Bounded Error Adaptive Control. Part I,
Abstract
Adaptive identification and control problems when the output error between plant and model cannot be made to tend to zero are discussed. These include cases when the plant output is corrupted with noise and when plant parameters vary with time. The principal aim is to determine adaptive laws so that all the signals in the overall system are bounded. It is first shown that an error model can be derived which is described by a non-homogeneous differential equation. If the external disturbance, plant parameter variations, and input are bounded and the input is sufficiently rich the parameter error vector is bounded and explicit bounds are presented. If the input is not sufficiently rich, conditions for boundedness and unboundedness of the parameter error vector are derived and examples of unstable systems are given. Finally, for the control problem where the input cannot be assumed to be bounded, a nonlinear adaptation algorithm is suggested. The need for such an algorithm is shown by considering simple systems in which the parameter error, almost always, becomes unbounded if the disturbance does not tend to zero. By adjusting the parameters of the algorithm it is shown that the boundedness of all the signals in the system can be assured. The method can be extended to more general adaptive control problems which will be considered in greater detail in a subsequent report. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1980
- Accession Number
- ADA097628
Entities
People
- Benjamin B. Peterson
- Kumpati S. Narendra
Organizations
- Yale University