linear adaptation algorithm is presented for the control problem that insures the boundedness of the parameter error vector and all signals in the system.